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why does water depth affect wave velocity?

Water depth affects wave speed only for shallow water waves.

The short story is that waves long compared to the depth "feel" the bottom and it slows them down. The slope of the wave surface translates into a horizontal pressure gradient that is constant throughout the depth. This pressure gradient accelerates the water horizontally (Newton's force = mass x acceleration). The balance between the up-and-down motion of the surface and the back-and-forth of the water depends on the depth

speed = sqrt(gD)

where g is the accelerlation of gravity (a constant) and D is the depth.

As depth increases, the waves change over to the deep water regime where speed ~ sqrt(gL) where L is the wavelength.


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randy patton


Physical oceanography, surface and internal wave characteristics, ocean currents, fluid mechanics, geophysical fluid dynamics, ocean optics, coastal dynamics, modeling and simulation, data analysis, El Nino and related large scale dynamics Not an expert in marine biology (some in bioluminescence) or chemical oceanography


26 years as professional scientist for research company working mostly on Navy and other government contracts. Projects included modeling, simulations and data analysis related to Non-acoustic Anti-submarine Warfare (NAASW). Other projects included remote sensing of ocean features, statistical analysis of ship tracks, ocean optics instrumentation development, synthetic aperture radar (SAR) and sonar (SAS).

Journal of Physical Oceanography, 1984, "A Numerical Model for Low-Frequency Equatorial Dynamics" (with M. Cane)

MS Physical Oceanography, MIT, 1981 BS Applied Math, UC Berkeley, 1976

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