The moment of instability for internal solitary waves

TL;DR

This paper introduces a new measure called the moment of instability for internal solitary waves in stratified fluids, linking it to stability conditions and analyzing its behavior for small-amplitude waves.

Contribution

It defines the moment of instability for internal solitary waves and establishes its relation to the Fredholm condition, providing new insights into wave stability analysis.

Findings

m''(c)=0 as a Fredholm condition

m(c) has a definite sign for small-amplitude waves

The proposed moment of instability is suitable for stability analysis

Abstract

In this note, we define a moment of instability m(c) for internal solitary waves in continuously stratified fluids, which seems not to have been done before. To underline the suitability of the proposed moment of instability, we identify the relation m"(c)=0 as a formal Fredholm condition, and we show that m(c) displays a definite sign for small-amplitude waves.