Abstract
The effect of nonlinear coupling due to resonant interactions on a bimodal spectrum is examined in the case of deep-water waves. Following Hasselmann, a swell decay time scale is first estimated for a monochromatic swell coupled with a typical wind wave spectrum. This time scale indicates that the nonlinear coupling generally causes the swell to decay at a rate that decreases rapidly as the swell frequency moves away from the peak frequency of the short waves. It is also shown, however, that the coupling makes the swell grow at the expense of the local sea in the frequency range just below the peak frequency of the short waves. Estimation of the nonlinear transfer for a swell of finite bandwidth confirms these results and also indicates a maximum coupling when the swell direction is about 40° to the mean direction of the short waves.
When a double peaked spectrum is time integrated under the influence of the nonlinear interactions, the spectral distribution gradually changes into a unimodal shape where the local sea peak has disappeared and the swell has significantly broadened. These results are compared with laboratory observations where the wind wave growth has been shown to be greatly altered by a train of long waves. It is shown that the nonlinear coupling produces an energy flux that smooths out the high-frequency peak in agreement with the observations. Finally, the nonlinear coupling is discussed in the case of sea and swell in the ocean for which it is found that the coupling is generally negligible unless the two peaks are so close that the spectrum can be hardly qualified as bimodal.
