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A transformation for non-homentropic flows, with an application to large-amplitude motion in the atmosphere

Published online by Cambridge University Press:  28 March 2006

Chia-Shun Yih
Chia-Shun Yih
Affiliation:
Department of Engineering Mechanics, University of Michigan
At Department of Applied Mathematics and Theoretical Physics, University of Cambridge, during 1959–60.
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Abstract

A transformation has been found which reduces steady non-homentropic flows of a compressible fluid to homentropic flows, provided diffusive and gravity effect are negligible. With this transformation, the equation governing steady two-dimensional flows of a compressible fluid with variable entropy in a gravitational field is derived, which is then applied to the study of atmospheric waves in the lee of mountains. The corresponding equation governing swirling axisymmetric flows is also given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 9 , Issue 1 , September 1960 , pp. 68 - 80
Copyright
© 1960 Cambridge University Press

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References

Batchelor, G. K. 1953 The conditions for dynamic similarity of motions of a frictionless perfect-gas atmosphere. Quant. J. Roy. Soc. Met., 79, 224–35.Google Scholar
Crapper, G. D. 1959 A three-dimensional solution for waves in the lee of mountains. J. Fluid Mech., 6, 51–76.Google Scholar
Leipmann, H. W. & Puckett, A. E. 1947 Introduction to Aerodynamics of a Compressible Fluid. New York: Wiley and Sons.
Yih, C.-S. 1960a Gravity waves in a stratified fluid. J. Fluid Mech. 8, 481–508.Google Scholar
Yih, C.-S. 1960b Exact solutions for steady two-dimensional flows of a stratified fluid. J. Fluid Mech. 9, 161–174.Google Scholar