Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-11T06:17:37.910Z Has data issue: false hasContentIssue false
  • English
  • Français

On waves in a thin rotating spherical shell of slightly viscous fluid

Published online by Cambridge University Press:  26 February 2010

I. C. Walton
I. C. Walton
Affiliation:
Department of Mathematics, Imperial College, London..
Get access

Abstract

Stewartson and Rickard [1] have shown that Rossby waves in thin spherical shells of an inviscid fluid contain singularities at the critical circles. These may be removed by introducing another wave containing square-root singularities in the velocity on the characteristics which by reflection touch the inner boundary at the critical circles. Stewartson and Walton [2] continued this wave all round the shell and showed it to be an inertial wave. Here we consider the effect of a weak kinematic viscosity v on these waves.

Type
Research Article
Information
Mathematika , Volume 22 , Issue 1 , June 1975 , pp. 46 - 59
Copyright
Copyright © University College London 1975

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

1. Stewartson, K. and Rickard, J. A.. J. Fluid Mech., 35 (1969), 759.CrossRefGoogle Scholar
2. Stewartson, K. and Walton, I. C.. To appear in Geophys. Fluid Dynamics., 7.Google Scholar
3. Greenspan, H.. j. Fluid Mech., 21 (1964), 673.Google Scholar
4. Greenspan, H.. j. Fluid Mech., 22 (1965), 449.Google Scholar
5. Greenspan, H. and Howard, L. N., j. Fluid Mech., 17 (1963), 385.Google Scholar
6. Greenspan, H.. Theory of Rotating Fluids (Cambridge University Press, 1968).Google Scholar
7. Aldridgeand, K. and Toomre, J.. J. Fluid Mech., 37 (1969), 307.Google Scholar
8. Wood, W. W.. J. Fluid Mech., 22 (1965), 337.Google Scholar
9. Wood, W. W.. Proc. Roy. Soc. A, 293 (1966), 181.Google Scholar
10. Baines, P. G.. j. Fluid Mech., 30 (1967), 533.Google Scholar
11. Aldridge, K.. Mathematika, 19 (1972), 163.Google Scholar
12. Stern, M. E.. Tellus, 15 (1963), 246.Google Scholar
13. Bretherton, F. P.. Tellus, 16 (1964), 181.Google Scholar
14. Stewartson, K.. Tellus, 23 (1971), 506.Google Scholar
15. Stewartson, K.. Tellus, 24 (1972), 283.Google Scholar
16. Stewartson, K.. j. Fluid Mech., 54 (1972), 749.Google Scholar
17. Israeli, M.. Studies in Appl. Math., 51 (1972), 219.Google Scholar
18. Longuet-Higgins, M. S.. Proc. Roy. Soc. A, 279 (1964), 446.Google Scholar
19. Longuet-Higgins, M. S.. Proc. Roy. Soc. A, 284 (1965), 40.Google Scholar
20. Walton, I. C.. To appear in Proc. Roy. Soc.Google Scholar
21. Phillips, O. M.. Phys. Fluids, 6 (1963), 513.Google Scholar
22. Hide, R. and Stewartson, K.. Rev. Geophys. and Space Phys., 10 (1972), 579.Google Scholar
23. Erdelyi, A.. Higher Transcendental Functions (McGraw-Hill, 1953).Google Scholar
24. Reynolds, A. J.. ZAMP, 13 (1962), 561.Google Scholar
25. Moore, D. W. and Saffman, P. G.. Phil. Trans. Roy. Soc. A, 264 (1969), 597.Google Scholar
26. Stewartson, K.. j. Fluid Mech., 26 (1966), 131.Google Scholar
27. Lindzen, R. S.. Geophys. Fluid Dynamics. 1 (1970), 303.CrossRefGoogle Scholar