Hydraulic Structures: Fourth Edition

Figures 14.3 and 14.4 show, respectively, the variations of the linear wave

celerity and period as functions of wavelength and depth. In deep water,

for which d/Lis large, tanh(kd) tends to unity. Hence, equation (14.13)

approximates to

c^2 g/kgL/2π. (14.14)

On the other hand, for waves in shallow water, the wavelength is large in

relation to the depth. Thus in shallow water, for which tanh(kd)→kd, the

celerity of the linear wave is given as

c^2 gd. (14.15)

In deep water the longer the wave, the greater is the celerity. This phe-

nomenon is usually called the normal dispersion. Equation (14.14) is a

very close approximation for celerity for values of d/Lgreater than 0.5. On

the other hand, the shallow-water result of equation (14.15) is a good

approximation for values of L/dgreater than 20.

580 WAVES AND OFFSHORE ENGINEERING

Fig. 14.3 Wave celerity as a function of wavelength and depth