| Title page |
| Basic wave theory |
| Deep water waves |
| Shallow water waves |
| Waves in water of varying depth |
| Wave trains |
| Beach waves |
| Applets |
| References |
| Symbols Legend |
| Troubleshooting |
Shallow Water Waves
Again, recall that the motion of our waves is governed by the formulas
| yx(x,y,t) = | rcosh(k(h+y))
sinhkh |
sin(wt-kx)+x
|
| yy(x,y,t) = | rsinh(k(h+y))
sinhkh |
cos(wt-kx)
|
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