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On the stability of stratified viscous plane Couette flow. Part 1. Constant buoyancy frequency

Published online by Cambridge University Press:  11 April 2006

A. Davey  and
W. H. Reid
A. Davey
Affiliation:
School of Mathematics, University of Newcastle upon Tyne, England
W. H. Reid
Affiliation:
Department of Mathematics, University of Chicago, Illinois 60637
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Abstract

This paper is concerned with a general study of the modal structure for stratified viscous plane Couette flow with a constant buoyancy frequency. When the overall Richardson number Ri is zero, the velocity and temperature modes are distinct but as Ri is increased there is an intricate interaction between them. Some simple analytical results are obtained for large and small values of the Reynolds number and more detailed results are given for $Ri = 0, \frac{1}{8}, \frac{1}{4}$ and ½. The present theory would appear to be reasonably complete for 0 [les ] Ri [les ] ¼; for Ri > ¼, however, an important open question concerns the relationship between the limiting form of the viscous modes as the Reynolds number tends to infinity and the spectrum of internal gravity waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 3 , 2 May 1977 , pp. 509 - 525
Copyright
© 1977 Cambridge University Press

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References

Baldwin, P. & Roberts, P. H. 1970 Mathematika 17, 102.
Conte, S. D. 1966 Siam Rev. 8, 309.
Drazin, P. G. & Howard, L. N. 1966 Adv. in Appl. Mech. 9, 1–89.
Eliassen, A., Høiland, E. & Riis, E. 1953 Two-Dimensional Perturbation of a Flow with Constant Shear of a Stratified Fluid. Institute for Weather and Climate Research, Norwegian Academy of Sciences and Letters, publ. no. 1.
Gage, K. S. & Reid, W. H. 1968 J. Fluid Mech. 33, 21.
Gallagher, A. P. 1974 J. Fluid Mech. 65, 29.
Gallagher, A. P. & Mercer, A. McD. 1962 J. Fluid Mech. 13, 91.
Gallagher, A. P. & Mercer, A. McD. 1964 J. Fluid Mech. 18, 350.
Godunov, S. 1961 Usp. Mat. Nauk 16, 171.
Grohne, D. 1954 Z. angew. Math. Mech. 34, 344. (Trans. N.A.C.A. Tech. Memo. no. 1417.)
Høiland, E. 1953 Geofys. Publ. 18, no. 10.
Howard, L. N. 1961 J. Fluid Mech. 10, 509.
Howard, L. N. & Maslowe, S. A. 1973 Boundary-Layer Met. 4, 511.
Hughes, T. H. & Reid, W. H. 1968 Phil. Trans. Roy. Soc. A 263, 57.
Huppert, H. E. 1973 J. Fluid Mech. 57, 361.
Koppel, D. 1964 J. Math. Phys. 5, 963.
Miles, J. W. 1961 J. Fluid Mech. 10, 496.
Reid, W. H. 1972 Studies in Appl. Math. 51, 341.
Reid, W. H. 1974 Studies in Appl. Math. 53, 91.
Tveitereid, M. 1974 Z. angew. Math. Mech. 54, 533.
Wasow, W. 1953 J. Res. Nat. Bur. Stand. 51, 195.
Wazzan, A. R., Okamura, T. T. & Smith, A. M. O. 1968 Douglas Aircraft Co. Rep. DAC-67086.
Zondek, B. & Thomas, L. H. 1953 Phys. Rev. (2) 90, 738.