The impact of damping and nonlinear modulation on frequency downshift in three dimensional wave trains

Abstract

We study the evolution of a three dimensional wave train subject to nonlinear modulation and damping. In particular, we are interested in gaining insight about the impact of nonlinear modulation and damping on the frequency downshift that is sometimes observed in three dimensional wave trains. As a motivation for the upcoming simulations, we begin the discussion with the analysis of an experiment that contains both modulation, damping and downshift. Then, starting from the modified nonlinear Schrödinger (MNLS) equation, we add the effects of viscous damping and wave breaking. The equations are solved numerically using a second order multi-component splitting method. The main result is that the non-conservative effects can influence the downshift of the peak; viscous damping may postpone the downshift, while wave breaking may accelerate it.