Decay of helical Kelvin waves on a quantum vortex filament
We study the dynamics of helical Kelvin waves moving along a quantum vortex filament driven by a normal fluid flow. We employ the vector form of the quantum local induction approximation (LIA) due to Schwarz. For an isolated filament, this is an adequate approximation to the full HallVinenBekarevichKhalatnikov dynamics. The motion of such Kelvin waves is both translational (along the quantum vortex filament) and rotational (in the plane orthogonal to the reference axis). We first present an exact closed form solution for the motion of these Kelvin waves in the case of a constant amplitude helix. Such solutions exist for a critical wave number and correspond exactly to the DonnellyGlaberson instability, so perturbations of such solutions either decay to line filaments or blowup. This leads us to consider helical Kelvin waves which decay to line filaments. Unlike in the case of constant amplitude helical solutions, the dynamics are much more complicated for the decaying helical waves, owing to the fact that the rate of decay of the helical perturbations along the vortex filament is not constant in time. We give an analytical and numerical description of the motion of decaying helical Kelvin waves, from which we are able to ascertainmore »
 Authors:

^{[1]}
 Department of Mathematics, University of Central Florida, Orlando, Florida 328161364 (United States)
 Publication Date:
 OSTI Identifier:
 22311238
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Fluids (1994); Journal Volume: 26; Journal Issue: 7; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; FILAMENTS; FLUID FLOW; INSTABILITY; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PERTURBATION THEORY; VELOCITY; VORTICES