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On the stability of fine-scaled turbulent free shear flows

Published online by Cambridge University Press:  19 April 2006

Hartmut H. Legner  and
Michael L. Finson
Hartmut H. Legner
Affiliation:
Avco Everett Research Laboratory, Inc., Everett, Massachusetts Present address: Physical Sciences Inc., Woburn, Massachusetts.
Michael L. Finson
Affiliation:
Avco Everett Research Laboratory, Inc., Everett, Massachusetts Present address: Physical Sciences Inc., Woburn, Massachusetts.
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Abstract

A theoretical model has been developed to investigate the stability of a disturbance in an incompressible turbulent shear flow dominated by turbulence scales that are small with respect to the cross-stream dimension of the flow. The approach utilizes the ‘phase average’ concept to derive the differential equations governing the mechanics of a potential flow disturbance. Turbulence closure is effected at second order. The result is an Orr–Sommerfeld-type equation with complications introduced by the turbulence model. Integration of the linear eigenvalue problem for a wake disturbance leads to the result that the critical eddy-viscosity-based Reynolds number is markedly increased by decreasing the turbulence scale. The viscoelastic behaviour of background turbulence, further complicated by the effects of mean shear, appears to provide stabilization and is discussed in some detail.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 2 , 25 September 1980 , pp. 303 - 319
Copyright
© 1980 Cambridge University Press

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