Perturbations of vortex ring pairs

Abstract

We study pairs of co-axial vortex rings starting from the action for a classical bosonic string in a three-form background. We complete earlier work on the phase diagram of classical orbits by explicitly considering the case where the circulations of the two vortex rings are equal and opposite. We then go on to study perturbations, focusing on cases where the relevant four-dimensional transfer matrix splits into two-dimensional blocks. When the circulations of the rings have the same sign, instabilities are mostly limited to wavelengths smaller than a dynamically generated length scale at which single-ring instabilities occur. When the circulations have the opposite sign, larger wavelength instabilities can occur.

62 pages, 21 figures

References in corpus (4)

• Sound-induced vortex interactions in a zero-temperature two-dimensional superfluid
• Scattering and leapfrogging of vortex rings in a superfluid
• The incompressible fluid revisited: vortex-sound interactions
• Quantum vorticity in nature

Cited by in corpus (5)

• Symmetry-breaking instability of leapfrogging vortex rings in a Bose-Einstein condensate
• Vortex lines attached to dark solitons in Bose-Einstein condensates and Boson-Vortex Duality in 3+1 Dimensions
• Three-dimensional stability of leapfrogging quantum vortex rings
• A multipole-expanded effective field theory for vortex ring-sound interactions
• Relativistic two-fluid hydrodynamics with quantized vorticity from the nonlinear Klein-Gordon equation