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Asymmetric wave-stress tensors and wave spin

Published online by Cambridge University Press:  29 March 2006

W. L. Jones
W. L. Jones
Affiliation:
Department of Physics, University of Canterbury, Christchurch, New Zealand
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Abstract

Linearized wave-stress tensors derived from Hamilton's variational principle may be asymmetric. If interpreted as momentum fluxes, they would lead to lack of conservation of orbital angular momentum. It is shown that changes in internal angular momentum or spin of waves and torque coupling to external fields can adequately provide conservation of total angular momentum in such cases, Examples are given for acoustic, internal gravity, Rossby and plasma waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 4 , 22 May 1973 , pp. 737 - 747
Copyright
© 1973 Cambridge University Press

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References

Akhiezer, A. J. & Berestetskii, V. B. 1965 Quantum Electrodynamics, pp. 214–236.
Bogoliubov, N. N. & Shirkov, D. V. 1959 Introduction to the Theory of Quantized Fields, pp. 10–57. Interscience.
Bretherton, F. P. 1969 Momentum transport by gravity waves. Quart. J. Roy. Met. Soc. 95, 213–243.Google Scholar
Bretherton, F. P. & Garrett, C. J. R. 1968 The propagation of wave trains in moving media. Proc. Roy. Soc. A 302, 529–554.Google Scholar
Brillowin, L. 1969 Tensors in Mechanics and Elasticity, pp. 364–398. Academic.
Buchwalder, V. T. 1972 Energy and energy flux in planetary waves. Proc. Roy. Soc. A 328, 37–48.Google Scholar
Crawford, F. S. 1965 Waves (Berkeley Phys Course, vol. 3), pp. 364–366. McGraw-Hill.
Eckart, C. 1963 Some transformations of the hydrodynamic equations. Phys. Fluids, 6, 1037–1041.Google Scholar
Garrett, C. J. R. 1968 On the interaction between internal gravity waves and a shear flow. J. Fluid Meeh. 34, 711–720.Google Scholar
Hayes, W. D. 1970 Conservation of action and modal wave action. Proc. Roy. Soc. A 320, 209–226.Google Scholar
Jones, W. L. 1971 Energy-momentum tensor for linearized waves in Material media. Rev. Geophys. & Space Phys. 9, 917–952.Google Scholar
Longuet-Higgins, M. S. 1964 On group velocity and energy flux in planetary wave motions. Deep Sea Res. 11, 35–42.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1969 Radiation stresses in water waves; a physical discussion with applications. Deep Sea Res. 11, 529–562.Google Scholar
Mclennan, J. A. 1966 Symmetry of the stress tensor. Physsica, 32, 689–692.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics, vol. 1. McGraw-Hill.
Sturrock, P. A. 1961 Energy-momentum tensor for plane waves, Phys. Rev. 121, 18–19.Google Scholar
Sturrock, P. A. 1962 Energy and momentum in the theory of waves in plasmas. In Plasma Hydromagnetics (ed. D. Bershsder), pp. 47–57. Stanford University Press.