Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-24T23:36:39.402Z Has data issue: false hasContentIssue false
  • English
  • Français

On the rapid rotation of a massive sphere in a monatomic gas

Published online by Cambridge University Press:  29 March 2006

M. R. Foster
M. R. Foster
Affiliation:
Department of Aeronautical and Astronautical Engineering, The Ohio State University, Columbus
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the rapid rotation, in the sense of large Reynolds number ε−1, of a gravitating solid sphere in a monatomic gas. The flow is characterized by a thin boundary layer on the sphere and a thin, swirling, buoyant, radial jet in the equatorial plane. When the Prandtl number σ is of order unity, the boundary layer and jet are to first order uncoupled from the outer flow. For sufficiently small Prandtl number (which may be interpreted as approximating an optically thick radiating gas), the outer flow is boundary-layer driven. The parameter boundary between these two dissimilar steady states is σ = O(ε⅙).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 64 , Issue 1 , 3 June 1974 , pp. 17 - 31
Copyright
© 1974 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Banks W. H. H.1965 J. Mech. Appl. Math. 18, 443.
Chapman, S. & Cowling T. B.1952 Mathematical Theory of Non-uniform Gases. Cam-bridge University Press.
Cole J. D.1968 Perturbation Methods in Applied Mathematics. Blaisdell.
Foster M. R.1970 Studies in Appl. Math. 49, 259.
Foster M. R.1972 Phys. Fluids, 15, 2079.
Fox J.1964 N.A.S.A. Tech. Note, TND-2491.
Friedman A.1964 Partial Differential Equations of Parabolic Type. Prentice-Hall.
Howarth L.1951 Phil. Mag. 42, 1308.
Jeffreys, H. & Jeffreys B. S.1956 Methods of Mathematical Physics, 3rd edn. Cambridge University Press.
Lagerstrom P.1964 Lamina flow theory. In Theory of Laminar Flows (ed. F. K. Moore). Princeton University Press.
Manohar R.1967 Z. angew. Math. Phys. 18, 320.
Nigam S. D.1954 Z. angew. Math. Phys. 5, 151.
Singh S. M.1970 Phys. Fluids, 13, 2453.
Squire H. B.1955 In 50 Jahre Grenzschichtforschung (ed. Gortler & Tollmien), p. 47.
Stewartson K.1958 In Grenzschichtforschung, I UTAM Symposium, p. 57.
Stewartson K.1964 The Theory of Laminar Boundary Layers in Compressible Fluids. Oxford University Press.