Meaning of in the English dictionary

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Further exposure to that wind could only cause a dissipation of energy due to the breaking of wave tops. Gedney received the praise of the city, as well as a silver service.

May 2017 The lunitidal interval, measures the time lag from the passing , to the next high or low. This value can be used to calibrate and wristwatches to allow for simple but crude tidal predictions. This is because in shallow water the Stokes perturbation series needs many terms before convergence towards the solution, due to the peaked crests, while the KdV or Boussinesq models give good approximations for these long nonlinear waves. New York subsidized this service which undercut rival ports, major road improvements allowing for trucking and containerization diminished the need.

Meaning of in the English dictionary - The lunar tide and solar tide are synchronized near the full moon, the two tides are unsynchronized near the first and last quarter moon. Change in hydrodynamic forces, e.

This article's may be too long for the length of the article. Please help by moving some material from it into the body of the article. Please read the and to ensure the section will still be inclusive of all essential details. Please discuss this issue on the article's. May 2017 The lunitidal interval, measures the time lag from the passing , to the next high or low. It is also called the high water interval HWI. Sometimes a term is not used for the time lag, but instead the terms age of the tide or the establishment of the tide are used for the entry that is in the tidal tables. Tides are known to be mainly caused by the Moon's. Theoretically, peak tidal forces at a given location would concur when the Moon the , but a delay usually precedes high tide, depending largely on the shape of the coastline and the. This is caused by the time interval associated with the solar tides. Hundreds of factors are involved in the lunitidal interval, especially near the shoreline. However, for those far away enough from the coast, the dominating consideration is the speed of , which increases with the water's depth. It is proportional to the square root of the depth, for the extremely long gravity waves that transport the water that is following the Moon around the Earth. The oceans are about 4 km deep and would have to be at least 22 km deep for these waves to keep up with the Moon, as mentioned above, a similar time lag accompanies the solar tides, a complicating factor that varies with the. By observing the age of leap tides, it becomes clear that the delay can actually exceed 24 hours in some locations. The approximate lunitidal interval can be calculated if the moonrise, moonset, and high tide times are known for a location; in the , the Moon reaches its when it is southernmost in the sky. Lunar data are available from printed or online. The difference between these two times is the lunitidal interval, this value can be used to calibrate and wristwatches to allow for simple but crude tidal predictions. Grant Gross, Oceanography, second edition, Charles E. It is the fifth-largest natural satellite in the Solar System, following Jupiters satellite Io, the Moon is second-densest satellite among those whose densities are known. The average distance of the Moon from the Earth is 384,400 km, the Moon is thought to have formed about 4. It is the second-brightest regularly visible celestial object in Earths sky, after the Sun and its surface is actually dark, although compared to the night sky it appears very bright, with a reflectance just slightly higher than that of worn asphalt. Its prominence in the sky and its cycle of phases have made the Moon an important cultural influence since ancient times on language, calendars, art. The Moons gravitational influence produces the ocean tides, body tides, and this matching of apparent visual size will not continue in the far future. The Moons linear distance from Earth is currently increasing at a rate of 3. Occasionally, the name Luna is used, in literature, especially science fiction, Luna is used to distinguish it from other moons, while in poetry, the name has been used to denote personification of our moon. The principal modern English adjective pertaining to the Moon is lunar, a less common adjective is selenic, derived from the Ancient Greek Selene, from which is derived the prefix seleno-. Both the Greek Selene and the Roman goddess Diana were alternatively called Cynthia, the names Luna, Cynthia, and Selene are reflected in terminology for lunar orbits in words such as apolune, pericynthion, and selenocentric. The name Diana is connected to dies meaning day, several mechanisms have been proposed for the Moons formation 4. These hypotheses also cannot account for the angular momentum of the Earth—Moon system. This hypothesis, although not perfect, perhaps best explains the evidence, eighteen months prior to an October 1984 conference on lunar origins, Bill Hartmann, Roger Phillips, and Jeff Taylor challenged fellow lunar scientists, You have eighteen months. Go back to your Apollo data, go back to computer, do whatever you have to. Dont come to our conference unless you have something to say about the Moons birth, at the 1984 conference at Kona, Hawaii, the giant impact hypothesis emerged as the most popular. Afterward there were only two groups, the giant impact camp and the agnostics. Giant impacts are thought to have been common in the early Solar System, computer simulations of a giant impact have produced results that are consistent with the mass of the lunar core and the present angular momentum of the Earth—Moon system 2. Some shorelines experience a semi-diurnal tide—two nearly equal high and low tides each day, other locations experience a diurnal tide—only one high and low tide each day. A mixed tide—two uneven tides a day, or one high, Tides vary on timescales ranging from hours to years due to a number of factors. To make accurate records, tide gauges at fixed stations measure water level over time, gauges ignore variations caused by waves with periods shorter than minutes. These data are compared to the level usually called mean sea level. Tidal phenomena are not limited to the oceans, but can occur in other systems whenever a gravitational field varies in time. For example, the part of the Earth is affected by tides. Tide changes proceed via the following stages, Sea level rises over several hours, covering the intertidal zone, the water rises to its highest level, reaching high tide. Sea level falls over several hours, revealing the intertidal zone, the water stops falling, reaching low tide. Oscillating currents produced by tides are known as tidal streams, the moment that the tidal current ceases is called slack water or slack tide. The tide then reverses direction and is said to be turning, slack water usually occurs near high water and low water. But there are locations where the moments of slack tide differ significantly from those of high, Tides are commonly semi-diurnal, or diurnal. The two high waters on a day are typically not the same height, these are the higher high water. Similarly, the two low waters each day are the low water and the lower low water. The daily inequality is not consistent and is small when the Moon is over the equator. From the highest level to the lowest, Highest Astronomical Tide — The highest tide which can be predicted to occur, note that meteorological conditions may add extra height to the HAT. Mean High Water Springs — The average of the two high tides on the days of spring tides, mean High Water Neaps — The average of the two high tides on the days of neap tides. Mean Sea Level — This is the sea level 3. Since energy and mass are equivalent, all forms of energy, including light, on Earth, gravity gives weight to physical objects and causes the ocean tides. Gravity has a range, although its effects become increasingly weaker on farther objects. The most extreme example of this curvature of spacetime is a hole, from which nothing can escape once past its event horizon. More gravity results in time dilation, where time lapses more slowly at a lower gravitational potential. Gravity is the weakest of the four fundamental interactions of nature, the gravitational attraction is approximately 1038 times weaker than the strong force,1036 times weaker than the electromagnetic force and 1029 times weaker than the weak force. As a consequence, gravity has an influence on the behavior of subatomic particles. On the other hand, gravity is the dominant interaction at the macroscopic scale, for this reason, in part, pursuit of a theory of everything, the merging of the general theory of relativity and quantum mechanics into quantum gravity, has become an area of research. While the modern European thinkers are credited with development of gravitational theory, some of the earliest descriptions came from early mathematician-astronomers, such as Aryabhata, who had identified the force of gravity to explain why objects do not fall out when the Earth rotates. Later, the works of Brahmagupta referred to the presence of force, described it as an attractive force. Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and this was a major departure from Aristotles belief that heavier objects have a higher gravitational acceleration. Galileo postulated air resistance as the reason that objects with less mass may fall slower in an atmosphere, galileos work set the stage for the formulation of Newtons theory of gravity. In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. Newtons theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the position of the planet. A discrepancy in Mercurys orbit pointed out flaws in Newtons theory, the issue was resolved in 1915 by Albert Einsteins new theory of general relativity, which accounted for the small discrepancy in Mercurys orbit. The simplest way to test the equivalence principle is to drop two objects of different masses or compositions in a vacuum and see whether they hit the ground at the same time. Such experiments demonstrate that all objects fall at the rate when other forces are negligible 4. Consequently, it also the horizons north and south points. A celestial meridian matches the projection of a terrestrial meridian onto the celestial sphere, hence, the number of astronomical meridians are infinite. There are several ways in which the meridian can be divided into semicircles, in one way, it is divided into the local meridian and the antimeridian. The former semicircle contains the zenith and is terminated by the celestial poles, in the horizontal coordinate system the meridian is divided into halves terminated by the horizons north and south points. The upper meridian passes through the zenith, and the lower meridian, a celestial object will appear to drift past the local meridian as the Earth spins, for the meridian is fixed to the local horizon. At culmination, the object reaches its highest point in the sky when crossing, or transiting, using an objects right ascension and the local sidereal time it is possible to determine the time of its culmination. The term meridian comes from the Latin meridies, which means both midday and south, meridian Prime meridian Longitude Millar, William. The Amateur Astronomers Introduction to the Celestial Sphere 5. Most of the oceans have a structure, created by common physical phenomena, mainly from tectonic movement. The mid-ocean ridge, as its name implies, is a