Stability of Diffusive Shear Layers

TL;DR

This paper introduces a new stability analysis method for diffusive shear layers that accounts for base flow expansion, revealing extended instability growth and revising traditional turbulence transition timelines.

Contribution

It develops a self-similar ansatz incorporating diffusive base-state expansion, improving predictions of shear layer stability beyond classical methods.

Findings

The new framework captures extended instability lifespan and growth rates.

Numerical simulations confirm the accuracy of the stability predictions.

Revises the understanding of shear-induced mixing timelines.

Abstract

As one of the cornerstones of fluid mechanics, stability analyses provide essential physical insights into the growth of perturbations and eventual transition to turbulence. However, classical \enquote{frozen-time} stability analyses implicitly assume a time-independence of their base flow and thus fail for \enquote{rapidly} diffusing shear layers. Here, we propose a self-similar ansatz to naturally incorporate the \enquote{diffusive} base-state expansion into the stability operator. Our approach reveals two competing physical mechanisms: an \enquote{expansion wind} delays the Kelvin-Helmholtz instability whereas a diminishing effective viscosity sustains this instability far beyond classical predictions. Direct numerical simulations confirm that our framework accurately captures the instability's extended lifespan, growth rate, and spectral topology, eventually revising the timeline of shear-induced mixing fundamentally.