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The stability of a thermally radiating stratified shear layer

Published online by Cambridge University Press:  29 March 2006

Joseph J. Dudis
Joseph J. Dudis
Affiliation:
Research Institute for Advanced Studies, Martin Marietta Corporation, Baltimore, Maryland
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Abstract

A linear stability analysis is applied to a stratified, thermally radiating, un-bounded shear layer. Temperature disturbances are assumed to be optically thin. Both viscous and inviscid neutral stability boundaries are determined numerically for hyperbolic-tangent mean velocity and potential-temperature profiles. For these profiles, long-wavelength disturbances are completely destabilized (the critical Richardson number Ric → ∞ as the wavenumber k → 0) in the inviscid limit. A similar situation is found for the case of discontinuous step-function profiles. However, in contrast to the non-radiating problem, the functional form of the neutral stability boundary is not the same for both the continuous and discontinuous profiles in the limit k → 0. Application of the viscous results to the atmospheres of the earth and Venus yield critical Richardson numbers in excess of ¼.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 1 , 20 March 1973 , pp. 81 - 96
Copyright
© 1973 Cambridge University Press

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