7/30/2019 Water Wave Celerity

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7/30/2019 Water Wave Celerity

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30/12 Water Wave Celerity

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Note that in deep water the celerity is independent of water depth, which is not surprising in view of the fact thatthe waves do not interact with the bottom. What is interesting, however, is that the celerity depends on thewave length. Water is therefore a dispersive medium with respect to deep water surface waves, in much thesame way that it is a dispersive medium for light waves. Shallow water surface waves, on the other hand, do feelthe bottom, and slow down as the square root of the depth. Their speed is not a function of the wave length.

As surface waves travel across various depths of water their period T does not change (for a proof see thearticle entitled "Constancy of Wave Period"). In deep water, therefore, the wave length is constant, but as wavesapproach a beach the wave length decreases as the square root of the depth.

Wind-generated waves typically have periods from 1 to 25 seconds, wave lengths from 1 to 1000 meters,speeds from 1 to 40 m/s, and heights less than 3 meters. Seismic waves, or tsunamis , have periods typicallyfrom 10 minutes to one hour, wave lengths of several hundreds of kilometers, and mid-ocean heights usually lessthan half a meter. Because of their long wavelengths, tsunamis often satisfy the criterion for shallow-water waves.For example, when a tsunami with a wave length of 200 km passes over a depth of 4 km (the average depth of the oceans) the relative depth is d/L=.02. Since this is less than .05, this tsunami is a "shallow-water wave", andits celerity depends only on the water depth.

REFERENCES:

Robert M. Sorensen, "Basic Wave Mechanics for Coastal and Ocean Engineers" (John Wiley & Sons,1993), Chapter 2..

Last Modified: 10:11pm , April 28, 1997