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Propagation of Alfvén-gravitational waves in a stratified perfectly conducting flow with transverse magnetic field

Published online by Cambridge University Press:  29 March 2006

N. Rudraiah  and
M. Venkatachalappa
N. Rudraiah
Affiliation:
Department of Mathematics (Post-Graduate Studies), University Visvesvaraya College of Engineering, Bangalore University, Bangalore
M. Venkatachalappa
Affiliation:
Department of Mathematics (Post-Graduate Studies), University Visvesvaraya College of Engineering, Bangalore University, Bangalore
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Abstract

Alfvén-gravitational waves are found to propagate in a Boussinesq, inviscid, adiabatic, perfectly conducting fluid in the presence of a uniform transverse magnetic field in which the mean horizontal velocity U is independent of vertical height z. The governing wave equation is a fourth-order ordinary differential equation with constant coefficients and is not singular when the Doppler-shifted frequency Ωd = 0, but is singular when the Alfvén frequency ΩA = 0.If Ω2d < Ω2A the waves are attenuated by a factor exp − [2ΩA(N2−Ω2d)½−Ω2d + Ω2A]z, which tends to zero as z → ∞. This attenuation is similar to the viscous attenuation of waves discussed by Hughes & Young (1966). The interpretation of upward and downward propagation of waves is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 54 , Issue 2 , 25 July 1972 , pp. 209 - 215
Copyright
© 1972 Cambridge University Press

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References

Booker, J. R. & Bretherton, F. 1967 J. Fluid Mech. 27, 513.
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Hughes, W. F. & Young, F. J. 1966 The Electromagnetodynamics of Fluids. Wiley.
MacDonald, J. F. 1962 N.A.S.A. Tech. Rep. R-143.
Rudraiah, N. & Venkatachalappa, M. 1972 J. Fluid Mech. 54, 217.
Yanowitch, M. 1967 J. Fluid Mech. 29, 209.