Evolution of a nonlinear wave field along a tank: experiments and numerical simulations based on the spatial Zakharov equation

Abstract

Evolution of a nonlinear wave field along a laboratory tank is studied experimentally and numerically. The numerical study is based on the Zakharov nonlinear equation, which is modified to describe slow spatial evolution of unidirectional waves as they move along the tank. Groups with various initial shapes, amplitudes and spectral contents are studied. It is demonstrated that the applied theoretical model, which does not impose any constraints on the spectral width, is capable of describing accurately, both qualitatively and quantitatively, the slow spatial variation of the group envelopes. The theoretical model also describes accurately the variation along the tank of the spectral shapes, including free wave components and the bound waves.