Frequency downshifting in decaying wavetrains on the ocean surface covered by ice floes

TL;DR

This paper investigates how frequency-dependent dissipation causes frequency downshifting in ocean surface waves covered by ice floes, using analytical and numerical methods within linear and nonlinear models.

Contribution

It introduces a comprehensive theory for frequency downshifting due to power-law dissipation and validates it with numerical simulations for realistic oceanic conditions.

Findings

Frequency downshifting is more pronounced with wider spectra.

Nonlinear adiabatic evolution results in smaller downshifts than linear models.

Interactions between wave groups cause rapid spectral broadening and downshifting.

Abstract

We study analytically and numerically a frequency downshifting due to power-type frequency-dependent decay of surface waves in the ocean covered by ice floes. The downshifting is obtained both within the linear model and within the nonlinear Schr\"odinger (NLS) equation augmented by viscous terms for the initial condition in the form of an NLS envelope soliton. It is shown that the frequency-dependent dissipation produces a more substantial downshifting when the spectrum is relatively wide. As a result, the nonlinear adiabatic scenario of wavetrain evolution provides a downshifting remarkably smaller in magnitude than in the linear regime. Meanwhile, interactions between nonlinear wavegroups lead to spectral broadening and thus, result in fast substantial frequency downshifts. Analytic estimates are obtained for an arbitrary power $n$ of the dependence of a dissipation rate on frequency $\sim \omega^n$. The developed theory is validated by the numerical modelling of the generalized NLS equation with dissipative terms. Estimates of frequency downshift are given for oceanic waves of realistic parameters.