Analytical Estimate of Phase Mixing Time of Longitudinal Akhiezer - Polovin Wave

TL;DR

This paper analytically derives the dependence of phase mixing time of longitudinal Akhiezer-Polovin waves on wave parameters and verifies it through numerical simulations, enhancing understanding of wave breaking mechanisms.

Contribution

It provides an analytical expression for phase mixing time of Akhiezer-Polovin waves and confirms it with numerical simulations, which was not previously established.

Findings

Phase mixing time depends linearly on wave phase velocity.

It varies inversely with the square of maximum fluid velocity.

It is inversely proportional to the perturbation amplitude.

Abstract

Phase mixing and eventual breaking of longitudinal Akhiezer - Polovin wave subjected to a small amplitude longitudinal perturbation is studied analytically. It is well known that longitudinal Akhiezer - Polovin wave breaks via the process of phase mixing at an amplitude well below its breaking amplitude, when subjected to arbitrarily small longitudinal perturbation[Phys. Rev. Lett.108, 125005 (2012)]. Here we analytically show that the phase mixing time (breaking time) has a linear dependence with phase velocity of the wave, inverse square dependence with the maximum fluid velocity and it is inversely proportional to the amplitude of perturbation. This analytical dependence of phase mixing time on the above three parameters is further verified using numerical simulations based on Dawson Sheet Model.