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Name: Robert
Status: Other
Age: 50s
Location: N/A
Country: N/A
Date: N/A 

Why is the speed of tsunami waves in the open sea a function of water depth. (The wave speed is the square root of the product of the gravity constant (g) and water depth.)

The formula that you mention is a very close approximation of the speed of waves with long wavelengths (like waves in the ocean). Wave speed is also somewhat dependent on wavelength.

A tsunami wave qualifies as having a long wavelength. Tsunamis are normally produced by an earthquake or displacement of the seafloor due to plate shifts, etc. This produces a very large wave very rapidly, which then possesses significant energy.

The energy is distributed through the depth of the water initially, as it is displaced, but because of gravity and friction with the seabed, tends to decrease with increasing depth after a short while. In deep water, the frictional affect on the wave speed is negligible near the surface. The more shallow the water (for instance as it approaches shore), the greater the affect of friction in slowing the mass of water above the seabed; most of the energy of the wave is transferred to the seabed, a small portion is lost to the atmosphere and in heating of the water.

Therefore, the more shallow the water, the slower the wave speed.

David R. Cook
Atmospheric Research Section
Environmental Research Division
Argonne National Laboratory

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