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Stability analysis adjacent to neutral solutions of the Taylor–Goldstein equation when Howard's formula breaks down

Published online by Cambridge University Press:  20 April 2006

L. Engevik ,
P. M. Haugan  and
S. Klemp
L. Engevik
Affiliation:
Department of Mathematics, University of Bergen, Norway
P. M. Haugan
Affiliation:
Department of Mathematics, University of Bergen, Norway Permanent address: Norsk Hydro, P.O. Box 4313, 5013 Bergen, Norway.
S. Klemp
Affiliation:
Department of Mathematics, University of Bergen, Norway Permanent address: Statoil, P.O. Box 300, 4001 Stavanger, Norway.
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Abstract

The Taylor–Goldstein problem for stability of stratified shear flows of inviscid Boussinesq fluids is treated. Perturbation of a known neutral curve is used to obtain the stability characteristics in the neighbourhood of the curve. In the cases that are studied Howard's technique for perturbing neutral modes breaks down. This is related to the vanishing of a coefficient in the expansion of the dispersion relation near the neutral curve. In that case instability may occur on either side of the neutral curve. Examples are used to illustrate how unexpected behaviour arises, such as instability on both sides of a neutral curve.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 159 , October 1985 , pp. 347 - 358
Copyright
© 1985 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Baldwin, P. & Roberts, P. H. 1970 Mathematica 17, 102.
Banks, W. H. H. & Drazin, P. G. 1973 J. Fluid Mech. 58, 763.
Charney, J. G. 1947 J. Meteor. 4, 135.
Drazin, P. G. & Howard, L. N. 1961 J. Engng Mech. Div ASCE 87, 101.
Drazin, P. G. & Howard, L. N. 1963 Trans. ASCE 128, 849.
Drazin, P. G. & Howard, L. N. 1966 Adv. Appl. Mech. 9, 1.
Engevik, L. 1973a Rep. 43, Dept Appl. Maths, Univ. Bergen.
Engevik, L. 1973b Acta Mech. 18, 285.
Engevik, L. 1974 Acta Mech. 19, 169.
Engevik, L. 1975 Acta Mech. 21, 159.
Engevik, L. 1978 J. Fluid Mech. 86, 395.
Engevik, L. 1982 J. Fluid Mech. 117, 457.
Holmboe, J. 1962 Geofys. Publ. 24, 67.
Høiland, E. & Riis, E. 1968 Geofys. Publ. 27, 1.
Howard, L. N. 1963 J. Fluid Mech. 16, 333.
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.
Miles, J. W. 1963 J. Fluid Mech. 16, 209.
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.