Experimental study of extreme waves based on nonlinear Schrödinger equation under background of a random sea

Abstract

The Peregrine breather (PB) solution of the nonlinear Schrödinger equation is used to model ocean extreme waves in a water wave flume. Triangular spectral features of wave elevations are observed over the nonlinear evolution of the extreme waves, which can be applied for early detection of the formation of extreme waves. To model a more realistic sea state, a background random wave is superposed to the PB in this study. We examine the spectral features of the nonlinear wave evolution with random background waves by the spectral analysis. It is found that the wave elevations show similar triangular spectral features for extreme waves with a relatively mild background wave. Moreover, we find that the second harmonic elevations of the extreme waves also show triangular spectral features, suggesting the potential use of the second harmonic elevations (in addition to the first) for detection of the formation of extreme waves.