Instability of diverging and converging flows in an annulus

TL;DR

This paper investigates the stability of diverging and converging flows in an annular region, revealing that such flows are generally unstable to small perturbations, with instability persisting even when viscosity is considered.

Contribution

It provides a detailed analysis of the inviscid and viscous stability of irrotational flows in an annulus, highlighting their inherent oscillatory instability across various parameters.

Findings

Flow is unstable to small 2D perturbations

Instability is inviscid and oscillatory

Persistence of instability with viscosity

Abstract

The stability of two-dimensional diverging and converging flows in an annulus between two permeable cylinders is examined. The basic flow is irrotational and has both the radial and azimuthal components. It is shown that for a wide range of the parameters of the problem, the basic flow is unstable to small two-dimensional perturbations. The instability is inviscid and oscillatory and persists if the viscosity of the fluid is taken into consideration.