Stability and eigenvalue bounds for micropolar shear flows

TL;DR

This paper establishes eigenvalue bounds and stability criteria for two-dimensional micropolar shear flows, extending classical fluid stability analysis to micropolar fluids and deriving bounds on wave speeds.

Contribution

It introduces eigenvalue bounds and stability conditions specifically for micropolar shear flows, a novel extension of classical fluid stability theory.

Findings

Eigenvalue bounds for micropolar shear flows

Sufficient conditions for linear stability

Wave speed bounds for disturbances

Abstract

We prove eigenvalue bounds for two-dimensional linearized disturbances of parallel flows of micropolar fluids, deriving the Orr-Sommerfeld equations and providing a sufficient condition for linear stability of such flows. We also derive wave speed bounds.