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

Michael Edgeworth McIntyre

In revision for the Journal of Fluid Mechanics


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 local recoil from the Stokes-drift-mediated Craik-Leibovich force on a classical vortex, which occurs when a wavetrain overlaps the vortex core. This local recoil corresponds 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 only relevant wave-refraction property is the Aharonov-Bohm topological phase jump. In most cases, other wave-refraction properties are also relevant and have comparable importance.

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 Ursell `anti-Stokes flow'.

This has turned into quite an epic since the original submission to the Journal of Fluid Mechanics on 11 May 2018. The paper has undergone two major revisions, and was sent back to the journal on 3 March and 25 July 2019. I do think, however, that the readability of the paper has been enormously improved. The current preprint incorporates the very latest corrections and clarifications and I am very grateful indeed to the referees, and to other colleagues, for their many comments and suggestions.


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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 9 Aug 2018
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