Non-linear Instabilities

TL;DR

This paper reviews the role of wave resonance in non-linear fluid flow instabilities, highlighting their long-term effects and distinct differences from linear instability mechanisms.

Contribution

It summarizes two decades of research on non-linear instabilities driven by wave resonance, emphasizing their unique consequences in fluid dynamics.

Findings

Wave resonance causes non-linear instabilities affecting fluid flow evolution.

Non-linear instabilities have distinct behaviors from linear ones.

Long-term effects of wave resonance are significant in fluid dynamics.

Abstract

Wave resonance is the fundamental mechanism of non-linear instabilities of fluid flows, and affects the long-time evolution of fluid motions and other physical problems described by non-linear differential equations. Some significant consequences, not well known and completely different from linear instabilities, are summarized in this paper from the studies of past two decades.