Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-21T08:21:37.506Z Has data issue: false hasContentIssue false
  • English
  • Français

ThickE¼ Stewartson layers in a rapidly rotating gas

Published online by Cambridge University Press:  21 April 2006

Lennart S. Hultgren  and
Fritz H. Bark
Lennart S. Hultgren
Affiliation:
Department of Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL 60616
Fritz H. Bark
Affiliation:
Department of Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of circumferential curvature and strong density variation on E¼ Stewartson layers are investigated. The solution of the third-order ordinary differential equation found to govern the flow is obtained by numerical integration for layers extending in the positive radial direction and in terms of a Frobenius-series solution for layers extending in the opposite direction. Due to the variation of the basic density field, the E¼ layer is compressed in the positive radial direction. E1/4 layers extending in the negative radial direction are likely to extend fully to the axis of symmetry because of the density variation and, consequently, a distinction in terms of a geostrophic flow and an E¼ layer flow cannot be made. Curvature effects are found to play a significant role in this case. A simple case of driving by a differential rotation of part of the horizontal boundaries is examined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 169 , August 1986 , pp. 307 - 322
Copyright
© 1986 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

Bark, F. H. & Bark, T. H. 1976 On vertical boundary layers in a rapidly rotating gas. J. Fluid Mech. 78, 749.Google Scholar
Bark, F. H. & Bark, T. H. 1979 On axially antisymmetric geostrophic flows in rapidly rotating gases. J. Méc. 18, 47.Google Scholar
Bark, F. H. & Hultgren, L. S. 1979 On the effects of thermally insulating boundaries on geostrophic flows in rapidly rotating gases. J. Fluid Mech. 95, 97.Google Scholar
Bark, F. H. & Meijer, P. S. 1982 Effects of circumferential curvature and radial stratification on Stewartson E1/3 layers in a rapidly rotating gas. FFA Tech. Note 1982-44.
Collatz, L. 1960 The Numerical Treatment of Differential Equations, 3rd edn. Springer.
Durivault, J. & Louvet, P. 1976 Etude de la couche de Stewartson compressible dans une centrifugeuse à contre-courant thermique. C. R. Acad. Sci. Paris 283 (B), 79.Google Scholar
Durivault, J., Louvet, P., Rouvillos, G. & Soubbaramayer, X. 1976 Thermal counter current and isotope separation in a centrifuge with an isothermal side wall. C. R. Acad. Sci. Paris 283 (B), 17.Google Scholar
Hashimoto, K. 1977 Flows in a rapidly rotating cylinder. Ph.D. thesis, Kyoto University, Japan.
Howard, L. N. 1970 Rotating and stratified flows. In Mathematical Problems in the Geophysical Sciences. Lectures in Applied Mathematics, vol. 13, p. 121. American Mathematics Society.
Hultgren, L. S., Meijer, P. S. & Bark, F. H. 1981 On axisymmetric time-dependent source flows in a rapidly rotating gas. J. Méc. 20, 135.Google Scholar
Louvet, P. & Durivault, J. 1976 Paper presented at the Symposium on Singular Perturbation Problems and Boundary-layer Theory, Lyon, France.
Mikami, H. 1973 Thermally induced flow in gas centrifuge. J. Nucl. Sci. Tech. 10, 580.Google Scholar
Nakayama, H. M. & Usui, S. 1974 Flow in a rotating cylinder of a gas centrifuge. J. Nucl. Sci. Tech. 11, 242.Google Scholar
Olander, D. R. 1978 The gas centrifuge. Sci. Am. 239 (2), 27.Google Scholar
Sakurai, T. & Matsuda, T. 1974 Gasdynamics of a centrifugal machine. J. Fluid Mech. 62, 727.Google Scholar
Wood, H. G., Jordan, J. A. & Gunzburger, M. D. 1984 The effects of curvature on the flow field in rapidly rotating gas centrifuges. J. Fluid Mech. 140, 373.
Wood, H. G. & Morton, J. B. 1980 Onsager's pancake approximation for the fluid dynamics of a gas centrifuge. J. Fluid Mech. 101, 1.Google Scholar