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The stability of free boundary layers between two uniform streams

Published online by Cambridge University Press:  28 March 2006

T. Tatsumi  and
K. Gotoh
T. Tatsumi
Affiliation:
Department of Physics, Faculty of Science, University of Kyoto, Japan
K. Gotoh
Affiliation:
Department of Physics, Faculty of Science, University of Kyoto, Japan
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Abstract

Hydrodynamic stability of free boundary-layer flows is treated in general. It is found that the situations at low Reynolds numbers are universal for all velocity profiles of free boundary-layer type. Curves of constant amplification are calculated as far as O(R3). In particular, the asymptotic form of the neutral curves for R [eDot ] 0 is found to be α = R/(4√3), so that the critical Reynolds numbers of these flows are identically zero. The phase velocity of the disturbance is also found to be zero, for all disturbances, up to the second approximation.

A method of normalizing the velocity profiles is suggested, and existing results for the stability of various profiles at large Reynolds numbers are discussed from a new point of view.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 7 , Issue 3 , March 1960 , pp. 433 - 441
Copyright
© 1960 Cambridge University Press

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References

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Howard, L. N. 1959 J. Math. Phys. 37, 283.
Lessen, M. 1950 Rep. Nat. Adv. Comm. Aero., Wash. no. 979.
Squire, H. B. 1933 Proc. Roy. Soc. A, 142, 621.
Tatsumi, T. & Kakutani, T. 1958 J. Fluid Mech. 4, 261.