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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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References

Arendt, S. 1993a On the dynamical buoyancy of vortices. Astrophys. J. 412, 664–674.Google Scholar
Arendt, S. 1993b Vorticity in stratified fluids I: general formulation. Geophys. Astrophys. Fluid Dyn. 68, 59–83.Google Scholar
Arendt, S. 1993c Vorticity in stratified fluids II: finite cross section tubes and rings. Geophys. Astrophys. Fluid Dyn. 70, 161–193.Google Scholar
Bray, R. J., Loughhead, R. E. & Durrant, C. J. 1984 The Solar Granulation. Cambridge University Press.
Cattaneo, F., Brummel, N. H., Toomre, J., Malagoli, A. & Hurlburt, N. E. 1992 Turbulent compressible convection. Astrophys. J. 370, 282–294.Google Scholar
Hurlburt, N. E., Toomre, J. & Massaguer, J. M. 1984 Two-dimensional compressible convection extending over multiple scale heights. Astrophys. J. 282, 557–573.Google Scholar
Low, B. C. 1994 Time-dependent inviscid vortices in global self-similar expansion. Phys. Fluids A 6, 253–262.Google Scholar
Moffatt, H. K. 1969 The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117–129.Google Scholar
Parker, E. N. 1991 Dynamical buoyancy of hydrodynamic eddies. Astrophys. J. 380, 251–255.Google Scholar
Prendergast, K. H. 1956 The equilibrium of a self-gravitating incompressible fluid sphere with a magnetic field. I. Astrophys. J. 123, 498–507.Google Scholar
Stein, R. & Nordlund, A. 1989 Topology of convection beneath the solar surface. Astrophys. J. (Lett.) 342, L95–L98.Google Scholar
Zel'dovich, Ya. B. & Raizer, Yu. P. 1968 Elements of Gasdynamics and the Classical Theory of Shock Waves. Academic.