rise through the middle of all the oceans. Typically a rift runs along the edge of this ridge, along tectonic plate edges there are typically oceanic trenches — deep valleys, created by the mantle circulation movement from the mid-ocean mountain ridge to the oceanic trench. Hotspot volcanic island ridges are created by volcanic activity, erupting periodically, in areas with volcanic activity and in the oceanic trenches there are hydrothermal vents — releasing high pressure and extremely hot water and chemicals into the typically freezing water around it. Deep ocean water is divided into layers or zones, each with features of salinity, pressure, temperature and marine life. Lying along the top of the plain is the abyssal zone. The hadal zone — which includes the oceanic trenches, lies between 6, 000—11,000 metres and is the deepest oceanic zone, the acronym mbsf meaning meters below the seafloor is a convention used for depths below the seafloor. Benthos is the community of organisms which live on, in, or near the seabed and this community lives in or near marine sedimentary environments, from tidal pools along the foreshore, out to the continental shelf, and then down to the abyssal depths. The benthic zone is the region on, in and immediately above the seabed, including the sediment surface. Benthos generally live in relationship with the substrate bottom. Examples of contact soil layers include sand bottoms, rocky outcrops, coral, each area of the seabed has typical features such as common soil composition, typical topography, salinity of water layers above it, marine life, magnetic direction of rocks, and sedimentation. Seabed topography is flat where sedimentation is heavy and covers the tectonic features, marine life is abundant in the deep sea, especially around hydrothermal vents. Large deep sea communities of life have been discovered around black and white smokers—vents emitting chemicals toxic to humans. This marine life receives its energy both from the temperature difference and from chemosynthesis by bacteria. Brine pools are another seabed feature, usually connected to cold seeps, the seabed has been explored by submersibles such as Alvin and, to some extent, scuba divers with special equipment. The process that adds new material to the ocean floor is seafloor spreading. In recent years satellite images show a very clear mapping of the seabed, some childrens play songs include elements such as Theres a hole at the bottom of the sea, or A sailor went to sea 6. It is one of the largest natural harbors in the world, although the United States Board on Geographic Names does not use the term, New York Harbor has important historical, governmental, commercial, and ecological usages. The aboriginal population of the 16th century New York Harbor, the Lenape, used the waterways for fishing and it is fairly firmly held by historians that his ship anchored at the approximate location where the Verrazano-Narrows Bridge touches down in Brooklyn today. He also observed what he believed to be a freshwater lake to the north. He apparently did not travel north to observe the existence of the Hudson River, in 1609 Henry Hudson entered the Harbor and explored a stretch of the river that now bears his name. His journey prompted others to explore the region and engage in trade with the local population, in 1624 the first permanent European settlement was started on Governors Island, and eight years later in Brooklyn, soon these were connected by ferry operation. This prepared New York as a port for the British colonies. In 1686, the British colonial officials gave the municipality control over the waterfront, in 1808, Lieutenant Thomas Gedney of the United States Coast Survey discovered a new, deeper channel through The Narrows into New York Harbor. Because of the difficulty of the required, since 1694. The new channel Gedney discovered was 2 feet deeper, enough of a margin that fully laden ships could come into the harbor even at slack tide. Gedneys Channel, as it came to be called, was shorter than the previous channel, another benefit appreciated by the ship owners. Gedney received the praise of the city, as well as a silver service. In 1824 the first American drydock was completed on the East River, the Morris Canal, carrying anthracite and freight from Pennsylvania through New Jersey to its terminus at the mouth of the Hudson in Jersey City. Portions in the harbor are now part of Liberty State Park, in 1870, the city established the Department of Docks to systematize waterfront development, with George B. McClellan as the first engineer in chief. By the turn of the 20th century numerous railroad terminals lined the banks of the North River in Hudson County. The freight was ferried across by the railroads with small fleets of towboats, barges. New York subsidized this service which undercut rival ports, major road improvements allowing for trucking and containerization diminished the need. The Statue of Liberty National Monument recalls the period of immigration to the United States at the turn of the 20th century 7. An example of such an interface is that between the atmosphere and the ocean, which rise to wind waves. A gravity wave results when fluid is displaced from a position of equilibrium, the restoration of the fluid to equilibrium will produce a movement of the fluid back and forth, called a wave orbit. Gravity waves on an interface of the ocean are called surface gravity waves or surface waves. Wind-generated waves on the surface are examples of gravity waves, as are tsunamis. Wind-generated gravity waves on the surface of the Earths ponds, lakes, seas. Shorter waves are affected by surface tension and are called gravity—capillary waves. Alternatively, so-called infragravity waves, which are due to nonlinear wave interaction with the wind waves, have periods longer than the accompanying wind-generated waves. In the Earths atmosphere, gravity waves are a mechanism that produce the transfer of momentum from the troposphere to the stratosphere and mesosphere, Gravity waves are generated in the troposphere by frontal systems or by airflow over mountains. At first, waves propagate through the atmosphere without appreciable change in mean velocity, but as the waves reach more rarefied air at higher altitudes, their amplitude increases, and nonlinear effects cause the waves to break, transferring their momentum to the mean flow. This transfer of momentum is responsible for the forcing of the many large-scale dynamical features of the atmosphere, thus, this process plays a key role in the dynamics of the middle atmosphere. The effect of gravity waves in clouds can look like altostratus undulatus clouds, and are confused with them. A wave in which the group and phase velocities differ is called dispersive, Gravity waves traveling in shallow water, are nondispersive, the phase and group velocities are identical and independent of wavelength and frequency. The lunar phases change cyclically as the Moon orbits the Earth, according to the positions of the Moon. The Moons rotation is locked by the Earths gravity, therefore the same lunar surface always faces Earth. This face is variously sunlit depending on the position of the Moon in its orbit, therefore, the portion of this hemisphere that is visible to an observer on Earth can vary from about 100% to 0%. The lunar terminator is the boundary between the illuminated and darkened hemispheres, each of the four intermediate lunar phases is roughly seven days but this varies slightly due to the elliptical shape of the Moons orbit. Aside from some craters near the lunar poles such as Shoemaker, all parts of the Moon see around 14. These are the instants when the Moons apparent geocentric celestial longitude minus the Suns apparent geocentric longitude is 0°, 90°, 180° and 270°. Each of these phases is instantaneous, lasting theoretically zero time, during the intervals between principal phases, the Moon appears either crescent-shaped or gibbous. These shapes, and the periods of time when the Moon shows them, are called the intermediate phases. They last, on average, one-quarter of a month, roughly 7. The descriptor waxing is used for a phase when the Moons apparent size is increasing, from new moon toward full moon. As the moon waxes, the lunar phases progress through new moon, crescent moon, first-quarter moon, gibbous moon, the moon is then said to wane as it passes through the gibbous moon, third-quarter moon, crescent moon and back to new moon. The terms old moon and new moon are not interchangeable, the old moon is a waning sliver until the moment it aligns with the sun and begins to wax, at which point it becomes new again. Half moon is used to mean the first- and third-quarter moons, while the term quarter refers to the extent of the moons cycle around the Earth. When a crescent Moon occurs, the phenomenon of earthshine may be apparent, in the Northern Hemisphere, if the left side of the Moon is dark then the light part is growing, and the Moon is referred to as waxing. If the right side of the Moon is dark then the part is shrinking. Assuming that the viewer is in the hemisphere, the right portion of the Moon is the part that is always growing. Nearer the Equator the Moon with its terminator will appear apparently horizontal during the morning and evening, the crescent Moon can open upward or downward, with the horns of the crescent pointing up or down, respectively 9. For other planets in the Solar System, north is defined as being in the celestial hemisphere relative to the invariable plane of the solar system as Earths North pole. Due to the Earths axial tilt, winter in the Northern Hemisphere lasts from the December solstice to the March Equinox, the dates vary each year due to the difference between the calendar year and the astronomical year. Its surface is 60. Its climate is characterized by cold winters and cool summers, precipitation mostly comes in the form of snow. The Arctic experiences some days in summer when the Sun never sets, the duration of these phases varies from one day for locations right on the Arctic Circle to several months near the North Pole, which is the middle of the Northern Hemisphere. Between the Arctic Circle and the Tropic of Cancer lies the Northern Temperate Zone, the changes in these regions between summer and winter are generally mild, rather than extreme hot or cold. However, a temperate climate can have very unpredictable weather, tropical regions are generally hot all year round and tend to experience a rainy season during the summer months, and a dry season during the winter months. In the Northern Hemisphere, objects moving across or above the surface of the Earth tend to turn to the right because of the coriolis effect, as a result, large-scale horizontal flows of air or water tend to form clockwise-turning gyres. These are best seen in circulation patterns in the North Atlantic. For the same reason, flows of air down toward the surface of the Earth tend to spread across the surface in a clockwise pattern. Thus, clockwise air circulation is characteristic of high pressure weather cells in the Northern Hemisphere, conversely, air rising from the northern surface of the Earth tends to draw air toward it in a counterclockwise pattern. Hurricanes and tropical storms spin counter-clockwise in the Northern Hemisphere, the shadow of a sundial moves clockwise in the Northern Hemisphere. When viewed from the Northern Hemisphere, the Moon appears inverted compared to a view from the Southern