Scattering and leapfrogging of vortex rings in a superfluid

The dynamics of vortex ring pairs in the homogeneous nonlinear Schrödinger equation is studied. The generation of numerically exact solutions of traveling vortex rings is described and their translational velocity compared to revised analytic approximations. The scattering behavior of co-axial vorte...

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Bibliographic Details
Published in:Physics of fluids (1994) 2014-09, Vol.26 (9)
Main Authors: Caplan, R. M., Talley, J. D., Carretero-González, R., Kevrekidis, P. G.
Format: Article
Language:English
Subjects:
Biot-Savart law
Collision dynamics
Computational fluid dynamics
Dependence
Equations of motion
Fluid dynamics
Fluids
Mathematical models
Physics
Scattering
Schrodinger equation
Superfluidity
Vortex rings
Vortices
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Summary:The dynamics of vortex ring pairs in the homogeneous nonlinear Schrödinger equation is studied. The generation of numerically exact solutions of traveling vortex rings is described and their translational velocity compared to revised analytic approximations. The scattering behavior of co-axial vortex rings with opposite charge undergoing collision is numerically investigated for different scattering angles yielding a surprisingly simple result for its dependence as a function of the initial vortex ring parameters. We also study the leapfrogging behavior of co-axial rings with equal charge and compare it with the dynamics stemming from a modified version of the reduced equations of motion from a classical fluid model derived using the Biot-Savart law.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.4894745