Comment on "Triggering Rogue Waves in Opposing Currents"

TL;DR

This paper critiques a previous study on rogue waves in nonuniform currents, demonstrating the inaccuracies of the used nonlinear Schrödinger equation and proposing a more precise alternative valid for strong currents.

Contribution

It identifies errors in the existing NLSE model for rogue waves in currents and introduces an improved equation applicable to larger current effects.

Findings

The original NLSE used in prior work is incorrect even at first order.

An accurate variant of NLSE is proposed for strong nonuniform currents.

The new model is valid when (1+4ωU/g) ≳ 0.2.

Abstract

The authors of a recent Letter ([1] M. Onorato, D. Proment, and A. Toffoli, Phys. Rev. Lett. 107, 184502 (2011)) based their study of rogue waves in nonuniform currents on a modified nonlinear Schr\"odinger equation (NLSE; see Eq.(1) in [1]). However, I show here that equation is not correct. It gives wrong solutions even in the first order on the supposedly small parameter $U/c_{\rm g}$, where $U(x)$ is a current, and $c_{\rm g}=g/(2 \omega)$ [here $\omega$ is a mean frequency of a quasi-monochromatic wave train, and $g$ is the gravity acceleration]. I also suggest an accurate variant of NLSE, valid in the presence of a large-scale nonuniform current under condition $(1+4\omega U/g) \gtrsim 0.2$.