Shallow Water Waves
Again, recall that the motion of our waves is governed by the formulas
As with deep water waves, we can approximate the coefficients in front of the trigonometric functions above. We say that a wave is a shallow water wave if the wavelength L=2p/k is large compared to the depth h (that is, kh<<1). This assumption allows the following approximations.
sinhkh » kh
sinh(k(h+y)) » k(h+y)
cosh(k(h+y)) » 1