A dissipative Nonlinear Schr\"{o}dinger model for wave propagation in the marginal ice zone

TL;DR

This paper develops a nonlinear Schrödinger model with dissipation to describe wave attenuation and spectral changes in the marginal ice zone, aligning with recent observations and highlighting nonlinear effects on wave statistics.

Contribution

It introduces a frequency-dependent dissipative nonlinear Schrödinger equation for wave propagation in the marginal ice zone, incorporating recent field data and emphasizing nonlinear dissipation effects.

Findings

High frequency wave components dissipate preferentially.

Spectral peak downshift occurs due to nonlinearity.

Wave energy decay is slower than exponential.

Abstract

Sea ice attenuates waves propagating from the open ocean. Here we model the evolution of energetic unidirectional random waves in the marginal ice zone with a nonlinear Schr\"{o}dinger equation, with a frequency dependent dissipative term consistent with current model paradigms and recent field observations. The preferential dissipation of high frequency components results in a concurrent downshift of the spectral peak that leads to a less than exponential energy decay, but at a lower rate compared to a corresponding linear model. Attenuation and downshift contrast nonlinearity, and nonlinear wave statistics at the edge tend to Gaussianity farther into the marginal ice zone.