Stability of Inviscid Parallel Flows between Two Parallel Walls

TL;DR

This paper analyzes the stability of inviscid parallel flows between two walls, concluding that such flows are neutrally stable with uniform velocity profiles and challenging the classical Rayleigh Theorem's inflection point criterion.

Contribution

It demonstrates that the classical flow profile is uniform and questions the validity of Rayleigh's inflection point theorem for inviscid parallel flows.

Findings

Flow disturbance propagates at flow velocity with neutral stability.

Classical Rayleigh Theorem on inflection points is potentially incorrect.

Flow profile for this problem is uniform.

Abstract

In this paper, the stability of inviscid parallel flow between two parallel walls is studied. Firstly, it is obtained that the profile of the base flow for this classical problem is a uniform flow. Secondly, it is shown that the solution of the disturbance equation is cr=U and ci=0, i.e., the propagation speed of the disturbance equals the flow velocity and the disturbance in this flow is neutral. Finally, it is suggested that the classical Rayleigh Theorem on inflectional velocity instability is incorrect which states that the necessary condition for instability of inviscid parallel flow is the existence of an inflection point on the velocity profile.