Hemisphere, the North Pole faces away from the galactic center of the Milky Way. The Northern Hemisphere is home to approximately 6. Astronomical data and various statistics are found in almanacs, such as the times of the rising and setting of the sun and moon, eclipses, hours of full tide, church festivals, and so on. The etymology of the word is unclear, but there are several theories, however, that word appears only once in antiquity, by Eusebius who quotes Porphyry as to the Coptic Egyptian use of astrological charts. The earliest almanacs were calendars that included agricultural, astronomical, or meteorological data, however, the earliest documented use of the word in any language is in Latin in 1267 by Roger Bacon, where it meant a set of tables detailing movements of heavenly bodies including the moon. One etymology report says, The ultimate source of the word is obscure and its first syllable, al-, and its general relevance to medieval science and technology, strongly suggest an Arabic origin, but no convincing candidate has been found. Another report similarly says of almanac, First seen in Roger Bacon, apparently from Spanish Arabic, al-manakh, but this is not an Arabic word. The word remains a puzzle. The OED similarly says the word has no etymon in Arabic, the reason why the proposed Arabic word is speculatively spelled al-manākh is that the spelling occurred as almanach, as well as almanac. The earliest use of the word was in the context of astronomy calendars, at that time in the West, it would have been prestigious to attach an Arabic appellation to a set of astronomical tables. Also around that time, prompted by that motive, the Latin writer Pseudo-Geber wrote under an Arabic pseudonym, an almanac is a text listing a set of events forthcoming in the next year. The set of events noted in an almanac are selected in view of a more or less specific group of readers e. The earlier texts considered to be almanacs have been found in the Near East and they have been called generally hemerologies, from the Greek hēmerā, meaning day. Among them is the so-called Babylonian Almanac, which lists favorable and unfavorable days with advice on what to do on each of them, successive variants and versions aimed at different readership have been found. Egyptians lists for good and bad moments, three each day, have also been found. Many of these prognostics were connected with celestial events, the first heliacal rising of Sirius was used for its prediction and this practice, the observation of some star and its connecting to some event apparently spread. The Greek almanac, known as parapegma, has existed in the form a stone on which the days of the month were indicated by movable pegs inserted into bored holes. There were also written texts and according to Diogenes Laërtius, Parapegma was the title of a book by Democritus, with the astronomical computations were expected weather phenomena, composed as a digest of observations made by various authorities of the past. Parapegmata had been composed for centuries, hence for him, weather prediction was a special division of astrology. The origins of the almanac can be connected to ancient Babylonian astronomy, similar treatises called Zij were later composed in medieval Islamic astronomy 11. Along many coastlines the Moon contributes the major part of the lunar and solar tides. The exact interval between tides is influenced by the position of the Moon and Sun relative to the Earth as well as the location on earth where the tide is being measured. Owing to the Moons orbital progress, it takes a point on the Earth 24 hours,50. A tide clock is divided into two six-hour-long tidal periods that shows the length of time between high and low tide in a semi-diurnal tide region such as most areas of the Atlantic Ocean. Therefore, compared with the time between the high lunar tides, tide clocks gain approximately 15 minutes per month and must be reset periodically. Traditional Mechanical Tide Clocks, The bottom of the clock dial is marked low tide. The left side of the dial is marked hours until high tide and has a count-down of hours from 5 to 1, there is one hand on the clock face, and along the left side it points to the number of hours until the high tide. The right hand side of the clock is marked hours until low tide and has a count-down of hours from 5 to 1, the number pointed to by the hand gives the time until the low tide. Some tide clocks incorporate time and even humidity and temperature in the same instrument, some tide clocks count down the number of hours from high or low tide, as in one hour past high or low tide. When the clock reaches the half way point, it counts the hours up to high tide or low tide. Generally, there is an adjustment knob on the back on the instrument which may be used to set the tide using official tide tables for a location at either high or low tide. Tides have an inherent lead or lag, known as the lunitidal interval and this is often complicated because the lead or lag varies during the course of the lunar month, as the lunar and solar tides fall into and out of synchronization. The lunar tide and solar tide are synchronized near the full moon, the two tides are unsynchronized near the first and last quarter moon. Also, in addition to the position of the moon and the elliptical pattern of the sun. All of these variables have less impact on the tide at the time of the full moon, if the tide clock is mounted on a moving boat, it will need to be reset more frequently. The best time to set the clock is at the new moon or the full moon, a simple tide clock will always be least reliable near the quarter moon. Tide range is the distance between the highest high tide and lowest low tide 12. A complete cycle is defined as the interval required for the waveform to return to its initial value. The graphic to the right shows how one cycle constitutes 360° of phase, the graphic also shows how phase is sometimes expressed in radians, where one radian of phase equals approximately 57. Phase can also be an expression of relative displacement between two corresponding features of two waveforms having the same frequency, in sinusoidal functions or in waves phase has two different, but closely related, meanings. One is the angle of a sinusoidal function at its origin and is sometimes called phase offset or phase difference. Another usage is the fraction of the cycle that has elapsed relative to the origin. Phase shift is any change that occurs in the phase of one quantity and this symbol, φ is sometimes referred to as a phase shift or phase offset because it represents a shift from zero phase. It has been shifted by π2 radians, Phase difference is the difference, expressed in degrees or time, between two waves having the same frequency and referenced to the same point in time. Two oscillators that have the frequency and no phase difference are said to be in phase. Two oscillators that have the frequency and different phases have a phase difference. The amount by which such oscillators are out of phase with each other can be expressed in degrees from 0° to 360°, if the phase difference is 180 degrees, then the two oscillators are said to be in antiphase. If two interacting waves meet at a point where they are in antiphase, then interference will occur. It is common for waves of electromagnetic, acoustic or other energy to become superposed in their transmission medium, when that happens, the phase difference determines whether they reinforce or weaken each other. Complete cancellation is possible for waves with equal amplitudes, time is sometimes used to express position within the cycle of an oscillation. A phase difference is analogous to two athletes running around a track at the same speed and direction but starting at different positions on the track. They pass a point at different instants in time, but the time difference between them is a constant - same for every pass since they are at the same speed and in the same direction. If they were at different speeds, the difference is undefined 13. It is the oldest federal cultural institution in the United States, the Library is housed in three buildings on Capitol Hill in Washington, D. The Library of Congress claims to be the largest library in the world and its collections are universal, not limited by subject, format, or national boundary, and include research materials from all parts of the world and in more than 450 languages. Two-thirds of the books it acquires each year are in other than English. The Library of Congress moved to Washington in 1800, after sitting for years in the temporary national capitals of New York. Beckley, who became the first Librarian of Congress, was two dollars per day and was required to also serve as the Clerk of the House of Representatives. The small Congressional Library was housed in the United States Capitol for most of the 19th century until the early 1890s, most of the original collection had been destroyed by the British in 1814, during the War of 1812. To restore its collection in 1815, the bought from former president Thomas Jefferson his entire personal collection of 6,487 books. After a period of growth, another fire struck the Library in its Capitol chambers in 1851, again destroying a large amount of the collection. The Library received the right of transference of all copyrighted works to have two copies deposited of books, maps, illustrations and diagrams printed in the United States. It also began to build its collections of British and other European works and it included several stories built underground of steel and cast iron stacks. Although the Library is open to the public, only high-ranking government officials may check out books, the Library promotes literacy and American literature through projects such as the American Folklife Center, American Memory, Center for the Book, and Poet Laureate. And for fitting up an apartment for containing them. Books were ordered from London and the collection, consisting of 740 books and 3 maps, was housed in the new Capitol, as president, Thomas Jefferson played an important role in establishing the structure of the Library of Congress. The new law also extended to the president and vice president the ability to borrow books and these volumes had been left in the Senate wing of the Capitol. One of the only congressional volumes to have survived was a government account book of receipts and it was taken as a souvenir by a British Commander whose family later returned it to the United States government in 1940. Within a month, former president Jefferson offered to sell his library as a replacement 14. It was set up by Brewster Kahle and Bruce Gilliat, and is maintained with content from Alexa Internet, the service enables users to see archived versions of web pages across time, which the archive calls a three dimensional index. Since 1996, the Wayback Machine has been archiving cached pages of websites onto its large cluster of Linux nodes and it revisits sites every few weeks or months and archives a new version. Sites can also be captured on the fly by visitors who enter the sites URL into a search box, the intent is to capture and archive content that otherwise would be lost whenever a site is changed or closed down. The overall vision of the machines creators is to archive the entire Internet, the name Wayback Machine was chosen as a reference to the WABAC machine, a time-traveling device used by the characters Mr. Peabody and Sherman in The Rocky and Bullwinkle