Steady axisymmetric vortices in radial stagnation flows

TL;DR

This paper introduces a new class of axisymmetric vortex solutions superposed on radial stagnation flows, generalizing classical vortices and analyzing their stability with respect to disturbances.

Contribution

It presents a generalized vortex solution incorporating a volumetric line source, extending classical models like Burgers' and Sullivan's vortices, and studies their stability properties.

Findings

Generalized vortices approach classical Burgers' vortex as source strength increases.

These vortices are unstable to 2D disturbances above a critical Reynolds number.

The solutions expand understanding of vortex behavior in radial stagnation flows.

Abstract

A class of axisymmetric vortex solutions superposed upon radial stagnation flows is described. The new vortex solutions generalize the classical Burgers' vortex and Sullivan's vortex solutions in the presence of a volumetric line source at the symmetry axis, the former approaching the Burgers' vortex sheet when the source strength becomes very large. The stability of the generalized Burgers' vortex is studied. In a different manner from the classical solution, the generalized Burgers' vortices are found to be unstable for two-dimensional disturbances when the vortex Reynolds number is increased above a critical value, for a fixed strength of the volumetric source.