Vortex dynamics in the nonlinear Schrodinger equation

TL;DR

This paper investigates the behavior of two-dimensional vortices within the nonlinear Schrödinger equation, revealing damping effects, resonance phenomena, and force components acting on vortex cores.

Contribution

It provides a detailed analysis of vortex dynamics, including the effects of finite core size and external mass, within the nonlinear Schrödinger framework, highlighting damping and resonance behaviors.

Findings

Bare vortex motion is damped at all frequencies.

Finite core exhibits a single resonant frequency.

Fluid forces include dissipative and Magnus components at low frequencies.

Abstract

The dynamics of a two-dimensional vortex are analyzed within the framework of the nonlinear Schrodinger equation. Both a bare vortex and a vortex with an external mass trapped in a finite-sized core are considered. The bare vortex motion is found to be damped at all frequencies, while the finite core has a single resonant frequency. The force exerted by the fluid on the finite core can be expressed as a sum of dissipative and Magnus forces for sufficiently low frequencies, even when the core is small.