Abstract
A study is made of over-reflection of acoustic-gravity waves incident upon a magnetic shear layer in an isothermal compressible electrically conducting fluid in the presence of an external magnetic field. The reflection and transmission coefficients of hydromagnetic acoustic-gravity waves incident upon magnetic shear layer are calculated. The invariance of wave-action flux is used to investigate the properties of reflection, transmission and absorption of the waves incident upon the shear layer, and then to discuss how these properties depend on the wavelength, length scale of the shear layers, and the ratio of the flow speed and phase speed of the waves. Special attention is given to the relationship between the wave-amplification and critical-level behaviour. It is shown that there exists a critical level within the shear layer and the wave incident upon the shear layer is over-reflected, that is, more energy is reflected back towards the source than was originally emitted. The mechanism of the over-reflection (or wave amplification) is due to the fact that the excess reflected energy is extracted by the wave from the external magnetic field. It is also found that the absence of critical level within the shear layer leads to non-amplification of waves. For the case of very large vertical wavelength of waves, the coefficients of incident, reflected and transmitted energy are calculated. In this limiting situation, the wave is neither amplified nor absorbed by the shear layer. Finally, it is shown that resonance occurs at a particular value of the phase velocity of the wave.
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References
Acheson D J, The critical level for hydromagnetic waves in a rotating fluid.J. Fluid. Mech. 53 (1972) 401–415
Acheson D J, On over-reflexion,J. Fluid. Mech. 77 (1976) 433–472
Booker J R and Britherton F P, The critical layer for internal gravity waves in a shear layer.J. Fluid. Mech. 27 (1967) 513–539
Breeding R J, A nonlinear investigation of critical levels for internal atmospheric gravity waves.J. Fluid. Mech. 50 (1971) 545–563
Chandrasekhar S,Hydrodynamic and hydromagnetic stability (Oxford: University Press) (1961)
Eltayeb I A and McKenzie J F, Critical-level behaviour and wave amplification of a gravity wave incident upon a shear layer,J. Fluid. Mech. 72 (1975) 661–671
Jonos W L, Reflexion and stability of waves in stably stratified fluids with shear flow: a numerical study,J. Fluid. Mech. 34 (1968) 604–624
Jones W L and Houghton D D, The coupling of momentum between internal gravity waves and mean flows: A numerical study,J. Atmos. Sci. 28 (1971) 604–608
McKenzie J F, Reflection and amplification of acoustic-gravity waves at a density and velocity discontinuity,J. Geophys. Res. 77 (1972) 2915–2926
Kandaswamy P and Palaniswamy E M, Over reflexion of a hydromagnetic gravity wave incident upon a magnetic shear layer.Proc. Indian Natn. Sci. Acad. 53 (N.4) (1987) 499–505
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Kandaswamy, P. On over-reflection of acoustic-gravity waves incident upon a magnetic shear layer in a compressible fluid. Proc. Indian Acad. Sci. (Math. Sci.) 105, 105–122 (1995). https://doi.org/10.1007/BF02840594
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DOI: https://doi.org/10.1007/BF02840594