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

Published online by Cambridge University Press:  24 October 2019

Michael Edgeworth McIntyre Open the ORCID record for Michael Edgeworth McIntyre [Opens in a new window]
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Abstract

Three examples of non-dissipative yet cumulative interaction between a single wavetrain and a single vortex are analysed, with a focus on effective recoil forces, local and remote. Local recoil occurs when the wavetrain overlaps the vortex core. All three examples comply with the pseudomomentum rule. The first two examples are two-dimensional and non-rotating (shallow water or gas dynamical). The third is rotating, with deep-water gravity waves inducing an Ursell ‘anti-Stokes flow’. The Froude or Mach number, and the Rossby number in the third example, are assumed small. Remote recoil is all or part of the interaction in all three examples, except in one special limiting case. That case is found only within a severely restricted parameter regime and is the only case in which, exceptionally, the effective recoil force can be regarded as purely local and identifiable with the celebrated Craik–Leibovich vortex force – which corresponds, in the quantum fluids literature, to the Iordanskii force due to a phonon current incident on a vortex. Another peculiarity of that exceptional case is that the only significant wave refraction effect is the Aharonov–Bohm topological phase jump.

JFM classification

Vortex Flows: Vortex dynamics Waves/Free-surface Flows: Wave scattering
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 182 - 217
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Copyright
© 2019 Cambridge University Press 

