Page 34 - kursus eBook

Figure 10.4.3 The frequency, phase speed and group velocity of surface gravity waves as
a function of wavenumber (inverse wavelength)

Note that the phase speed of the wave is different for different wavenumbers; the waves
are dispersive, a disturbance composed of a superposition of plane waves in a Fourier

composition will therefore alter its shape as each component propagates at its own speed.

Long waves, i.e. small KD propagate fastest and in the limit of waves that are very long
compared to the depth , KD<<1, the phase speed becomes independent o f wavelength.

For very long waves,

(
for KD = 2!D << 1, # ! gD) 1/2 K,
" (10.4. 33 a,b)
(
1/2
c = gD) ,
so the phase speed is independent of wavelength and depends only on the water depth,

while for very short waves,

Chapter 10 28