Interaction of surface waves at very close wavenumbers

Abstract

We show that interaction of two monochromatic waves at the water surface enters a different dynamic regime if their wavenumbers become very close. The study is conducted by means of a fully nonlinear wave model. In the course of evolution of the two waves, downshifting of the initial wave energy and growth of the first mode occur depending on wave steepness and dk/k. Behaviour of these features changes if dk/k < 0.0025: both downshifting and growth rate become independent of dk/k, accompanied by rapid transfer of wave energy to large scales. © 2014 Springer-Verlag Berlin Heidelberg.