CETN IV-17
March 1999
period is relatively long, even though the current is strong. The change in wavelength because of
the current is relatively small (about 10 percent), and thus shoaling because of wave-current
interaction is also small. For the weak interaction cases, the breaking criterion given by
Equation 4 acts much like the depth-limited criterion (Equation 9). For reference, an additional
curve is included that shows the wave-height transformation for the case where current is
neglected. Because the depth variation is relatively small, there is little wave-height variation
without wave-current interaction. But, even in the case of weak wave-current interaction, the
wave height is significantly overpredicted by neglecting the current and current-induced breaking.
In addition to wave height and breaking status, the wave-current interaction program also
provides wavelength, wave steepness (H/L), wave celerity (C), and wave celerity relative to the
current (Cr). Changes in wave steepness can be used to evaluate navigability at a coastal
entrance.
Strong interaction is illustrated in Figure 4 with incident wave conditions Hmo = 9 ft and peak
period of 5 sec, and maximum current of -6 ft/sec. The wave-current interaction is strong in this
case because the wave period is relatively short and current is strong. The waves are close to
being blocked by the current. Blocking occurs if the current is so strong that it stops waves from
propagating into the inlet (there is no solution to the wave-dispersion equation) and the wave
energy is dissipated by breaking or reflected offshore. The shortening of wavelength because of
the current is significant (about 50 percent), and thus shoaling because of wave-current interaction
is also large. The waves are breaking for x > 750 ft because of steepening of the waves (solid
curve). For strong interaction cases, limiting wave height using the depth-limited criterion
(dashed curve) performs poorly (at x = 2,300 ft, the predicted wave height is 10 ft, and the
measured wave height is less than 2 ft).
ADDITIONAL INFORMATION:
For additional information, contact Dr. Jane McKee Smith, Coastal Processes Branch, Coastal
Sediments and Engineering Division, Coastal and Hydraulics Laboratory, U.S. Army Engineer
Research and Development Center, Vicksburg, MS (Voice: (601)634-2079, FAX: (601) 634-
4314, e-mail: ). This technical note should be cited as follows:
Smith, J. M. (1999). "Wave breaking on an opposing current," Coastal
Engineering Technical Note CETN IV-17, U.S. Army Engineer Research and
Development Center, Vicksburg, MS. http://bigfoot.wes.army.mil/cetn.index.htm
REFERENCES:
Holthuijsen, L. H., Ris, R. C., and Booij, N. (1998). "A verification of the third-generation wave
model `SWAN.'" Proc., 5th International Workshop on Wave Hindcasting and
Forecasting. Environment Canada, 223-230.
Jonsson, I. G. (1990). "Wave-current interactions." The sea. Chapter 7, B. Le Mhaut and D.
Hanes, ed., John Wiley & Sons, New York, 65-120.
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