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Topic: Dispersion (water waves)

	Dispersion (water waves) - Wikipedia, the free encyclopedia
		That is, water, in fluid dynamics, is generally considered to be a dispersive medium; which means that the velocity of the wave front travels as a function of frequency so that spacial and temporal phase properties of the wave propogation are constantly changing.
		So, for example, waves travelling in water with a longer wavelength and period travel faster than those with a shorter wavelength and period.
		The height here refers to the surface wave phenomena and is incorporated into the given form of the dispersion relation.
	en.wikipedia.org /wiki/Dispersion_(water_waves) (255 words)

	Waves
		Waves travelling in water shallower than 1/20 the wavelength are considered to be shallow-water waves and their speed is determined only by water depth.
		When wave enter shallow enough water they break because the motion of water in the lower part of the wave nearest the bottom is slowed by friction so that the motion of water molecules in their orbits in the crest of the wave is faster than its supporting portion at the bottom.
		Waves on the ocean surface occur at the boundary between the air and the water.
	core.ecu.edu /geology/woods/WAVES.htm (1659 words)

	Surface wave - Wikipedia, the free encyclopedia
		A seismic wave is a wave that travels through the Earth, often as the result of an earthquake or explosion.
		The Rayleigh waves, also known as "ground rolls", are a type of surface wave associated on the Earth with earthquakes and subterranean movement of magma.
		An example is the waves at the surface of water and air, ocean surface waves, or ripples in the sand on the interface of water or wind.
	en.wikipedia.org /wiki/Surface_wave (1492 words)

	Dispersion - Wikipedia, the free encyclopedia
		A phenomenon that causes the separation of a wave into components of varying frequency.
		When dealing with optical fibres there can also be dispersion of different modes in the fibre and of different polarizations.
		Dispersive mass transfer is spreading of mass from highly concentrated areas to lower concentrated areas.
	en.wikipedia.org /wiki/Dispersion (192 words)

	Sound and Water Waves
		It is determined by the ratio of the water's depth to the wavelength of the wave.
		Water on the side of the earth facing the moon therefore forms a bulge outward from the center of the earth and toward the moon.
		Water on the side of the earth facing away from the moon forms a bulge outward from the center of the earth and away from the moon.
	electron9.phys.utk.edu /phys135d/modules/m10/sound.htm (2520 words)

	Untitled (Site not responding. Last check: 2007-10-13)
		A wave's energy is present as potential energy, due to the change in elevation of the water surface, and as kinetic energy, due to the motion of the water particles in their orbits.
		Since wave energy is proportional to the wave height, the waves gain in height as their wavelength is shortened over the submerged ridge, and more energy is expended on a unit length of shore at the point of the headland than on a unit length of shore elsewhere.
		Average water run-up on the shore was 5 m (16 ft) with a maximum of 19.8 m (65 ft) at the northeast corner of the island.
	www.saddleback.cc.ca.us /faculty/jvalencic/ocean/textbook/chap9/chap9.html (12669 words)

	Oceanogr. Notes Chapter 10
		wave speed depends on the period, with the longer period waves moving faster than the shorter period waves (and the longer period waves have the longer wave lengths).
		In contrast to surface waves in which horizontal particle velocities are largest at the surface and either decay quickly with depth (in deep water waves) or are independent of depth (in shallow water waves), horizontal water movement in internal waves is largest near the surface and bottom and minimal at mid-depth.
		This phenomenon is known as "dead water" and is common in fjords, where the interface is produced by a shallow layer of freshwater from glacier runoff overlying oceanic water underneath.
	www.es.flinders.edu.au /~mattom/IntroOc/notes/lecture10.html (1199 words)

	Chapter10Part1
		In the first part of the lesson on ocean waves, we will discuss the various ways in waves are classified, why wave phase speed is a function of either the length of the wave or the depth of the water, and how a chaotic sea is dispersed into swell.
		They are orbital because, as the wave form passes a certain point, the water particles under the wave move with orbital paths.
		Waves also may be classified by the method of their generation.
	www4.ncsu.edu /eos/users/c/ceknowle/public/chapter10/part1.html (1614 words)

	Oxford Brookes - Geology - WAVES: - Generation, Movement, Erosion and Deposition (Site not responding. Last check: 2007-10-13)
		When the wave finally enters water with a depth of less than one twentieth the wavelength the wave becomes a Shallow water wave (the length and speed of the deep water wave are determined by the wave period the shallow water waves length and speed are controlled only by the water depth).
		Wave ripples are generated on a non cohesive sediment surface when the oscillatory motion of water molecules is strong enough to move the grains.
		The crests of wave ripples are sharp and the round troughs are often indented.
	www.brookes.ac.uk /geology/8361/1998/craig/craig.html (4242 words)