Show, an animated cartoon. These crawlers also respect the robots exclusion standard for websites whose owners opt for them not to appear in search results or be cached, to overcome inconsistencies in partially cached websites, Archive-It. Information had been kept on digital tape for five years, with Kahle occasionally allowing researchers, when the archive reached its fifth anniversary, it was unveiled and opened to the public in a ceremony at the University of California, Berkeley. Snapshots usually become more than six months after they are archived or, in some cases, even later. The frequency of snapshots is variable, so not all tracked website updates are recorded, Sometimes there are intervals of several weeks or years between snapshots. After August 2008 sites had to be listed on the Open Directory in order to be included. In 2009, the Internet Archive migrated its customized storage architecture to Sun Open Storage, in 2011 a new, improved version of the Wayback Machine, with an updated interface and fresher index of archived content, was made available for public testing. The index driving the classic Wayback Machine only has a bit of material past 2008. In January 2013, the company announced a ground-breaking milestone of 240 billion URLs, in October 2013, the company announced the Save a Page feature which allows any Internet user to archive the contents of a URL. This became a threat of abuse by the service for hosting malicious binaries, as of December 2014, the Wayback Machine contained almost nine petabytes of data and was growing at a rate of about 20 terabytes each week. Between October 2013 and March 2015 the websites global Alexa rank changed from 162 to 208, in a 2009 case, Netbula, LLC v. Netbula objected to the motion on the ground that defendants were asking to alter Netbulas website, in an October 2004 case, Telewizja Polska USA, Inc. Physical oceanography is one of several sub-domains into which oceanography is divided, others include biological, chemical and geological oceanography. Physical oceanography may be subdivided into descriptive and dynamical physical oceanography, descriptive physical oceanography seeks to research the ocean through observations and complex numerical models, which describe the fluid motions as precise as possible. Dynamical physical oceanography focuses primarily upon the processes that govern the motion of fluids with emphasis upon theoretical research and these are part of the large field of Geophysical Fluid Dynamics that is shared together with meteorology. The fundamental role of the oceans in shaping Earth is acknowledged by ecologists, geologists, meteorologists, climatologists, an Earth without oceans would truly be unrecognizable. Roughly 97% of the water is in its oceans. The tremendous heat capacity of the oceans moderates the planets climate, the oceans influence extends even to the composition of volcanic rocks through seafloor metamorphism, as well as to that of volcanic gases and magmas created at subduction zones. Though this apparent discrepancy is great, for land and sea, the respective extremes such as mountains and trenches are rare. Because the vast majority of the oceans volume is deep water. The same percentage falls in a salinity range between 34—35 ppt, there is still quite a bit of variation, however. Surface temperatures can range from below freezing near the poles to 35 °C in restricted tropical seas, in terms of temperature, the oceans layers are highly latitude-dependent, the thermocline is pronounced in the tropics, but nonexistent in polar waters. The halocline usually lies near the surface, where evaporation raises salinity in the tropics and these variations of salinity and temperature with depth change the density of the seawater, creating the pycnocline. Energy for the ocean circulation comes from solar radiation and gravitational energy from the sun, perhaps three quarters of this heat is carried in the atmosphere, the rest is carried in the ocean. The atmosphere is heated from below, which leads to convection, by contrast the ocean is heated from above, which tends to suppress convection. Instead ocean deep water is formed in regions where cold salty waters sink in fairly restricted areas. This is the beginning of the thermohaline circulation, oceanic currents are largely driven by the surface wind stress, hence the large-scale atmospheric circulation is important to understanding the ocean circulation. The Hadley circulation leads to Easterly winds in the tropics and Westerlies in mid-latitudes and this leads to slow equatorward flow throughout most of a subtropical ocean basin. The return flow occurs in an intense, narrow, poleward western boundary current, like the atmosphere, the ocean is far wider than it is deep, and hence horizontal motion is in general much faster than vertical motion 16. They result from the wind blowing over an area of fluid surface, Waves in the oceans can travel thousands of miles before reaching land. Wind waves on Earth range in size from small ripples, to waves over 100 ft high, when directly generated and affected by local winds, a wind wave system is called a wind sea. After the wind ceases to blow, wind waves are called swells, more generally, a swell consists of wind-generated waves that are not significantly affected by the local wind at that time. They have been generated elsewhere or some time ago, wind waves in the ocean are called ocean surface waves. Wind waves have an amount of randomness, subsequent waves differ in height, duration. The key statistics of wind waves in evolving sea states can be predicted with wind wave models, although waves are usually considered in the water seas of Earth, the hydrocarbon seas of Titan may also have wind-driven waves. The great majority of large breakers seen at a result from distant winds. Water depth All of these work together to determine the size of wind waves. Further exposure to that wind could only cause a dissipation of energy due to the breaking of wave tops. Waves in an area typically have a range of heights. For weather reporting and for analysis of wind wave statistics. This figure represents an average height of the highest one-third of the waves in a time period. The significant wave height is also the value a trained observer would estimate from visual observation of a sea state, given the variability of wave height, the largest individual waves are likely to be somewhat less than twice the reported significant wave height for a particular day or storm. Wave formation on a flat water surface by wind is started by a random distribution of normal pressure of turbulent wind flow over the water. This pressure fluctuation produces normal and tangential stresses in the surface water and it is assumed that, The water is originally at rest. There is a distribution of normal pressure to the water surface from the turbulent wind. Correlations between air and water motions are neglected, the second mechanism involves wind shear forces on the water surface 17. The theory assumes that the layer has a uniform mean depth. This theory was first published, in form, by George Biddell Airy in the 19th century. Further, several second-order nonlinear properties of gravity waves, and their propagation. Airy wave theory is also a good approximation for tsunami waves in the ocean and this linear theory is often used to get a quick and rough estimate of wave characteristics and their effects. This approximation is accurate for small ratios of the height to water depth. Airy wave theory uses a potential approach to describe the motion of gravity waves on a fluid surface. This is due to the fact that for the part of the fluid motion. Airy wave theory is used in ocean engineering and coastal engineering. Diffraction is one of the effects which can be described with Airy wave theory. Further, by using the WKBJ approximation, wave shoaling and refraction can be predicted, earlier attempts to describe surface gravity waves using potential flow were made by, among others, Laplace, Poisson, Cauchy and Kelland. But Airy was the first to publish the correct derivation and formulation in 1841, soon after, in 1847, the linear theory of Airy was extended by Stokes for non-linear wave motion — known as Stokes wave theory — correct up to third order in the wave steepness. Even before Airys linear theory, Gerstner derived a nonlinear wave theory in 1802. Airy wave theory is a theory for the propagation of waves on the surface of a potential flow. The waves propagate along the surface with the phase speed cp. The angular wavenumber k and frequency ω are not independent parameters, surface gravity waves on a fluid are dispersive waves — exhibiting frequency dispersion — meaning that each wavenumber has its own frequency and phase speed. While the surface shows a propagating wave, the fluid particles are in an orbital motion 18. The species present in the littoral zone therefore indicate the degree of the shores exposure, an abbreviated summary of the scale is given below. The scale runs from 1 an extremely exposed shore, to 8 an extremely sheltered shore, the littoral zone generally is the zone between low and high tides. The supra-littoral is above the barnacle line, the eulittoral zone is dominated by barnacles and limpets with a coralline belt in the very low littoral along with other Rhodophyta and Alaria in the upper sublittoral. Exposed shores show a Verrucaria belt mainly above the tide, with Porphyra. The mid shore is dominated by barnacles, limpets and some Fucus, Himanthalia and some Rhodophyta such as Mastocarpus and Corallina are found in the low littorral with Himanthalia, Alaria and Laminaria digitata dominant in the upper sublittoral. Semi-exposed shores show a Verrucaria belt just above high tide with clear Pelvetia in the upper-littoral, limpets, barnacles and short Fucus vesiculosus midshore. Laminaria and Saccorhiza polyschides and small algae common in the sublittoral, sheltered shores show a narrow Verrucaria zone at high water and a full sequence of fucoids, Pelvetia, Fucus spiralis, Fucus vesiculosus, Fucus serratus, Ascophyllum nodosum. Laminaria digitata is dominant the upper sublittoral, very sheltered shores show a very narrow zone of Verrucaria, the dominance of the littoral by a full sequence of the fucoids and Ascophyllum covering the rocks. Laminaria saccharina, Halidrys, Chondrus and or Furcellaria, a Biologically-defined Exposure Scale for the Comparative Description of Rocky Shores 19. Brooke Benjamin and Jim E. It is a mechanism for the generation of rogue waves. Modulation instability only happens under certain circumstances, the most important condition is anomalous group velocity dispersion, whereby pulses with shorter wavelengths travel with higher group velocity than pulses with longer wavelength. The instability is strongly dependent on the frequency of the perturbation, at certain frequencies, a perturbation will have little effect, whilst at other frequencies, a perturbation will grow exponentially. The overall gain spectrum can be derived analytically, as is shown below, random perturbations will generally contain a broad range of frequency components, and so will cause the generation of spectral sidebands which reflect the underlying gain spectrum. The tendency of a signal to grow makes modulation instability a form of amplification. The model includes group velocity dispersion described by the parameter β2, a periodic waveform of constant power P is assumed. Instability can now