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On the non-existence of steady confined flows of a barotropic fluid in a gravitational field

Published online by Cambridge University Press:  26 April 2006

Steve Arendt
Steve Arendt
Affiliation:
High Altitude Observatory & Advanced Study Program, National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307, USA
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Abstract

We consider a semi-infinite (bounded above) plane-parallel layer of barotropic fluid in a constant gravitational field. We present a proof that flows of such a fluid cannot be time-independent in a reference frame wherein the flow's velocity field falls off asymptotically faster than the inverse of the radial distance, R. This includes all flows of finite kinetic energy as such flows must fall off faster than R−1.5. The unsteadiness is due in part to the dynamical expansion of a compressible fluid in motion; this expansion leads to a density deficit so that in the presence of gravity the flow rises buoyantly and cannot be steady in time. The non-existence of certain classes of steady uniform-fluid flows is also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 271 , 25 July 1994 , pp. 341 - 350
Copyright
© 1994 Cambridge University Press

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