Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-19T06:18:18.807Z Has data issue: false hasContentIssue false

On the ‘wave momentum’ myth

Published online by Cambridge University Press:  20 April 2006

M. E. Mcintyre
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge

Abstract

Controversies over ‘the momentum’ of waves have repeatedly wasted the time of physicists for over half a century. The persistence of the controversies is surprising, since regardless of whether classical or quantum dynamics is used the facts of the matter are simple and unequivocal, are well checked by laboratory experiment, are clearly explained in several published papers, and on the theoretical side can easily be verified by straightforward calculations. They are illustrated here by some simple, classical examples involving acoustic and gravity waves.

Type
Research Article
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andrews, D. G. 1974 Mean flows forced by waves in stratified and rotating fluids. Ph.D. thesis, University of Cambridge.
Andrews, D. G. & McIntyre, M. E. 1978a An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 89, 609646.Google Scholar
Andrews, D. G. & McIntyre, M. E. 1978b On wave-action and its relatives. J. Fluid Mech. 89, 647664.Google Scholar
Ashkin, A. & Dziedzic, J. M. 1973 Radiation pressure on a free liquid surface. Phys. Rev. Lett. 30, 139142.Google Scholar
Baines, P. G. 1979 Observations of stratified flow over two-dimensional obstacles in fluid of finite depth. Tellus 31, 351371.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press, 615 pp.
Benjamin, T. B. 1970 Upstream influence. J. Fluid Mech. 40, 4979.Google Scholar
Bondi, H. 1967 Assumption and Myth in Physical Theory. Cambridge University Press, 88 pp.
Bretherton, F. P. 1969 On the mean motion induced by internal gravity waves. J. Fluid Mech. 36, 785803.Google Scholar
Bretherton, F. P. 1971 The general linearised theory of wave propagation, 6. Lectures in Applied Mathematics (American Math. Soc.), 13, 61102.Google Scholar
Bretherton, F. P. & Garrett, C. J. R. 1968 Wavetrains in inhomogeneous moving media. Proc. Roy. Soc. A 302, 529554.Google Scholar
Brillouin, L. 1925 On radiation stresses (in French). Annales de Physique 4, 528586.Google Scholar
Carroll, L. 1971 Through the Looking-Glass. London: Macmillan.
Dewar, R. L. 1970 Interaction between hydromagnetic waves and a time-dependent inhomogeneous medium. Phys. Fluids 13, 27102720.Google Scholar
Dewar, R. L. 1977 Energy-momentum tensors for dispersive electromagnetic waves. Aust. J. Phys. 30, 533575.Google Scholar
Dysthe, K. B. 1979 Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. Proc. Roy. Soc. London A 369, 105114.Google Scholar
Eckart, C. 1948 Vortices and streams caused by sound waves. Phys. Rev. 73, 6876.Google Scholar
Fubini-Ghiron, E. 1937 La tension de radiation acoustique et les ondes de grande amplitude. Rev. d'Acoustique 6, 69.Google Scholar
Gordon, J. P. 1973 Radiation forces and momenta in dielectric media. Phys. Rev. A 8, 1421.Google Scholar
Hasegawa, T. & Yosioka, J. 1975 Acoustic radiation force on fused silica spheres and intensity determination. J. Acoust. Soc. Amer. 58, 581585.Google Scholar
Hayes, W. D. 1970 Conservation of action and modal wave action. Proc. Roy. Soc. A 320, 187208.Google Scholar
Hertz, G. & Mende, H. 1939 Der Schallstrahlungsdruck in Flüssigkeiten. Z. Phys. 114, 354367.Google Scholar
Hollweg, J. V. 1978 Some physical processes in the solar wind. Revs Geophys. & Space Phys. 16, 689720.Google Scholar
Israel, W. 1977 Relativistic effects in dielectrics: an experimental decision between Abraham and Minkowski? Phys. Ljtlt. 67 B, 125128.Google Scholar
Jacques, S. A. 1977 Momentum and energy transport by waves in the solar atmosphere and solar wind. Astrophys. J 215, 942951.Google Scholar
Jacques, S. A. 1978 Solar wind models with Alfvén waves. Astrophys. J. 226, 632649.Google Scholar