be discovered by searching for solutions of the equation which grow exponentially. The nonlinear Schrödinger equation is constructed by removing the carrier wave of the light being modelled, therefore, ω m and k m dont represent absolute frequencies and wavenumbers, but the difference between these and those of the initial beam of light. Modulation instability of optical fields has been observed in systems, namely. Modulation instability occurs owing to inherent optical nonlinearity of the due to photoreaction-induced changes in the refractive index. Modulation instability, The beginning 20. The approximation is named after Joseph Boussinesq, who first derived them in response to the observation by John Scott Russell of the wave of translation, the 1872 paper of Boussinesq introduces the equations now known as the Boussinesq equations. The Boussinesq approximation for water waves takes into account the structure of the horizontal and vertical flow velocity. This results in partial differential equations, called Boussinesq-type equations. In coastal engineering, Boussinesq-type equations are used in computer models for the simulation of water waves in shallow seas. While the Boussinesq approximation is applicable to fairly long waves — that is and this is useful because the waves propagate in the horizontal plane and have a different behaviour in the vertical direction. Often, as in Boussinesqs case, the interest is primarily in the wave propagation and this elimination of the vertical coordinate was first done by Joseph Boussinesq in 1871, to construct an approximate solution for the solitary wave. Subsequently, in 1872, Boussinesq derived the equations known nowadays as the Boussinesq equations, thereafter, the Boussinesq approximation is applied to the remaining flow equations, in order to eliminate the dependence on the vertical coordinate. As a result, the partial differential equations are in terms of functions of the horizontal coordinates. As an example, consider potential flow over a bed in the plane, with x the horizontal. Now the Boussinesq approximation for the velocity potential φ, as given above, is applied in these boundary conditions, further, in the resulting equations only the linear and quadratic terms with respect to η and ub are retained. The cubic and higher terms are assumed to be negligible. This set of equations has been derived for a horizontal bed. When the right-hand sides of the equations are set to zero. From the terms between brackets, the importance of nonlinearity of the equation can be expressed in terms of the Ursell number, for the case of infinitesimal wave amplitude, the terminology is linear frequency dispersion. The frequency dispersion characteristics of a Boussinesq-type of equation can be used to determine the range of wave lengths, for which it is a valid approximation 21. The most generally familiar sort of breaking wave is the breaking of surface waves on a coastline. Wave breaking generally occurs where the amplitude reaches the point that the crest of the wave actually overturns—though the types of breaking water waves are discussed in more detail below. Certain other effects in fluid dynamics have also been termed breaking waves, wave breaking also occurs in plasmas, when the particle velocities exceed the waves phase speed. Breaking of water surface waves may occur anywhere that the amplitude is sufficient, however, it is particularly common on beaches because wave heights are amplified in the region of shallower water. See also waves and shallow water, there are four basic types of breaking water waves. They are spilling, plunging, collapsing, and surging, when the ocean floor has a gradual slope, the wave will steepen until the crest becomes unstable, resulting in turbulent whitewater spilling down the face of the wave. This continues as the approaches the shore, and the waves energy is slowly dissipated in the whitewater. Because of this, spilling waves break for a time than other waves. Onshore wind conditions make spillers more likely, a plunging wave occurs when the ocean floor is steep or has sudden depth changes, such as from a reef or sandbar. A plunging wave breaks with more energy than a significantly larger spilling wave, the wave can trap and compress the air under the lip, which creates the crashing sound associated with waves. With large waves, this crash can be felt by beachgoers on land, offshore wind conditions can make plungers more likely. This is the tube that is so highly sought after by surfers, the surfer tries to stay near or under the crashing lip, often trying to stay as deep in the tube as possible while still being able to shoot forward and exit the barrel before it closes. A plunging wave that is parallel to the beach can break along its length at once, rendering it unrideable. Surfers refer to waves as closed out. The outcome is the movement of the base of the wave up the swash slope. The front face and crest of the wave remain relatively smooth with little foam or bubbles, resulting in a very narrow surf zone, or no breaking waves at all 22. The standing waves alternately rise and fall in a mirror image pattern, as energy is converted to potential energy. This may also occur at sea between two different wave trains of near equal wavelength moving in opposite directions, but with unequal amplitudes, in partial clapotis the wave envelope contains some vertical motion at the nodes. When a wave strikes a wall at an oblique angle. In this situation, the individual crests formed at the intersection of the incident and this wave motion, when combined with the resultant vortices, can erode material from the seabed and transport it along the wall, undermining the structure until it fails. Clapotic waves on the sea surface also radiate infrasonic microbaroms into the atmosphere, clapotis has been called the bane and the pleasure of Sea kayaking. Rogue wave Boussinesq, J. Théorie des ondes liquides périodiques, mémoires présentés par divers savants à lAcadémie des Sciences. Essai sur la théorie des eaux courantes, mémoires présentés par divers savants à lAcadémie des Sciences. Clapotis and Wave Reflection, With an Application to Vertical Breakwater Design, clapotis Wave Action — via YouTube 23. These solutions are in terms of the Jacobi elliptic function cn and they are used to describe surface gravity waves of fairly long wavelength, as compared to the water depth. The cnoidal wave solutions were derived by Korteweg and de Vries, in their 1895 paper in which they also propose their dispersive long-wave equation, in the limit of infinite wavelength, the cnoidal wave becomes a solitary wave. The Benjamin—Bona—Mahony equation has improved short-wavelength behaviour, as compared to the Korteweg—de Vries equation, cnoidal wave solutions can appear in other applications than surface gravity waves as well, for instance to describe ion acoustic waves in plasma physics. The KdV equation is a wave equation, including both frequency dispersion and amplitude dispersion effects. Shallow water equations — are also nonlinear and do have amplitude dispersion, Boussinesq equations — have the same range of validity as the KdV equation, but allow for wave propagation in arbitrary directions, so not only forward-propagating waves. The drawback is that the Boussinesq equations are more difficult to solve than the KdV equation. Airy wave theory — has full frequency dispersion, so valid for arbitrary depth and wavelength, however, for long waves the Boussinesq approach—as also applied in the KdV equation—is often preferred. This is because in shallow water the Stokes perturbation series needs many terms before convergence towards the solution, due to the peaked crests, while the KdV or Boussinesq models give good approximations for these long nonlinear waves. The KdV equation can be derived from the Boussinesq equations, further improvements in short-wave performance can be obtained by starting to derive a one-way wave equation from a modern improved Boussinesq model, valid for even shorter wavelengths. The cnoidal wave solutions of the KdV equation were presented by Korteweg and de Vries in their 1895 paper, solitary wave solutions for nonlinear and dispersive long waves had been found earlier by Boussinesq in 1872, and Rayleigh in 1876. The search for these solutions was triggered by the observations of this solitary wave by Russell, cnoidal wave solutions of the KdV equation are stable with respect to small perturbations. Further cn is one of the Jacobi elliptic functions and K is the elliptic integral of the first kind. The latter, m, determines the shape of the cnoidal wave, for m equal to zero the cnoidal wave becomes a cosine function, while for values close to one the cnoidal wave gets peaked crests and flat troughs. For values of m less than 0. The demarcation zone between—third or fifth order—Stokes and cnoidal wave theories is in the range 10—25 of the Ursell parameter. Based on the analysis of the nonlinear problem of surface gravity waves within potential flow theory 24. This may occur when waves from one weather system continue despite a shift in wind. Waves generated by the new wind run at an angle to the old, creating a shifting, two weather systems that are far from each other may create a cross sea when the waves from the systems meet, usually at a place far from either weather system. Until the older waves have dissipated, they create a sea hazard among the most perilous and this sea state is fairly common and a larger percentage of ship accidents were found to have occurred in this state. A cross swell is generated when the systems are longer period swell 25. Water waves, in context, are waves propagating on the water surface, with gravity. As a result, water with a surface is generally considered to be a dispersive medium. For a certain depth, surface gravity waves — i. On the other hand, for a wavelength, gravity waves in deeper water have a larger phase speed than in shallower water. In contrast with the behavior of gravity waves, capillary waves propagate faster for shorter wavelengths, besides frequency dispersion, water waves also exhibit amplitude dispersion. This is an effect, by which waves of larger amplitude have a different phase speed from small-amplitude waves. This section is about frequency dispersion for waves on a fluid layer forced by gravity, for surface tension effects on frequency dispersion, see surface tension effects in Airy wave theory and capillary wave. The simplest propagating wave of unchanging form is a sine wave. The dispersion relation will in general depend on other parameters in addition to the wavenumber k. For gravity waves, according to theory, these are the acceleration by gravity g. The dispersion relation for these waves is, an equation with tanh denoting the hyperbolic tangent function. A sinusoidal wave, of small amplitude and with a constant wavelength, propagates with the phase velocity. While the phase velocity is a vector and has an associated direction, according to linear theory for waves forced by gravity, the phase speed depends on the wavelength and the water depth 26. Wave trapping is the result of the Earths rotation and its shape which combine to cause the magnitude of the Coriolis force to increase rapidly away from the equator. Equatorial waves are present in both the atmosphere and ocean and play an important role in the evolution of many climate phenomena such as El Niño. Equatorial waves may be separated into a series of subclasses depending