7.3. FIRST-ORDER WAVE GENERATION
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7.3.1 Piston-Type and Flap-Type Wavemakers
For the particular wave board shown in Figure 7.1 that has geometry specified by Eqn. 7.28, the coefficients A and Cn can be obtained (after some
algebra) as
2aS0
. ,
(1 —coshfc/i)
A = ,/ rxT'ï---- ttttt sinhkh + -——--- —L
fc(smh2fc/i + 2kh)
k(h + ï)
and
2trSo
f.
(cosfcn/i-l)
— ~ z , _ _
_ _ sinkfih f
,
.
in(sm 2knh 4- 2knh)
kn(h 4- /)
(7.55)
(7.56)
where the numerical subscripts on the wavenumbers, k\ and k$n, have been
dropped for convenience.
Wave Height-to-Stroke Ratio
Substituting Eqn. 7.55 into Eqn. 7.54 and making use of the dispersion
relationship given by Eqn. 7.45 yields
General First-Order Wavemaker Solution
H
4smh kh
. ,
(1 —coshfch)
— =
---- rrr sinh kh 4----- m---- r—
So
sinh 2kh 4- 2kh
k(h 4- /)
(7.57)
For the special case when / —♦ 00, the second term in Eqn. 7.57 vanishes,
and the wave board motion is that of a piston, i.e.,
First-Order Piston Wavemaker Solution
H_ _
4sinh2fc/i
H
2(cosh 2fc/z - 1)
5g.
So ~ sinh 2kh 4- 2kh
°1
S~o~ sinh2fch + 2kh
The special case of a wave board hinged at the bottom of the wave tank is
found from Eqn. 7.57 when I = 0, viz.,
First-Order Flap Wavemaker Solution
H
4sinh£h
F. ...
(1 — coshkh)
—— = ------------------- sinh kh 4--------- r;
"
So
sinh 2kh 4- 2kh
kh
(7.59)