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Stability of plane parallel flows of electrically conducting fluids

Published online by Cambridge University Press:  24 October 2008

D. H. Michael
D. H. Michael
Affiliation:
Gonville and Caius CollegeCambridge
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Extract

The ordinary theory of stability of plane parallel flows is considerably simplified by a result due to Squire (2) which says that if a velocity profile becomes unstable to a small three-dimensional disturbance at a given Reynolds number, then it will become unstable to a small two-dimensional disturbance at a lower Reynolds number. This result enables us to restrict investigation of the stability to the cases of two-dimensional disturbances.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 1 , January 1953 , pp. 166 - 168
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Batchelor, G. K.Proc. roy. Soc. A, 201 (1950), 405.Google Scholar
(2)Squire, H. B.Proc. roy. Soc. A, 142 (1933), 621.Google Scholar