on their fundamental dynamics, at shortest periods are the equatorial gravity waves while the longest periods are associated with the equatorial Rossby waves. In addition to these two subclasses, there are two special subclasses of equatorial waves known as the mixed Rossby-gravity wave and the equatorial Kelvin wave. The latter two share the characteristics that they can have any period and also that they may carry only in an eastward direction. The remainder of this article discusses the relationship between the period of waves, their wavelength in the zonal direction and their speeds for a simplified ocean. Rossby-gravity waves, first observed in the stratosphere by M. Yanai, but, oddly, their crests and troughs may propagate westward if their periods are long enough. The eastward speed of propagation of waves can be derived for an inviscid slowly moving layer of fluid of uniform depth H. Once the frequency relation is formulated in terms of ω, the angular frequency and these three solutions correspond to the equatorial gravity waves, the equatorially trapped Rossby waves and the mixed Rossby-gravity wave. Equatorial gravity waves can be either westward- or eastward-propagating, the governing equations for these equatorial waves are similar to those presented above, except that there is no meridional velocity component. Kelvin waves have been connected to El Niño in recent years in terms of precursors to this atmospheric and oceanic phenomenon, the weak low pressure in the Indian Ocean typically propagates eastward into the North Pacific Ocean and can produce easterly winds. This wave can be observed at the surface by a rise in sea surface height of about 8 cm. If the Kelvin wave hits the South American coast, its water gets transferred upward 27. It also plays a part in longshore drift as well. Fetch length, along with the speed, determines the size of waves produced. The wind direction is considered constant, the longer the fetch and the faster the wind speed, the more wind energy is imparted to the water surface and the larger the resulting sea state will be. Sea state Ocean surface wave Storm surge 28. An example of such an interface is that between the atmosphere and the ocean, which rise to wind waves. A gravity wave results when fluid is displaced from a position of equilibrium, the restoration of the fluid to equilibrium will produce a movement of the fluid back and forth, called a wave orbit. Gravity waves on an interface of the ocean are called surface gravity waves or surface waves. Wind-generated waves on the surface are examples of gravity waves, as are tsunamis. Wind-generated gravity waves on the surface of the Earths ponds, lakes, seas. Shorter waves are affected by surface tension and are called gravity—capillary waves. Alternatively, so-called infragravity waves, which are due to nonlinear wave interaction with the wind waves, have periods longer than the accompanying wind-generated waves. In the Earths atmosphere, gravity waves are a mechanism that produce the transfer of momentum from the troposphere to the stratosphere and mesosphere, Gravity waves are generated in the troposphere by frontal systems or by airflow over mountains. At first, waves propagate through the atmosphere without appreciable change in mean velocity, but as the waves reach more rarefied air at higher altitudes, their amplitude increases, and nonlinear effects cause the waves to break, transferring their momentum to the mean flow. This transfer of momentum is responsible for the forcing of the many large-scale dynamical features of the atmosphere, thus, this process plays a key role in the dynamics of the middle atmosphere. The effect of gravity waves in clouds can look like altostratus undulatus clouds, and are confused with them. A wave in which the group and phase velocities differ is called dispersive, Gravity waves traveling in shallow water, are nondispersive, the phase and group velocities are identical and independent of wavelength and frequency. The amplitude of infragravity waves is most relevant in shallow water, in particular along coastlines hit by high amplitude and long period wind waves, wind waves and ocean swells are shorter, with typical dominant periods of 1 to 25 s. This distinguishes infragravity waves from normal oceanic gravity waves, which are created by wind acting on the surface of the sea, whatever the details of their generation mechanism, discussed below, infragravity waves are these subharmonics of the impinging gravity waves. Technically infragravity waves are simply a subcategory of gravity waves and refer to all gravity waves with greater than 30 s. This could include such as tides and oceanic Rossby waves. The term infragravity wave appears to have coined by Walter Munk in 1950. Two main processes can explain the transfer of energy from the wind waves to the long infragravity waves. The most common process is the interaction of trains of wind waves which was first observed by Munk and Tucker and explained by Longuet-Higgins. Because wind waves are not monochromatic they form groups, the Stokes drift induced by these groupy waves transports more water where the waves are highest. The waves also push the water around in a way that can be interpreted as a force, combining mass and momentum conservation, Longuet-Higgins and Stewart give, with three different methods, the now well-known result. Namely, the sea level oscillates with a wavelength that is equal to the length of the group, with a low level where the wind waves are highest. This oscillation of the sea surface is proportional to the square of the wave amplitude. Another process was proposed later by Graham Symonds and his collaborators and it appears that this is probably a good explanation for infragravity wave generation on a reef. In the case of coral reefs, the infragravity periods are established by resonances with the reef itself, infragravity waves generated along the Pacific coast of North America have been observed to propagate transoceanically to Antarctica and there to impinge on the Ross Ice Shelf. Their frequencies more closely couple with the ice shelf natural frequencies, further, they are not damped by sea ice as normal ocean swell is. As a result, they flex floating ice shelves such as the Ross Ice Shelf, media related to Gravity waves at Wikimedia Commons 30. Internal waves, also called gravity waves, go by many other names depending upon the fluid stratification, generation mechanism, amplitude. If propagating horizontally along an interface where the density decreases with height. If the interfacial waves are large amplitude they are called solitary waves or internal solitons. If moving vertically through the atmosphere where substantial changes in air density influences their dynamics, If generated by flow over topography, they are called Lee waves or mountain waves. If the mountain waves break aloft, they can result in strong winds at the ground known as Chinook winds or Foehn winds. If generated in the ocean by tidal flow over submarine ridges or the continental shelf, If they evolve slowly compared to the Earths rotational frequency so that their dynamics are influenced by the Coriolis effect, they are called inertia gravity waves or, simply, inertial waves. Internal waves are usually distinguished from Rossby waves, which are influenced by the change of Coriolis frequency with latitude. An internal wave can readily be observed in the kitchen by slowly tilting back, clouds that reveal internal waves launched by flow over hills are called lenticular clouds because of their lens-like appearance. Less dramatically, a train of waves can be visualized by rippled cloud patterns described as herringbone sky or mackerel sky. The outflow of air from a thunderstorm can launch large amplitude internal solitary waves at an atmospheric inversion. In northern Australia, these result in Morning Glory clouds, used by some daredevils to glide along like a surfer riding an ocean wave, satellites over Australia and elsewhere reveal these waves can span many hundreds of kilometers. According to Archimedes principle, the weight of an object is reduced by the weight of fluid it displaces. This holds for a parcel of density ρ surrounded by an ambient fluid of density ρ0. Its weight per volume is g, in which g is the acceleration of gravity. Dividing by a density, ρ00, gives the definition of the reduced gravity. Because water is more dense than air, the displacement of water by air from a surface gravity wave feels nearly the full force of gravity 31. In these flows, mass and momentum equations can be combined to yield a kinematic wave equation, depending on the flow configurations, the kinematic wave can be linear or non-linear, which depends on whether the wave celerity is a constant or a variable. In general, the wave can be advecting and diffusing, however, in simple situation, the kinematic wave is mainly advecting. Oblique incoming wind squeezes water along the coast, and so generates a current which moves parallel to the coast. Longshore drift is simply the sediment moved by the longshore current and this current and sediment movement occurs within the surf zone. Beach sand is moved on such oblique wind days, due to the swash and backwash of water on the beach. Breaking surf sends water up the beach at an oblique angle, thus beach sand can move downbeach in a zig zag fashion many tens of meters per day. This process is called beach drift but some regard it as simply part of longshore drift because of the overall movement of sand parallel to the coast. Longshore drift affects numerous sediment sizes as it works in different ways depending on the sediment. Sand is largely affected by the force of breaking waves. There are numerous calculations that take into consideration the factors that produce longshore drift, some of these are, Geological changes, e. Change in hydrodynamic forces, e. Alterations of the sediment budget, e. The sediment budget takes into consideration sediment sources and sinks within a system, a good example of the sediment budget and longshore drift working together in the coastal system is inlet ebb-tidal shoals, which store sand that has been transported by long shore transport. As well as storing sand these systems may also transfer or by pass sand into other systems, therefore inlet ebb-tidal systems provide a good sources. Long shore occurs in a 90 to 80 degree backwash so it would be presented as an angle with the wave line. This section consists of features of long shore drift that occur on a coast where long shore drift occurs uninterrupted by man-made structures, spits are formed when longshore drift travels past a point where the dominant drift direction and shoreline do not veer in the same direction. As well as dominant drift direction, spits are affected by the strength of wave driven current, wave angle, spits are landforms that have two important features, with the first feature being the region at the up-drift end or proximal end. As an example, the New Brighton spit in Canterbury, New Zealand, was created by longshore drift of sediment from the Waimakariri River to the north and this spit system is currently in equilibrium but undergoes phases of deposition and erosion 33. This principle is named after J. Luke, who published it in 1967, Lukes Lagrangian formulation can also be recast into a Hamiltonian formulation in terms of the surface elevation and velocity potential at the free surface. This is often used when modelling the spectral density