	Dispersive Waves
		Most waves in material media are dispersive, however, and wave forms originally set up are bound to change in a manner that the wave energy is more spatially spread out or dispersed.
		Animation 3 shows superposition of two sinusoidal waves in dispersive case, sin(x - t) + sin(1.2x - 1.1t) (group velocity = half of phase velocity), while the last animation shows the case of nondisperve wave, sin(x - t) + sin(1.2x - 1.2t).
		Note that in the dispersive case (Animation 3), wave propagation is not simple parallel shift.
	physics.usask.ca /~hirose/ep225/animation/dispersion/anim-dispersion.html (270 words)

	he Asian Tsunami in Sri Lanka: A Personal Experience: Discussion (Site not responding. Last check: 2007-10-13)
		The dispersion curves for this function are shown in Figures 1 and 2.
		The dispersion curve for gravity water waves, with the short- and long-wavelength limits illustrated, and the derivation of the phase c and group v velocity from this curve.
		The phase and group velocities for gravity water waves, derived from the dispersion curve in Figure 1. The dashed lines show the long-wavelength approximations.
	www.agu.org /eos_elec/000929e1.html (494 words)

	Exponential-FS-Gravity-Wave (Site not responding. Last check: 2007-10-13)
		>>depth) the waves are non-dispersive; that is, the speed of propagation is constant.
		depth) the waves are dispersive; that is, the speed of propagation is dependent upon the wavelength (wavenumber).
		Here then, the evolution of the wave profile cannot be determined by using d'Alembert's solution alone based on the initial wave profile.
	www.uvm.edu /~dhitt/me305/simulations/Exponential-FS-Gravity-Wave.htm (253 words)

	Mathematical Description of Water Waves (Site not responding. Last check: 2007-10-13)
		The energy of gravity waves in deep water therefore travels at half of the phase velocity, and at the phase velocity in shallow water.
		When gravity waves are observed in deep water, therefore, they appear at the rear of a group, advance forward because the phase velocity is greater than the group velocity, and vanish at the front of the group.
		In deep water, the particles have circular trajectories whose diameter decreases exponentially with depth.
	www.ph.ed.ac.uk /~ted/thesis/node8.html (624 words)

	[No title]
		This states that waves of a given frequency (in water of a certain depth), have a wavelength determined by the dispersion relation.
		Examples: If you observed a wave with period of 10 s in the middle of deep ocean (h=4000m), what is the wave speed c and wavelength L? Solution: this is a deep water wave with period T = 10s.
		Thus EMBED Equation.3 =156 m, and EMBED Equation.3 =15.6 m/s If this wave propagates towards to a coast area with water depth as 5m, what is the wave speed c and wavelength L? Solution: As this wave approaching the coast, water depth becomes shallower and shallower, and smaller compare to the wavelength.
	marine.rutgers.edu /dmcs/ms451/2002/practice4.doc (419 words)

	Dicussion 10 (Site not responding. Last check: 2007-10-13)
		Tides, tsunamis are shallow water waves because they have wavelengths of hundreds or thousands or kilometers.
		In deep water, the group speed is 1/2 the wave (phase) speed.
		In shallow water, the group speed is the same as the phase speed.
	www.geog.ucsb.edu /~dennison/fall97/discussion10.html (518 words)

	The Backward Wave
		Wave packets with a dominant frequency ω and propagation vector k move, approximately, with this velocity.
		The phase velocity is given by the slope of the line from the origin to a point on the dispersion curve, while the group velocity is given by the slope of a tangent to the dispersion curve.
		If the dispersion curve has only tangents in the same direction as the radius from the origin, then the phase and group velocities are in the same direction, and all the waves are forward.
	www.du.edu /~jcalvert/tech/back.htm (2308 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		The other remarkable thing about deep water waves, that can be seen in both the animation and the movie, is that the wave crests move faster than the energy.
		The passage of waves past each observation point showed the expected dispersion—with the wave packet quickly passing stations that are close to the storm while the further the station from the storm the longer it takes the wave packet to pass.
		The natural period of oscillation of a quarter wave resonator is Quarter Wave Resonance T=4L/sqrt(gh) Note that the Bay of Fundy also converges—and that this the continuity equation requires the consideration of the converging channel.
	marine.rutgers.edu /dmcs/ms451/main/notes/Waves_Tides.doc (2502 words)

	Dalrymple's Coastal Engineering Java Page
		Wave Calculator: Using incident deep water wave data, it calculates the local wave variables in shallower water.
		Linear Wave Kinematics: Given wave properties, the orbital motions of the water particles are shown graphically.
		Wavemaker Theory: Depending on the type of wavemaker being used (piston or flap), the stroke and power necessary to generate a wave in a given depth of water is determined.
	www.coastal.udel.edu /faculty/rad (869 words)