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References

Aharonov, Y. & Bohm, D. 1959 Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491.Google Scholar
Andrews, D. G. & McIntyre, M. E. 1978 An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 89, 609–646.Google Scholar
Baldwin, M. P., Gray, L. J., Dunkerton, T. J., Hamilton, K., Haynes, P. H., Randel, W. J., Holton, J. R., Alexander, M. J., Hirota, I., Horinouchi, T. et al. 2001 The quasi-biennial oscillation. Rev. Geophys. 39, 179–229.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Belyaev, I. V. & Kopiev, V. F. 2008 On the statement of the problem of sound scattering by a cylindrical vortex. Acoust. Phys. 54, 603–614.Google Scholar
Berloff, N. G. 2004 Padé approximations of solitary wave solutions of the Gross–Pitaevskii equation. J. Phys. A 37, 1617–1632.Google Scholar
Berry, M. V., Chambers, R. G., Large, M. D., Upstill, C. & Walmsley, J. C. 1980 Wavefront dislocations in the Aharonov–Bohm effect and its water wave analogue. Eur. J. Phys. 1, 154–162.Google Scholar
Bretherton, F. P. 1969 On the mean motion induced by internal gravity waves. J. Fluid Mech. 36, 785–803.Google Scholar
Bretherton, F. P. & Garrett, C. J. R. 1968 Wavetrains in inhomogeneous moving media. Proc. R. Soc. Lond. A 302, 529–554.Google Scholar
Brillouin, L. 1936 On radiation pressures and stresses (in French). Rev. Acoust. 5, 99–111.Google Scholar
Bühler, O. 2014 Waves and Mean Flows, 2nd edn. Cambridge University Press.Google Scholar
Bühler, O. & McIntyre, M. E. 2003 Remote recoil: a new wave–mean interaction effect. J. Fluid Mech. 492, 207–230.Google Scholar
Bühler, O. & McIntyre, M. E. 2005 Wave capture and wave–vortex duality. J. Fluid Mech. 534, 67–95.Google Scholar
Coste, C., Lund, F. & Umeki, M. 1999 Scattering of dislocated wave fronts by vertical vorticity and the Aharonov–Bohm effect. I. Shallow water. Phys. Rev. E 60, 4908–4916.Google Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73, 401–426.Google Scholar
Dritschel, D. G. & McIntyre, M. E. 2008 Multiple jets as PV staircases: the Phillips effect and the resilience of eddy-transport barriers. J. Atmos. Sci. 65, 855–874.Google Scholar
Ford, R. & Llewellyn Smith, S. G. 1999 Scattering of acoustic waves by a vortex. J. Fluid Mech. 386, 305–328.Google Scholar
Fritts, D. C. 1984 Gravity wave saturation in the middle atmosphere: a review of theory and observations. Rev. Geophys. Space Phys. 22, 275–308.Google Scholar
Garcia, R. R., Smith, A. K., Kinnison, D. E., de la Cámara, Á. & Murphy, D. J. 2017 Modification of the gravity wave parameterization in the Whole Atmosphere Community Climate Model: motivation and results. J. Atmos. Sci. 74, 275–291.Google Scholar
Guo, Y. & Bühler, O. 2014 Wave–vortex interactions in the nonlinear Schrödinger equation. Phys. Fluids 26, 027105.Google Scholar
Haney, S. & Young, W. R. 2017 Radiation of internal waves from groups of surface gravity waves. J. Fluid Mech. 829, 280–303.Google Scholar
Hasselmann, K. 1970 Wave driven inertial oscillations. Geophys. Fluid Dyn. 1, 463–502.Google Scholar
Holton, J. R., Haynes, P. H., McIntyre, M. E., Douglass, A. R., Rood, R. B. & Pfister, L. 1995 Stratosphere–troposphere exchange. Rev. Geophys. 33, 403–439.Google Scholar
Humbert, T., Aumaître, S. & Gallet, B. 2017 Wave-induced vortex recoil and nonlinear refraction. Phys. Rev. Fluids 2, 094701, 1–14.Google Scholar
Kida, S. 1981 Motion of an elliptic vortex in a uniform shear flow. J. Phys. Soc. Japan 50, 3517–3520.Google Scholar
Lane, E. M., Restrepo, J. M. & McWilliams, J. C. 2007 Wave–current interaction: a comparison of radiation-stress and vortex-force representations. J. Phys. Oceanogr. 37, 1122–1141.Google Scholar
Leibovich, S. 1980 On wave–current interaction theories of Langmuir circulations. J. Fluid Mech. 99, 715–724.Google Scholar
Lelong, M.-P. & Riley, J. J. 1991 Internal wave-vortical mode interactions in strongly stratified flows. J. Fluid Mech. 232, 1–19.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1964 Radiation stress in water waves; a physical discussion, with applications. Deep-Sea Res. 11, 529–562.Google Scholar
McComas, C. H. & Bretherton, F. P. 1977 Resonant interaction of oceanic internal waves. J. Geophys. Res. 82, 1397–1412.Google Scholar
McIntyre, M. E. 1973 Mean motions and impulse of a guided internal gravity wave packet. J. Fluid Mech. 60, 801–811.Google Scholar
McIntyre, M. E. 1981 On the ‘wave momentum’ myth. J. Fluid Mech. 106, 331–347.Google Scholar
McIntyre, M. E. 1988 A note on the divergence effect and the Lagrangian-mean surface elevation in water waves. J. Fluid Mech. 189, 235–242.Google Scholar
McIntyre, M. E. 2017 On multi-level thinking and scientific understanding. Adv. Atmos. Sci. 34, 1150–1158.Google Scholar
McIntyre, M. E. & Palmer, T. N. 1985 A note on the general concept of wave breaking for Rossby and gravity waves. Pure Appl. Geophys. 123, 964–975.Google Scholar
Pollard, R. T. 1970 Surface waves with rotation: an exact solution. J. Geophys. Res. 75, 5895–5898.Google Scholar
Sakov, P. V. 1993 Sound scattering by a vortex filament. Acoust. Phys. 39, 280–282.Google Scholar
Sonin, E. 1997 Magnus force in superfluids and superconductors. Phys. Rev. B 55, 485–501.Google Scholar
Stone, M. 2000a Iordanskii force and the gravitational Aharonov–Bohm effect for a moving vortex. Phys. Rev. B 61, 11780–11786.Google Scholar
Stone, M. 2000b Acoustic energy and momentum in a moving medium. Phys. Rev. E 62, 1341–1350.Google Scholar
Thomas, J. 2017 New model for acoustic waves propagating through a vortical flow. J. Fluid Mech. 823, 658–674.Google Scholar
Thomas, J., Bühler, O. & Smith, K. S. 2018 Wave-induced mean flows in rotating shallow water with uniform potential vorticity. J. Fluid Mech. 839, 408–429.Google Scholar
Thomas, J. & Yamada, R. 2019 Geophysical turbulence dominated by inertia–gravity waves. J. Fluid Mech. 875, 71–100.Google Scholar
Ursell, F. 1950 On the theoretical form of ocean swell on a rotating earth. Mon. Not. R. Astron. Soc. Geophys. Suppl. 6, 1–8.Google Scholar
Wagner, G. L. & Young, W. R. 2015 Available potential vorticity and wave-averaged quasi-geostrophic flow. J. Fluid Mech. 785, 401–424.Google Scholar
Wallace, J. M. & Holton, J. R. 1968 A diagnostic numerical model of the quasi-biennial oscillation. J. Atmos. Sci. 25, 280–292.Google Scholar
Ward, M. L. & Dewar, W. K. 2010 Scattering of gravity waves by potential vorticity in a shallow-water fluid. J. Fluid Mech. 663, 478–506.Google Scholar
Wexler, C. & Thouless, D. J. 1998 Scattering of phonons by a vortex in a superfluid. Phys. Rev. B 58, R8897(R).Google Scholar