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Similarity of steady stratified flows

Published online by Cambridge University Press:  20 April 2006

Chia-Shun Yih
Chia-Shun Yih
Affiliation:
The University of Michigan, Ann Arber, Michigan 48109
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Abstract

Steady flows of an incompressible, inviscid, and non-diffusive fluid of variable density in a gravitational field are first considered. By a transformation it is shown conclusively that there are infinitely many flows with the same flow pattern, provided the density gradients of these flows at any section (e.g. far upstream) differ only by a multiplicative constant. These flows have identical local internal Froude numbers at all corresponding points of the flows and, hence, identical local Richardson numbers. They are therefore dynamically similar. Every time a solution for one stratification is obtained, one has in fact obtained the solutions for infinitely many stratifications.

The creation of vorticity in steady stratified flows is then examined, and it is shown that this creation can be divided into two parts, one part being entirely due to the inertial effect and the other originating from the gravity effect of density variation.

Finally, compressibility is considered and the results on similarity of stratified flows and on vorticity and circulation are extended to apply to steady flows of gases stratified in entropy.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 108 , July 1981 , pp. 241 - 246
Copyright
© 1981 Cambridge University Press

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References

Yih, C.-S. 1958 On the flow of a stratified fluid. Proc. 3rd U.S. Nat. Congr. Appl. Mech., pp. 857–861.Google Scholar
Yih, C.-S. 1960 A transformation for non-homentropic flows, with an application to largeamplitude motion in the atmosphere. J. Fluid Mech. 9, 68–80.Google Scholar
Yih, C.-S. 1980 Stratified Flows. Academic.