# Instability of a smooth shear layer through wave interactions

## TL;DR

This paper extends wave interaction theory to smooth shear layers, demonstrating that stable vorticity wave interactions can predict instability in these flows, which were previously analyzed mainly with piecewise-linear profiles.

## Contribution

It introduces a method to identify stable vorticity wave modes in smooth shear profiles and shows their interactions explain shear flow instability.

## Key findings

- Stable vorticity wave interactions predict shear layer instability.
- Method effectively describes stability properties of smooth shear flows.
- Wave interaction mechanism is confirmed in smooth shear profiles.

## Abstract

Wave interaction theory can be used as a tool to understand and predict instability in a variety of homogeneous and stratified shear flows. It is however, most often limited to piecewise-linear profiles of the shear layer background velocity, in which stable vorticity wave modes can be easily identified, and their interaction quantified. This approach to understanding shear flow instability is extended herein to smooth shear layer profiles. We describe a method, by which the stable vorticity wave modes can be identified, and show that their interaction results in an excellent description of the stability properties of the smooth shear layer, thus demonstrating the presence of the wave interaction mechanism in smooth shear flows.