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An energy principle for dissipative fluids

Published online by Cambridge University Press:  29 March 2006

E. M. Barston
E. M. Barston
Affiliation:
Courant Institute of Mathematical Sciences, New York University
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Abstract

An energy principle is presented which gives necessary and sufficient conditions for exponential stability for a large class of dissipative systems. The maximal growth rate Ω of an unstable system is shown to be the least upper bound of a certain functional, giving a variational expression for Ω. These results are used to discuss the gravitational stability of incompressible viscous fluids and resistive magnetofluids in arbitrary geometries.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 1 , 4 June 1970 , pp. 97 - 109
Copyright
© 1970 Cambridge University Press

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References

Barston, E. M. 1969a Phys. Fluids, 12, 2162.
Barston, E. M. 1969b Comm. Pure and Appl. Math. 22, 62.
Barston, E. M. 1970 Phys. Fluids. (To be published.)
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Turnbull, R. J. & Melcher, J. R. 1969 Phys. Fluids, 12, 1160.