Stability criteria for the 2D $\alpha$-Euler equations

TL;DR

This paper extends classical fluid stability theorems to the 2D alpha-Euler equations, providing new criteria for stability and instability in this modified fluid model.

Contribution

It introduces stability and instability criteria analogous to classical theorems specifically for the 2D alpha-Euler equations, a novel adaptation.

Findings

Derived alpha-Euler stability criteria similar to Rayleigh and Fjortoft theorems

Established Arnold stability conditions for the 2D alpha-Euler equations

Provided instability conditions in the alpha-Euler context

Abstract

We derive analogues of the classical Rayleigh, Fjortoft and Arnold stability and instability theorems in the context of the 2D $\alpha$-Euler equations.