7.6. IRREGULAR (2-D) WAVE GENERATION
415
Important Note: For the case of a flap-type wave board with
variable draft (see Figure 7.5), Sand and Donslund (1985) replaced / (the distance of the wave board hinge above the bottom) in Eqn. 7.87 with — I so that the equation would be the
same as when the wave board is hinged beneath the bottom
(see Eqn. 7.28). Therefore, in the following equations, I should
be replaced with -I if the variable-draft wave board
is being considered. (The variable-draft flap-type board is
denoted as I < 0.)
Nnm^ (0 — (®n
)El COs( AunmZ ) 4" (<2n
d" ^n^m ) F\ Sin( Awnrn ^ )
(7.219)
with
Ei - En + Ei2
(7.220)
The term Fn in Eqn. 7.220 leads to suppression of the parasitic long
wave, and it is given by
F _ GnrnAk* 2 f(h 4- /)[(Afcnm - Afcy) sinh(An) + (Afcnm + Afc/) sinh(Bn )]
2(A.k2m — Ak2) sinhÇAknmh^Akf(h 4- /) sinh(Afc//i) — cosh(Afc//i) 4- &']
(7.221)
where
for I > 0
(3' = cosh(—Akjl) for I < 0
and the long wave number, Akj, has to be determined from the dispersion
relationship
(Aunm)2 = gAkj tanh(Afcj/i)
(7.224)
The transfer function, Gnm, was given previously by Eqn. 7.213, along with
Eqns. 7.214 - 7.217.
The term F12 in Eqn. 7.220 suppresses the displacement long wave that
arises from movement of the wave board away from its mean position, and
it is expressed by the complicated function
An = (Aknrnh 4- Akjh.)
and
and
Bu=(Aknmh-Akfh)
(7.222)
1
(7.223)