A New Coastal Wave Model. Part V: Five-Wave Interactions

Abstract

The authors study the action flux associated with three-dimensional wave?wave interactions of ocean surface waves. Over deep water, two-dimensional wave?wave interactions are dominant: the three-dimensional five-wave interactions are two orders of magnitude smaller than the two-dimensional four-wave interactions. However, the five-wave interactions become increasingly important as the water depth decreases. Because of the effects of finite depth, three-dimensional five-wave interactions, involving steep finite-amplitude waves, dominate over two-dimensional four-wave interactions. Specifically, when the water depth h is less than 10 m, or nondimensionalizing with the spectral peak wavenumber Kp when Kph ≤ 3.6 and nonlinearity, ? = Ka(3 + tanh2Kh)/4 tanh3Kh ≥ 0.3, the five-wave interactions completely dominate. Results are consistent with the instability study by McLean.