ERDC/CHL CHETN-III-67
September 2003
0.44
⎧
⎛ H ⎞⎤ ⎫
⎡
M = 0.98 ⎨tanh ⎢2.24 ⎜ ⎟⎥ ⎬
(9)
⎝ h ⎠⎦ ⎭
⎣
⎩
⎡
⎛ H ⎞⎤
N = 0.69 tanh ⎢2.38 ⎜ ⎟⎥
(10)
⎝ h ⎠⎦
⎣
The empirically-fit equations (solid lines) are plotted along with the data points taken from the Shore
protection manual (1984) in Figure 3. The variation of maximum nondimensional wave momentum
flux for solitary waves as a function of H/h is shown in Figure 4. These values represent the upper
limit of nonlinear (Fourier) waves when h/(gT2 ) approaches zero.
APPLICATIONS: It is anticipated that the wave momentum flux parameter will prove useful for
developing improved semiempirical formulas to describe such wave/structure processes as runup,
overtopping, reflection, transmission, and armor stability. As an example, a simple expression for
wave runup on plane, impermeable slopes was derived by assuming the weight of water contained in
the volume above the still-water line at maximum runup is proportional to the maximum depth-
integrated wave momentum flux in the wave as it passes the structure toe. Hughes (in preparation)
confirmed this simple hypothesis by establishing empirical runup relationships based on the wave
Figure 3. Nonlinear curve fit to solitary wave N and M coefficients
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