ERDC/CHL CHETN-III-67
September 2003
Estimate Limit Wave Height: First check to be certain the specified wave height does not exceed
the steepness limited wave height for the given wave period and water depth. Calculate the circular
wave frequency and nondimensional depth as
2π
2π
ω = T = (8 s) = 0.7854 1/s
and
(0.7854 1/s)2(15 ft)
ω 2h
r=
=
= 0.287
(32.2 ft/s2)
g
The limiting wave height is given by rearranging Equation 3 and replacing the constants with the
given numerical values, i.e.,
⎛ 0.7879r + 2.0064r 2 - 0.0962r 3 ⎞
⎛ g ⎞
= ⎜ 2 ⎟ (1.0575) tanh ⎜
H limit
⎟
1 + 3.2924r - 0.2645r 2
⎝ω ⎠
⎝
⎠
Substituting for the variables ω, g, and r yields
⎡ 32.2 ft/s2 ⎤
⎥ (1.0575)
= ⎢
H limit
⎢ ( 0.7854 1/s ) ⎥
2
⎣
⎦
⎡ 0.7879 ( 0.287 ) + 2.0064 ( 0.287 )2 - 0.0962 ( 0.287 )3 ⎤
tanh ⎢
⎥
1 + 3.2924 ( 0.287 ) - 0.2645 ( 0.287 )
2
⎢
⎥
⎣
⎦
or
Hlimit= (55.2 ft) tanh (0.2023) = 11.0 ft
Because H < Hlimit, the specified wave condition is not steepness limited.
Calculate the Wave Momentum Flux Parameter: First calculate values of relative wave height
and relative depth as
H 9 ft
15 ft
h
= 0.0073
=
h = 15 ft = 0.6
and
(32.2 ft/s2)(8 s)2
gT 2
Next, find the values of the coefficient A0 and A1 from Equations 6 and 7, respectively as
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