Wave-vortex interactions, remote recoil, the Aharonov-Bohm effect and the Craik-Leibovich equation

Michael Edgeworth McIntyre

This paper studies three of the simplest possible examples of wave-vortex interaction and the surprising things that can happen -- surprising, at least, from some perspectives. The first two examples are in inertial reference frames and the third is in a rapidly-rotating frame, with geophysical contexts in mind. Wave-vortex interactions are fundamental both in geophysical fluid dynamics and in quantum superfluid dynamics. Attention is focused on the remote-recoil effects that are generic in problems of this kind, and in almost all cases act in addition to, or in place of, the Stokes-drift-mediated Craik-Leibovich force on a classical vortex, corresponding to the phonon-current-mediated Iordanskii force on a quantum vortex.

It is sometimes assumed in the quantum literature that remote recoil is always negligible, i.e. that the Iordanskii force is the only recoil force. In the problems studied this is shown to be correct only in an extremely special and restricted set of circumstances. It happens that these are the same special circumstances in which the Aharonov-Bohm effect is the only relevant wave-refraction property.

Remote recoil is also, contrary to an impression one might get from the geophysical/oceanographic literature, able to survive rapid rotation despite the phenomenon known as the `anti-Stokes flow'.  Here's the current preprint, submitted to the Journal of Fluid Mechanics on 19 Nov 2019 after extensive revision in the light of the referees' and other colleagues' comments, plus a few more corrections and clarifications.

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Michael Edgeworth McIntyre (mem at damtp.cam.ac.uk), DAMTP, University of Cambridge, Silver Street, Cambridge CB3 9EW

This page first posted 14 May 2018; last updated 3 March 2018
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