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Further experiments on the evolution of turbulent stresses and scales in uniformly sheared turbulence

Published online by Cambridge University Press:  26 April 2006

S. Tavoularis  and
U. Karnik
S. Tavoularis
Affiliation:
Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada KIN 6N5
U. Karnik
Affiliation:
Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada KIN 6N5
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Abstract

Measurements of the Reynolds stresses, integral lengthscales and Taylor microscales are reported for several cases of uniformly sheared turbulent flows with shear values in a range substantially wider than those of previous measurements. It is shown that such flows demonstrate a self-preserving structure, in which the dimensionless Reynolds stress ratios and the dissipation over production ratio, ε/P, remain essentially constant. Flows with sufficiently large $k_{\rm s} = (1/\overline{U_{\rm c}}){\rm d}\overline{U_1}dx_2$ have exponentially growing stresses and ε/P ≈ 0.68; a linear relationship between the coefficient in the exponentiallaw and ks is shown to be compatible with measurements having ks > 3. The possibility of a self-preserving structure with asymptotically constant stresses and ε/P ≈ 1.0 is also compatible with measurements, corresponding to flows with small values of ks. The integral lengthscales appear to grow according to a power law with an exponent of about 0.8, independent of the mean shear, while the Taylor microscales, in general, approach constant values. Various attempts to scale the stresses and to predict their evolution are discussed and the applicability of Hasen's theory is scrutinized. Finally, an ‘exact’ expression for the pressure-strain rate covariance is derived and compared to some popular models.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989 , pp. 457 - 478
Copyright
© 1989 Cambridge University Press

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