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The mixing layer: deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion

Published online by Cambridge University Press:  20 April 2006

G. M. Corcos  and
S. J. Lin
G. M. Corcos
Affiliation:
University of California, Berkeley, CA 94720
S. J. Lin
Affiliation:
University of California, Berkeley, CA 94720 Present address: Scientific Research Associates, Glastonbury, Conn.
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Abstract

Experimental evidence suggests that in the turbulent mixing layer the fundamental mechanism of growth is two-dimensional and little affected by the presence of vigorous three-dimensional motion. To quantify this apparent property and study the growth of streamwise vorticity, we write for the velocity field \[ {\boldmath V}(x, t) = {\boldmath U}(x, z, t) + {\boldmath u}(x, y, z, t), \] where U is two-dimensional and u is three-dimensional. In a first version of the problem U is independent of u, while in the second U is the spanwise average of V. In both cases the equation for u is linearized around U. The equations for U and u are solved simultaneously by a finite-difference calculation starting with a slightly disturbed parallel shear layer.

The solutions provide a detailed description of the growth of the three-dimensional motion. They show that its characteristics are dictated by the distribution of spanwise vorticity which results from roll-up and pairing. Pairing inhibits its growth. The solutions also demonstrate that even when the three-dimensional flow attains large amplitudes it has a negligible effect on the interaction of spanwise vortices and thus on the growth of the layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 139 , February 1984 , pp. 67 - 95
Copyright
© 1984 Cambridge University Press

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