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

Michael Edgeworth McIntyre

Journal of Fluid Mechanics 881, 182-217 (24 Oct 2019)


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 a vortex core. This local recoil corresponds to the phonon-current-mediated Iordanskii force on a quantum vortex.

It is sometimes taken for granted in the quantum literature that the Iordanskii force is the only recoil force, i.e. that there is no remote recoil. 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 less special circumstances, other wave-refraction properties are also relevant and have comparable importance, as has remote recoil.

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'.

After the original submission to the Journal of Fluid Mechanics on 11 May 2018 the paper underwent two major revisions and was finally published on 24 October 2019. Thanks to the refereeing process, the readability of the paper has been enormously improved. The final pre-publication preprint incorporates the latest corrections and clarifications and I am very grateful indeed to the referees, and to other colleagues, for their many comments and suggestions.

Here is a short version of the paper, summarizing the main results. It is to appear in the proceedings of the 2019 St Andrews conference on Geophysical and Astrophysical Vortex Interactions, in a special issue of Geophysical and Astrophysical Fluid Dynamics.


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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 6 Apr 2020
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