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Some vorticity theorems and conservation laws for non-barotropic fluids

Published online by Cambridge University Press:  20 April 2006

S. D. Mobbs
S. D. Mobbs
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds LS2 9JT and Geophysical Fluid Dynamics Laboratory, Meteorological Office, Bracknell, Berkshire RG12 2SZ
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Abstract

Some theorems concerning the vorticity in barotropic flows of perfect fluids are generalized for non-barotropic flows. The generalization involves replacing the velocity in certain parts of the equations by a time-dependent quantity which is a function of the velocity and thermodynamic properties of the fluid. Results which are generalized include Kelvin's circulation theorem and conservation laws for potential vorticity and helicity. It is shown how the results can be further generalized to include dissipative effects. The possibility of using some of the results in deriving a complete set of Lagrangian conservation laws for perfect fluids is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 108 , July 1981 , pp. 475 - 483
Copyright
© 1981 Cambridge University Press

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References

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