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On over-reflexion

Published online by Cambridge University Press:  11 April 2006

D. J. Acheson
D. J. Acheson
Affiliation:
Mathematical Institute, University of Oxford Present address: St Catherine'e College, Oxford.
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Abstract

Reflexion coefficients greater than unity have now been predicted for a variety of different systems involving waves propagating towards a shear layer, but almost invariably only in regions of parameter space for which the layer exhibits Kelvin-Helmholtz instability. This paper contains a study of two examples in which, for appropriate parameter values, there are no such instabilities to obscure (or even prevent) the ‘over-reflexion’ of an incident wave, namely (a) hydro-magnetic internal gravity waves meeting a vortex-current sheet in a stratified fluid and (b) magneto-acoustic waves meeting a vortex sheet in a compressible fluid. In the former case the energetic aspects of over-reflexion are examined in detail, thus displaying the way in which the excess reflected energy is extracted from the mean motion and the sense in which the transmitted wave may be viewed, by analogy with certain concepts employed in plasma physics, as a carrier of so-called ‘negative energy’.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 77 , Issue 3 , 8 October 1976 , pp. 433 - 472
Copyright
© 1976 Cambridge University Press

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