How Quartet Resonance Might or Might Not Amplify Large Waves Into Freak Waves
We have developed an approximate solution to Zakharov’s equations for the evolution of ocean surface waves. We have applied it with a spectral response surface method to estimate the probability of exceedance of crest elevation in random seas. The method avoids time-marching and allows probabilities to be estimated on practical time scales. The results indicate that quartet resonance can produce very large amplification of extreme crests in uni-directional seas. However, the effect is very much smaller in spread seas. Although the solution is approximate it provides a great deal of physical insight into the mechanisms by which a freak wave might develop and explains the difference in results between uni-directional and spread seas.