evolution of the free-surface in a sea state, both the Lagrangian and Hamiltonian formulations can be extended to include surface tension effects, and by using Clebsch potentials to include vorticity. Lukes Lagrangian formulation is for surface gravity waves on an—incompressible. This is in agreement with the principles for inviscid flow without a free surface. This may also include moving wavemaker walls and ship motion. The bed-level term proportional to h2 in the energy has been neglected, since it is a constant. Below, Lukes variational principle is used to arrive at the equations for non-linear surface gravity waves on a potential flow. The first integral on the right-hand side integrates out to the boundaries, in x and t, of the integration domain and is zero since the variations δΦ are taken to be zero at these boundaries. Considering the variation of the Lagrangian with respect to small changes δη gives, the Hamiltonian structure of surface gravity waves on a potential flow was discovered by Vladimir E. The Hamiltonian H is the sum of the kinetic and potential energy of the fluid and this is expressed by the Dirichlet-to-Neumann operator D, acting linearly on φ. Also the potential energy part of the Hamiltonian is quadratic, the source of non-linearity in surface gravity waves is through the kinetic energy depending non-linear on the free surface shape η 34. The mild-slope equation is used in coastal engineering to compute the wave-field changes near harbours. As a result, it describes the variations in wave amplitude, from the wave amplitude, the amplitude of the flow velocity oscillations underneath the water surface can also be computed. Most often, the equation is solved by computer using methods from numerical analysis. Also parabolic approximations to the equation are often used, in order to reduce the computational cost. In case of a constant depth, the equation reduces to the Helmholtz equation for wave diffraction. For a given angular frequency ω, the k has to be solved from the dispersion equation. The last equation shows that energy is conserved in the mild-slope equation. The effective group speed v g is different from the speed c g. The first equation states that the effective wavenumber κ is irrotational, a consequence of the fact it is the derivative of the wave phase θ. The second equation is the eikonal equation, otherwise, κ2 can even become negative. When the diffraction effects are neglected, the effective wavenumber κ is equal to k. The mild-slope equation can be derived by the use of several methods, here, we will use a variational approach. The fluid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational and these assumptions are valid ones for surface gravity waves, since the effects of vorticity and viscosity are only significant in the Stokes boundary layers. Because the flow is irrotational, the motion can be described using potential flow theory. The time-dependent mild-slope equation can be used to model waves in a band of frequencies around ω0. Using this in the time-dependent form of the equation, recovers the classical mild-slope equation for time-harmonic wave motion 35. The radiation stress tensor describes the additional forcing due to the presence of the waves, as a result, varying radiation stresses induce changes in the mean surface elevation and the mean flow. For the mean energy density in the part of the fluid motion. Radiation stress derives its name from the effect of radiation pressure for electromagnetic radiation. As a result, a long wave propagates together with the group. While, according to the relation, a long wave of this length should propagate at its own — higher — phase velocity. For uni-directional wave propagation — say in the x-coordinate direction — the component of the stress tensor of dynamical importance is Sxx. Further ρ is the density and g is the acceleration by gravity. The last term on the side, ½ρg2, is the integral of the hydrostatic pressure over the still-water depth. Propagating waves induce a — relatively small — mean mass transport in the propagation direction. Rogue waves present considerable danger for several reasons, they are rare, unpredictable, may appear suddenly or without warning, a 12-metre wave in the usual linear model would have a breaking force of 6 metric tons per square metre. Rogue waves seem not to have a single cause, but occur where physical factors such as high winds. Rogue waves can occur in other than water. They appear to be ubiquitous in nature and have also reported in liquid helium, in nonlinear optics. Recent research has focused on optical rogue waves which facilitate the study of the phenomenon in the laboratory, once considered mythical and lacking hard evidence for their existence, rogue waves are now proven to exist and known to be a natural ocean phenomenon. Eyewitness accounts from mariners and damage inflicted on ships have long suggested they occurred, the first scientific evidence of the existence of rogue waves came with the recording of a rogue wave by the Gorm platform in the central North Sea in 1984. A stand-out wave was detected with a height of 11 metres in a relatively low sea state. During that event, minor damage was inflicted on the platform, far above sea level, confirming that the reading was valid. In 2004 scientists using three weeks of radar images from European Space Agency satellites found ten rogue waves, each 25 metres or higher. A rogue wave is a natural phenomenon that is not caused by land movement, only lasts briefly, occurs in a limited location. Rogue waves are distinct from tsunamis. Tsunamis are caused by displacement of water, often resulting from sudden movement of the ocean floor. They are also distinct from megatsunamis, which are single massive waves caused by sudden impact, Rogue waves have now been proven to be the cause of the sudden loss of some ocean-going vessels. Well documented instances include the freighter MS München, lost in 1978 and the MV Derbyshire lost in 1980, the largest British ship ever lost at sea. A rogue wave has been implicated in the loss of other vessels including the Ocean Ranger which was a mobile offshore drilling unit that sank in Canadian waters on 15 February 1982. In 2007 the US National Oceanic and Atmospheric Administration compiled a catalogue of more than 50 historical incidents probably associated with rogue waves, in that era it was widely held that no wave could exceed 30 feet 37. Rossby waves are a subset of inertial waves, atmospheric Rossby waves on Earth are giant meanders in high-altitude winds that have a major influence on weather. These waves are associated with systems and the jet stream. Oceanic Rossby waves move along the thermocline, the boundary between the upper layer and the cold deeper part of the ocean. Atmospheric Rossby waves result from the conservation of vorticity and are influenced by the Coriolis force. A fluid, on the Earth, that moves toward the pole will deviate toward the east, the deviations are caused by the Coriolis force and conservation of potential vorticity which leads to changes of relative vorticity. This is analogous to conservation of momentum in mechanics. In planetary atmospheres, including Earth, Rossby waves are due to the variation in the Coriolis effect with latitude, carl-Gustaf Arvid Rossby first identified such waves in the Earths atmosphere in 1939 and went on to explain their motion. One can identify a terrestrial Rossby wave as its velocity, marked by its wave crest. However, the set of Rossby waves may appear to move in either direction with what is known as its group velocity. In general, shorter waves have a group velocity and long waves a westward group velocity. The terms barotropic and baroclinic are used to distinguish the structure of Rossby waves. Barotropic Rossby waves do not vary in the vertical, and have the fastest propagation speeds, the baroclinic wave modes, on the other hand, do vary in the vertical. They are also slower, with speeds of only a few centimeters per second or less, most investigations of Rossby waves has been done on those in Earths atmosphere. Rossby waves in the Earths atmosphere are easy to observe as large-scale meanders of the jet stream, the action of Rossby waves partially explains why eastern continental edges, such as the Northeast United States and Eastern Canada, are colder than Western Europe at the same latitudes. Deep convection to the troposphere is enhanced over very warm sea surfaces in the tropics and this tropical forcing generates atmospheric Rossby waves that have a poleward and eastward migration. Poleward-propagating Rossby waves explain many of the observed statistical connections between low- and high-latitude climates, one such phenomenon is sudden stratospheric warming. Poleward-propagating Rossby waves are an important and unambiguous part of the variability in the Northern Hemisphere, similar mechanisms apply in the Southern Hemisphere and partly explain the strong variability in the Amundsen Sea region of Antarctica 38. These waves have the same trapping scale as Kelvin waves, more known as the equatorial Rossby deformation radius. They always carry energy eastward, but their crests and troughs may propagate westward if their periods are long enough, the eastward speed of propagation of these waves can be derived for an inviscid slowly moving layer of fluid of uniform depth H. Once the frequency relation is formulated in terms of ω, the angular frequency and these three solutions correspond to the equatorially trapped gravity wave, the equatorially trapped Rossby wave and the mixed Rossby-gravity wave. If this Brunt—Vaisala frequency does not change, then these waves become vertically propagating solutions. They had the characteristics, 4—5 days, horizontal wavenumbers of 4, vertical wavelengths of 4—8 km. Also, the vertically propagating gravity wave component was found in the stratosphere with periods of 35 hours, horizontal wavelengths of 2400 km, and vertical wavelengths of 5 km 39. A sea state is characterized by statistics, including the height, period. The sea state varies with time, as the conditions or swell conditions change. The sea state can either be assessed by an observer, like a trained mariner, or through instruments like weather buoys. In case of measurements, the statistics are determined for a time interval in which the sea state can be considered to be constant. This duration has to be longer than the individual wave period. Typically, records of one hundred to one thousand wave-periods are used to determine the wave statistics, the WMO sea state code largely adopts the wind sea definition of the Douglas Sea Scale. The sea state is in addition to these two parameters also described by the wave spectrum S which is a function of a wave height spectrum S, some wave height spectra are listed below. In addition to the term wave statistics presented above, long term sea state statistics are often given as a joint frequency table of the significant wave height. From the long and short term statistical distributions it is possible to find the extreme values expected in the life of a ship. Surviving the once in 100 years or once in 1000 years sea state is a demand for design of ships. Beaufort scale Cross sea Douglas Sea Scale Bowditch, Nathaniel, American Practical Navigator,9, United States Hydrographic Office, OCLC31033357 Faltinsen, O. Sea Loads on Ships and Offshore Structures, ISBN 0-521-45870-6 40. Seiches and seiche-related phenomena have been