Jones, R. V. & Leslie, B. 1978 The measurement of optical radiation pressure in dispersive media. Proc. Roy. Soc. A 360, 347363.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press, 738 pp.
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, 1st Engl. ed. Pergamon, 536 pp.
Landau, L. D. & Lifshitz, E. M. 1975 The Classical Theory of Fields, 4th revised Engl. ed. Pergamon, 402 pp.
Lightill, M. J. 1978 Acoustic streaming. J. Sound Vib. 61, 391418.Google Scholar
Longuet-Higgins, M. S. 1977 The mean forces exerted by waves on floating or submerged bodies with applications to sand bars and wave power machines. Proc. Roy. Soc. Lond. A 352, 463480.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1962 Radiation stress and mass transport in gravity waves, with application to 'surf beats’. J. Fluid Mech. 13, 481504.Google Scholar
Markham, J. J. 1952 Second-order acoustic fields: streaming with viscosity and relaxation. Phys. Rev. 86, 497502.Google Scholar
McIntyre, M. E. 1972 On Long's hypothesis of no upstream influence in uniformly stratified or rotating flow. J. Fluid Mech. 52, 209243.Google Scholar
McIntyre, M. E. 1973 Mean motions and impulse of a guided internal gravity wave packet. J. Fluid Mech. 60, 801811.Google Scholar
McIntyre, M. E. 1981 Waves and Mean Flows. Monograph in preparation.
Moffett, M. B., Westervelt, P. J. & Beyer, R. T. 1971 Large-amplitude pulse propagation—a transient effect. II. J. Acoust. Soc. Amer. 49, 339343.Google Scholar
Nyborg, W. L. 1953 Acoustic streaming due to attenuated plane waves. J. Acoust. Soc. Amer. 25, 6875.Google Scholar
Peierls, R. E. 1976 The momentum of light in a refracting medium. Proc. Roy. Soc. A 347, 475491.Google Scholar
Peierls, R. E. 1979 Surprises in Theoretical Physics. Princeton University Press, 166 pp.
Penfield, P. & Haus, H. A. 1966 Hamilton's principle for electromagnetic fields. Phys. Fluids 9, 11951204.Google Scholar
Post, E. J. 1953 Radiation pressure and dispersion. J. Acoust. Soc. Amer. 25, 5560.Google Scholar
Plumb, R. A. & McEwan, A. D. 1978 The instability of a forced standing wave in a viscous, stratified fluid: a laboratory analogue of the quasi-biennial oscillation. J. Atmos. Sci. 35, 18271839.2.0.CO;2>CrossRefGoogle Scholar
Rayleigh, Lord 1902 On the pressure of vibrations. Phil. Mag. 3, 338346 [also Sci. Papers 5, 41–48].Google Scholar
Rayleigh, Lord 1905 On the momentum and pressure of gaseous vibrations, and on the connexion with the virial theorem. Phil. Mag. 10, 364374. [Scientific Papers 5, 262–271.]Google Scholar
Robinson, F. N. H. 1975 Electromagnetic stress and momentum in matter. Physics Reports (vidc. C of Physics Letters) 16, 314354.Google Scholar
Rooney, J. A. 1973a Does radiation pressure depend on B/A? J. Ajtlust. Soc. Amer. 54, 429430. [Note that B/A means 2(log c)/(log).]Google Scholar
Rooney, J. A. 1973b Determination of acoustic power outputs in the microwatt-milliwatt range. Ultraound in Med. & Biol. 1, 1316.Google Scholar
Sturrock, P. A. 1962a Field-theory analogs of the Lagrange and Poincaré invariants. J. Mathematical Physics 3, 4350. (VI, VII.)Google Scholar
Sturrock, P. A. 1962b Energy and momentum in the theory of waves in plasmas. Plasma Hydromagnetics (Lockheed Symposium, ed. D. Bershader), pp. 4757. Stanford U.P. (equation (4.7)).
Westervelt, P. J. 1953 The theory of steady rotational flow generated by a sound field. J. Acoust. Soc. Amer. 25, 6067.Google Scholar
Westervelt, P. J. 1957 Acoustic radiation pressure. J. Acoust. Soc. Amer. 29, 2629.Google Scholar
Westervelt, P. J. 1963 Parametric acoustic array. J. Acoust. Soc. Amer. 35, 535537.Google Scholar
Westervelt, P. J. 1977 Sound. McGraw Hill Yearbook Science & Technology (ed. D. N. Lapedes) 16, 389390.
Whitham, G. B. 1965 A general approach to linear and nonlinear dispersive waves using a Lagrangian. J. Fluid Mech. 22, 273283.Google Scholar
Whitham, G. B. 1970 Two-timing, variational principles and waves. J. Fluid Mech. 44, 373395.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley, Interscience. 636 pp.