CETN IV-17
March 1999
calculate wave-dissipation rates are given by Ris and Holthuijsen (1996) and Smith, Resio, and
Vincent (1997).
Current does not appear explicitly in Equations 3-8 for calculating wave breaking on a current.
Instead, current enters through changes in the wavelength in the equations. The ebb current
steepens the waves, which induces breaking. For flood current, the wave steepness is reduced,
and breaking and dissipation are decreased. The equations are applicable to breaking with or
without current. Wave height is determined by limiting the maximum transformed wave height
(e.g., calculated using Equation 1 with D = 0, the one-dimensional model given in CETN IV-9, or
a two-dimensional model) to the value given by the appropriate breaking criterion (Equations 3-
8).
EXAMPLES AND DISCUSSION: The wave-current interaction PC program presented in
CETN IV-9 has been modified to represent irregular waves as well as monochromatic waves. For
irregular waves, the input wave condition is a significant wave height (Hmo or H1/3), and the
breaking criterion applied is Equation 4 (or 5). The option remains to model monochromatic
waves using the Miche criterion for breaking. An application of the program is shown in Figure 1
and discussed in the following example.
Example 1
Waves approach an inlet entrance on an ebb current. The channel is long and narrow (thus the
one-dimensional assumption is valid). The wave height and the wave steepness in the inlet
channel are required to evaluate navigation safety.
Find: Hmo, H1/100, and wave steepness for irregular waves entering a long, narrow inlet channel on
an ebb current.
Given: Offshore wave height Hmo = 8 ft, and peak period is 6 sec in a water depth d = 40 ft. Inlet
channel depth d = 8 ft, and the ebb current speed is U = 4 ft/sec.
Figure 1 shows the user interface for the one-dimensional wave-current interaction program. The
input conditions given above have been entered, and the output breaking wave height in the throat
is given by the program as Hmo = 4.2 ft. If the waves are breaking ("yes" flag printed in the last
output column), Equations 3 and 6-8 can be used to estimate other wave-height statistics using
the wavelength given in the program output (L = 64 ft). For example, H100 is estimated as
2π
H1/100 = 0.15 L tanh kd = 0.15(64) tanh
8 = 6.3 ft
64
Most often, the significant wave height is used in wave transformation studies, but if considering
navigation safety or other aspects of design, the higher waves may be of greater interest. The
wave steepness is given in Figure 1, based on Hmo, as 0.0656. Based on H1/100, the steepness is
0.0984 (= 6.3 ft/64.0 ft).
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