Evolution of nonlinear waves with heterogeneous damping and forcing

Abstract

Slowly modulated nonlinear-waves are ubiquitous in nature and their weakly nonlinear dynamics are described by the nonlinear Schrödinger equation (NLS) or its higher order version, i.e. Dysthe's equation. There is no inherent dissipation mechanism in these equations, however, in many physical systems the wave evolution is affected by energy gains and losses and therefore these NLS-like equations have to be modified to include these effects. Here, we focus on the evolution of wind-forced ocean waves propagating in ice-covered waters, such as in the polar regions. The peculiar feature of this physical system is the heterogeneous, frequency-dependent, attenuation. Here, we showcase the combined effect of higher order nonlinearity and heterogeneous dissipation on the wave dynamics.