### 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 language | English (US) |
---|---|

Article number | 027105 |

Journal | Physics of Fluids |

Volume | 26 |

Issue number | 2 |

DOIs | |

State | Published - Feb 21 2014 |

### ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes

## Fingerprint Dive into the research topics of 'Wave-vortex interactions in the nonlinear schrödinger equation'. Together they form a unique fingerprint.

## Cite this

*Physics of Fluids*,

*26*(2), [027105]. https://doi.org/10.1063/1.4865837