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The linear stability of viscous compressible plane Couette flow

  • W. Glatzel (a1)
Abstract

The structure of normal modes in viscous compressible plane Couette flow is investigated. The spectrum is found to consist of two types of modes: the viscous modes, which obtain finite phase velocities by the mechanism of mode pairing; and the sonic modes, whose phase velocity becomes distorted in the supersonic regime. This leads to mode crossings which unfold, depending on the type of crossing modes, either into purely sonic or viscous-sonic instability bands. The latter provide a new example for viscous instability. Both mode pairing of viscous modes and distortion of the phase velocity of sonic modes is caused by the shear. Critical Reynolds numbers for the instabilities are derived.

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© 1989 Cambridge University Press
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Blumen, W., Drazin, P. G. & Billings, D., 1975 J. Fluid Mech. 71, 305.
Cairns, R. A.: 1979 J. Fluid Mech. 92, 1.
Case, K. M.: 1961 J. Fluid Mech. 10, 420.
Davey, A.: 1977 J. Comp. Phys. 24, 331.
Drazin, P. G. & Davey, A., 1977 J. Fluid Mech. 82, 255.
Drazin, P. G. & Reid, W. H., 1981 Hydrodynamic Stability. Cambridge University Press.
Drury, L. O'C. 1985 Mon. Not. R. Astr. Soc. 217, 821.
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.
Glatzel, W.: 1987a Mon. Not. R. Astr. Soc. 225, 227.
Glatzel, W.: 1987b Mon. Not. R. Astr. Soc. 228, 77.
Glatzel, W.: 1988 Mon. Not. R. Astr. Soc. 231, 795.
Goldreich, P., Goodman, J. & Narayan, R., 1986 Mon. Not. R. Astr. Soc. 221, 339.
Landau, L.: 1946 J. Phys. USSR 10, 25.
Lin, C. C.: 1961 J. Fluid Mech. 10, 430.
Narayan, R., Goldreich, P. & Goodman, J., 1987 Mon. Not. R. Astr. Soc. 228, 1.
Orszag, S. A.: 1971 J. Fluid Mech. 50, 689.
Papaloizou, J. C. B. & Pringle, J. E. 1984 Mon. Not. R. Astr. Soc. 208, 721.
Papaloizou, J. C. B. & Pringle, J. E. 1985 Mon. Not. R. Astr. Soc. 213, 799.
Papaloizou, J. C. B. & Pringle, J. E. 1987 Mon. Not. R. Astr. Soc. 225, 267.
Ray, T. P.: 1982 Mon. Not. R. Astr. Soc. 198, 617.
Scott, M. R.: 1973 J. Comp. Phys. 12, 334.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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