### 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 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

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

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

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 26, no. 2, 027105. https://doi.org/10.1063/1.4865837

}

TY - JOUR

T1 - Wave-vortex interactions in the nonlinear schrödinger equation

AU - Guo, Yuan

AU - Buhler, Oliver

PY - 2014/2/21

Y1 - 2014/2/21

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84905170059&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905170059&partnerID=8YFLogxK

U2 - 10.1063/1.4865837

DO - 10.1063/1.4865837

M3 - Article

VL - 26

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 2

M1 - 027105

ER -