ERDC/CHL CHETN-III-67
September 2003
Figure 2. Goodness-of-fit of nonlinear momentum flux empirical equation
(Fourier wave theory)
Solitary Waves
An analytical derivation for the wave momentum flux parameter for solitary waves was given by
Hughes (in preparation) as
1 ⎡⎛ H ⎞
⎛ H ⎞⎤
2
⎛ MF ⎞
= ⎢⎜ ⎟ + 2 ⎜ ⎟⎥
⎜
2⎟
⎝ ρ gh ⎠max 2 ⎢⎝ h ⎠
⎝ h ⎠⎥
⎣
⎦
(8)
N 2 ⎛ H ⎞ ⎧ ⎡ M ⎛ H ⎞⎤ 1 3 ⎡ M ⎛ H ⎞⎤ ⎫
+
⎜ + 1⎟ ⎨tan ⎢ ⎜ + 1⎟⎥ + tan ⎢ ⎜ + 1⎟⎥ ⎬
2M ⎝ h
⎠⎩ ⎣ 2 ⎝ h
⎠⎦ 3
⎣2⎝h
⎠⎦ ⎭
The parameter is a function of only relative wave height H/h and two coefficients M and N that are
typically presented in graphical form. To accommodate calculations, a nonlinear curve fit was
applied to the plotted M and N curves to produce the following simple equations that give reasonable
values for M and N.
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