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A conjecture on the stability and mixing of non-parallel shear flows

Published online by Cambridge University Press:  12 April 2006

E. W. Graham
E. W. Graham
Affiliation:
Graham Associates, Shaw Island, Washington 98286
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Abstract

Non-parallel shear flows of an inviscid, incompressible, density-stratified fluid are considered. The stability is studied in terms of the possibility of complete mixing within a horizontal layer of given thickness. It is assumed that the energy interchange between the mixed region and the external fluid can be neglected. It is also assumed that the required turbulent energy is greater than the energy needed to invert the region to be mixed. The term ‘stable’ as used here means that the kinetic energy released by making the velocity constant over the layer thickness is not sufficient to provide the required turbulent energy for that layer thickness.

If each horizontal fluid plane has a translational velocity of the same magnitude and shear is produced by rotation of the velocity vector with increasing height, then ‘stability’ increases strongly with increasing layer thickness.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 4 , 29 August 1978 , pp. 785 - 788
Copyright
© 1978 Cambridge University Press

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References

Howard, L. N. 1961 J. Fluid Mech. 10, 509.
Miles, J. W. 1961 J. Fluid Mech. 10, 496.
Taylor, G. I. 1931 Proc. Roy. Soc. A 132, 499.
Yih, C.-S. 1965 Dynamics of Nonhomogeneous Fluids. Macmillan.
Yih, C.-S. 1974 In Nonlinear Waves (ed. Leibovich & Seebass), p. 263. Cornell University Press.