	No Title
		Under what conditions are the phase speed and group velocity of the damped shallow water waves equal to the phase speed and group velocity of the undamped shallow water waves?
		When deriving an approximate set of equations to describe the fluid motion, such as shallow water equations, it is extremely important that the dynamics retain important conservaiton laws and dynamical principles that accompany the original set of equations.
		(This is a classical example of wave dispersion in which an arbitrarily shaped initial disturbance in a dispersive medium eventually separates out into a well defined wave train of almost sinusoidal waves in which the wave number varies slowly along the wave train.)
	www.atmos.washington.edu /~dvimont/509/hw2/main/main.html (496 words)

	Phase vs. Group Velocity (Site not responding. Last check: 2007-10-13)
		for waves in the medium in question, for reasons that will be clear shortly.
		, in which waves of different wavelength, initially moving together in phase, will drift apart as the packet propagates, making it ``broader'' in both space and time.
		Such exotic-seeming wave phenomena are ubiquitous in all dispersive media, which are anything but rare.
	musr.physics.ubc.ca /~htb/phys/Waves/node12.html (318 words)

	Characteristic Velocities for Higher-Order Stokes Waves in Deep Water (Site not responding. Last check: 2007-10-13)
		The accuracy of asymptotic expressions for phase, wave energy, and wave action velocities for steady, plane gravity waves progressing in deep water and with no ambient currents is investigated.
		Using the dispersion relation correct to sixth order for arbitrary water depth, the phase velocity is calculated to fourth order in wave steepness for infinitely deep water; this is in accordance with a number of previously found results.
		Practical asymptotic formulas are introduced, enabling one to calculate the characteristic velocities explicitly from given wave height and period.
	www.pubs.asce.org /WWWdisplay.cgi?9902106 (227 words)

	NCAR - Institute for the Study of Society and Environment (Site not responding. Last check: 2007-10-13)
		Committee on Atmospheric Dispersion of Hazardous Material Releases (R.J. Serafin, Chair), 2003: Tracking and Predicting the Atmospheric Dispersion of Hazardous Material Releases: Implications for Homeland Security.
		Water Cycle Study Group (K.A. Miller, member), 2001: A Plan for a New Science Initiative on the Global Water Cycle.
		In Central Eurasian Water Crisis: Caspian, Aral, and Dead Seas (I. Kobori and M.H. Glantz, eds.).
	www.isse.ucar.edu /publications.jsp (10324 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Wave, C = 6.2 m/sec = 22.5 km/hr
		Waves Which Travel at 25m/sec = 90 km/hr.
		Thus, Long Period Wave Groups Race Ahead of Shorter Period Waves.
	www-personal.umich.edu /~tedmoore/DeepWater.html (320 words)

	Waves
		ª waves no longer grow - energy supplied by wind is balanced by energy lost by breaking waves
		ª dispersion - waves move away from generation area at celerity depending on period and wavelength
		ª critical value 1/7 - at this point wave collapses - i.e.
	www.clas.ufl.edu /users/jmartin/Oceanography/waves.html (267 words)

	ripples (Site not responding. Last check: 2007-10-13)
		then surface tension can be neglected, and the wave is called a
		"gravity wave", since the restoring force is gravity.
		The dispersion relation that combines them correctly is
	www.glue.umd.edu /~tajac/273b/ripples.html (222 words)

	Argo Bibliography
		Faure, Vincent and Kevin Speer, 2005: Labrador Sea Water circulation in the Northern North Atlantic Ocean.
		Núñez-Riboni, Ismael, Olaf Boebel, Michel Ollitrault, Yuzhu You, Philip L. Richardson and Russ Davis, 2005: Lagrangian circulation of Antarctic Intermediate Water in the subtropical South Atlantic.
		Speer, K.G., J. Gould and J. Lacasce, 1999: Year-long float trajectories in the Labrador Sea Water of the eastern North Atlantic Ocean.
	www.argo.ucsd.edu /NfBibliography.html (2964 words)

	Waves (Site not responding. Last check: 2007-10-13)
		• wave energy, NOT the water particles move across the surface of the sea
		– diameter of the orbit equaling wave height.
		• The speed or celerity of the wave is equal to
	www.mnstate.edu /leonard/waves.html (268 words)

	[No title]
		Description Using wave gages and a meter stick students are to measure wave period and wavelength for different water depths and wave amplitudes.
		Students are to calculate the phase speed based on measurements and linear wave theory.
		Stroke876540.5”*1.0”*1.5”Take measurements denoted with * The dispersion relation is EMBED Equation ( SEQ Equation \s1 1) or EMBED Equation ( SEQ Equation \s1 2) where EMBED Equation and EMBED Equation .
	ceeserver.cee.cornell.edu /pll3/cee435/lab_02.doc (431 words)

	Waves (Site not responding. Last check: 2007-10-13)
		What common characteristics are shared by all ocean waves - wind waves, tides, tsunami and seiches?
		Are these ocean waves "mechanical" or "electromagnetic" waves?
		What is it important to distinguish "deep" and "shallow" water waves?
	earthguide.ucsd.edu /oceanography/waves.html (119 words)

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