Speed of Tsunami Wave
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
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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Update: June 2012