eate one theory from another are shown in Fig. 14.6. In deep water, linear
theory is applicable as long as the steepness of the wave
H/L
1
1
6
tanh(kd). (14.26)The upper limit at which Stokes waves exist is determined by wave break-
ing, the criterion of which in deep water is
H/L
1
7
tanh(kd). (14.27)Thus Stokes non-linear theory for deep water is applicable for wave steep-
ness in the range given by equations (14.26) and (14.27).
In shallow water, the limit of linear theory is given as (Fig. 14.6)
HL^2 /d^3 32 π^2 /3. (14.28)Non-linear wave theories, in particular the cnoidal wave theory, are complex
and difficult to apply. For further information on non-linear waves, refer to
Dean and Dalrymple (1991). However, Skjelbreia and Hendrickson (1961)
provided tabulated solutions to fifth-order Stokes waves, and Wiegel (1964)
presented charts relevant to cnoidal waves for engineering applications.
Tables of results pertaining to wave properties for a wide range of conditions
produced by Williams (1985) are extremely useful in applications.
RANGE OF VALIDITY OF LINEAR THEORY 585
Fig. 14.6 Regions of validity of wave theories (Komar, 1976)