Dynamics of Vortex Pair in Radial Flow

TL;DR

This paper analyzes the behavior of vortex pairs in radial flows, revealing how their motion and velocity change depending on flow conditions, with potential applications in astrophysics and geophysics.

Contribution

It provides an exact solution for vortex pair dynamics in radial flow, including velocity changes and motion patterns, which were not previously characterized.

Findings

Vortex pairs can reverse motion within bounded regions.

Velocity increases or decreases after passing through source/sink regions.

Vortices follow logarithmic spiral trajectories in radial flow.

Abstract

The problem of vortex pair motion in two-dimensional plane radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases or increases after passing through the source/sink region, depending on whether the flow is diverging or converging, respectively. The rotational motion of two corotating vortexes in a quiescent environment transforms into motion along a logarithmic spiral in the presence of radial flow. The problem may have applications in astrophysics and geophysics.