7.6. IRREGULAR (2-D) WAVE GENERATION
423
Xnm2(X) ~
+ (a»iam ~ ^n^m)^23] COs((TCj/) —
— [(anam — bnbm)F-[ — (anbm + am6n)F23] sin(crcut)
(7.248)
with
Ei — Fu + Fi2
(7.249)
and
7 * 23 — E2 (F3,m + F^ n)
(7.250)
Sand and Mansard (1986) stated that the Fn-term allows the correct
second-order profile to exist without spurious effects arising from the bound
components reflecting on the wave board. They gave the dimensionless form
of Fi 1 as
p
[G„mÀ U ak2 jh2{ffkfh tanh akfh — akh tanh akh) (1 -|- £)]
^( j
(7.251)
where akj is the free wavenumber from the dispersion relationship
()2 = gcrkj tanh( (7.252)
and
/3' =
1
for I > 0
= cosh(akfl) for I < 0
(7.253)
and
(,+
knh A(l+tanh knh tanh kmh)
4 G+mhy/knh kmh tanh knh tanhfcmh
ak^htanhakjhy
4C?+mh
J ’
(
akhtanh akh
akjh tanh akfh
(7.254)
The transfer function G+m was given previously by Eqn. 7.241 along with
Eqns. 7.242 - 7.246.
The term F12 in Eqn. 7.249 suppresses spurious waves arising from the
product of wave board displacement and horizontal orbital wave accelerations and from the product of wave board displacement and vertical wave
U =