observed on lakes, reservoirs, swimming pools, bays, harbours, the key requirement for formation of a seiche is that the body of water be at least partially bounded, allowing the formation of the standing wave. The term was promoted by the Swiss hydrologist François-Alphonse Forel in 1890, the word originates in a Swiss French dialect word that means to sway back and forth, which had apparently long been used in the region to describe oscillations in alpine lakes. Seiches are often imperceptible to the eye, and observers in boats on the surface may not notice that a seiche is occurring due to the extremely long wavelengths. The effect is caused by resonances in a body of water that has been disturbed by one or more of a number of factors, most often meteorological effects, seismic activity or by tsunamis. Gravity always seeks to restore the surface of a body of liquid water. Vertical harmonic motion results, producing an impulse that travels the length of the basin at a velocity that depends on the depth of the water, the impulse is reflected back from the end of the basin, generating interference. Repeated reflections produce standing waves with one or more nodes, or points, the frequency of the oscillation is determined by the size of the basin, its depth and contours, and the water temperature. The longest natural period of a seiche is the associated with the fundamental resonance for the body of water—corresponding to the longest standing wave. Higher order harmonics are also observed, the period of the second harmonic will be half the natural period, the period of the third harmonic will be a third of the natural period, and so forth. Seiches have been observed on lakes and seas. The key requirement is that the body of water be partially constrained to allow formation of standing waves, regularity of geometry is not required, even harbours with exceedingly irregular shapes are routinely observed to oscillate with very stable frequencies. Low rhythmic seiches are almost always present on larger lakes and they are usually unnoticeable among the common wave patterns, except during periods of unusual calm. Harbours, bays, and estuaries are often prone to small seiches with amplitudes of a few centimetres, among other lakes well known for their regular seiches is New Zealands Lake Wakatipu, which varies its surface height at Queenstown by 20 centimetres in a 27-minute cycle. Seiches can also form in semi-enclosed seas, the North Sea often experiences a lengthwise seiche with a period of about 36 hours, the National Weather Service issues low water advisories for portions of the Great Lakes when seiches of 2 feet or greater are likely to occur. These can lead to extreme seiches of up to 5 m between the ends of the lake, the effect is similar to a storm surge like that caused by hurricanes along ocean coasts, but the seiche effect can cause oscillation back and forth across the lake for some time. The same storm system caused the 1995 seiche on Lake Superior produced a similar effect in Lake Huron. Nowadays it is defined as four times the standard deviation of the surface elevation — or equivalently as four times the square root of the zeroth-order moment of the wave spectrum. The original definition resulted from work by the oceanographer Walter Munk during World War II, the significant wave height was intended to mathematically express the height estimated by a trained observer. It is commonly used as a measure of the height of ocean waves, significant wave height, scientifically represented as Hs or Hsig, is an important parameter for the statistical distribution of ocean waves. The most common waves are less in height than Hs and this implies that encountering the significant wave is not too frequent. However, statistically, it is possible to encounter a wave that is higher than the significant wave. Generally, the distribution of the individual wave heights is well approximated by a Rayleigh distribution. However, in changing conditions, the disparity between the significant wave height and the largest individual waves might be even larger. Other statistical measures of the wave height are also widely used, the RMS wave height, which is defined as square root of the average of the squares of all wave heights, is approximately equal to Hs divided by 1. The maximum ever measured wave height from a satellite is 20. These respective countries meteorological offices are called Regional Specialized Meteorological Centers, in their weather products, they give ocean wave height forecasts in significant wave height. In the United States, NOAAs National Weather Service is the RSMC for a portion of the North Atlantic, the Ocean Prediction Center and the Tropical Prediction Centers Tropical Analysis and Forecast Branch issue these forecasts. RSMCs use wind-wave models as tools to predict the sea conditions. NOAAs WAVEWATCH III model is used heavily, a significant wave height is also defined similarly, from the wave spectrum, for the different systems that make up the sea. We then have a significant wave height for the wind-sea or for a particular swell 42. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium, solitons are the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described in 1834 by John Scott Russell who observed a solitary wave in the Union Canal in Scotland and he reproduced the phenomenon in a wave tank and named it the Wave of Translation. A single, consensus definition of a soliton is difficult to find, more formal definitions exist, but they require substantial mathematics. Moreover, some use the term soliton for phenomena that do not quite have these three properties. Dispersion and non-linearity can interact to produce permanent and localized wave forms, consider a pulse of light traveling in glass. This pulse can be thought of as consisting of light of different frequencies. Since glass shows dispersion, these different frequencies will travel at different speeds, however, there is also the non-linear Kerr effect, the refractive index of a material at a given frequency depends on the lights amplitude or strength. If the pulse has just the right shape, the Kerr effect will exactly cancel the effect, and the pulses shape will not change over time. See soliton for a detailed description. The soliton solutions are obtained by means of the inverse scattering transform. The mathematical theory of equations is a broad and very active field of mathematical research. Some types of tidal bore, a phenomenon of a few rivers including the River Severn, are undular. Other solitons occur as the internal waves, initiated by seabed topography. Atmospheric solitons also exist, such as the Morning Glory Cloud of the Gulf of Carpentaria, the recent and not widely accepted soliton model in neuroscience proposes to explain the signal conduction within neurons as pressure solitons. A topological soliton, also called a defect, is any solution of a set of partial differential equations that is stable against decay to the trivial solution. Soliton stability is due to constraints, rather than integrability of the field equations. Thus, the differential equation solutions can be classified into homotopy classes, there is no continuous transformation that will map a solution in one homotopy class to another 43. Or, it refers to the case of an oscillating plate in a viscous fluid at rest. In turbulent flow, this is named a Stokes boundary layer. The thickness of the boundary layer is called the Stokes boundary-layer thickness. This observation is also valid for the case of a turbulent boundary layer, outside the Stokes boundary layer — which is often the bulk of the fluid volume — the vorticity oscillations may be neglected. To good approximation, the velocity oscillations are irrotational outside the boundary layer. This significantly simplifies the solution of these problems, and is often applied in the irrotational flow regions of sound waves. The oscillating flow is assumed to be uni-directional and parallel to the plane wall, the only non-zero velocity component is called u and is in the x-direction parallel to the oscillation direction. Moreover, since the flow is taken to be incompressible, the velocity component u is only a function of time t, the Reynolds number is taken small enough for the flow to be laminar. As usual for the vorticity dynamics, the pressure out of the vorticity equation. Harmonic motion of a rigid plate — moving parallel to its plane — will result in the fluid near the plate being dragged with the plate. For instance, a particle floating at the surface of water waves, experiences a net Stokes drift velocity in the direction of wave propagation. More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a parcel, and the average Eulerian flow velocity of the fluid at a fixed position. This nonlinear phenomenon is named after George Gabriel Stokes, who derived expressions for this drift in his 1847 study of water waves. The Stokes drift is the difference in end positions, after an amount of time. The end position in the Lagrangian description is obtained by following a specific fluid parcel during the time interval, the Stokes drift velocity equals the Stokes drift divided by the considered time interval. Often, the Stokes drift velocity is referred to as Stokes drift. Stokes drift may occur in all instances of oscillatory flow which are inhomogeneous in space, for instance in water waves, tides and atmospheric waves. In the Lagrangian description, fluid parcels may drift far from their initial positions, as a result, the unambiguous definition of an average Lagrangian velocity and Stokes drift velocity, which can be attributed to a certain fixed position, is by no means a trivial task. However, such a description is provided by the Generalized Lagrangian Mean theory of Andrews. The Stokes drift is important for the transfer of all kind of materials. Further the Stokes drift is important for the generation of Langmuir circulations, for nonlinear and periodic water waves, accurate results on the Stokes drift have been computed and tabulated. But also other ways of labeling the fluid parcels are possible, different definitions of the average may be used, depending on the subject of study, see ergodic theory, time average, space average, ensemble average and phase average. Since a fluid parcel with label α traverses along a path of many different Eulerian positions x, a mathematically sound basis for an unambiguous mapping between average Lagrangian and Eulerian quantities is provided by the theory of the Generalized Lagrangian Mean by Andrews and McIntyre.
Another usage is the fraction of the cycle that has elapsed relative to the origin. In general, shorter waves have a group velocity and long waves a westward group velocity. The bed-level term proportional to h2 in the energy has been neglected, since it is a constant. While, according to the relation, a long wave of this length should propagate at its own — higher — phase velocity. The approximate lunitidal interval can be calculated if the moonrise, moonset, and high tide times are known for a location. When a crescent Moon occurs, the phenomenon of earthshine may be apparent, in the Northern Hemisphere, if the left side of the Moon is dark then the light part is growing, and the Moon is referred to as waxing. The interval between those two times in the Lunitidal interval. For the mean energy density in the part of the fluid motion. Its weight per volume is g, in which g is the acceleration of gravity.