73 FIRST-ORDER WAVE GENERATION
357
Figure 7.5: Variable-Draft Flap-Type Wave Board.
Substituting Eqns. 7.87 and 7.88 for /(z) in Eqns.7.50 and 7.51 and
performing the integrations yields the expressions
2aS0
fc(sinh 2kh 4- 2kh.)
sinh kh +
(cosh kl — cosh kh)
k(h - 1)
(7.89)
and
______ 2crS0______
.
,
(cos knh - cos knl)
kn(s'm2knh + 2knh)
”
kn(h - I)
(7.90)
where the numerical subscripts on the wavenumbers, ki and ksn, have been
dropped for convenience.
Wave Height-to-Stroke Ratio
Substituting Eqn. 7.89 into Eqn. 7.54 and making use of the dispersion
relationship given by a2 = gk tanh kh (Eqn. 7.45) yields