Wave-vortex interactions in the nonlinear schrödinger equation

Yuan Guo, Oliver Buhler

Research output: Contribution to journalArticle

Abstract

This is a theoretical study of wave-vortex interaction effects in the two-dimensional nonlinear Schr̈odinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wave-vortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wave-vortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.

Original languageEnglish (US)
Article number027105
JournalPhysics of Fluids
Volume26
Issue number2
DOIs
StatePublished - Feb 21 2014

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Nonlinear equations
nonlinear equations
Vortex flow
vortices
interactions
Ray tracing
ray tracing
Scattering
refracted waves
Schrodinger equation
Refraction
scattering
condensates
refraction
perturbation

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Wave-vortex interactions in the nonlinear schrödinger equation. / Guo, Yuan; Buhler, Oliver.

In: Physics of Fluids, Vol. 26, No. 2, 027105, 21.02.2014.

Research output: Contribution to journalArticle

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