The constitutive relation for the Reynolds stress tensor is considered for turbulence developing in axisymmetric strain fields. It is confirmed that the Reynolds stress tensor is aligned linearly with the mean strain rate. In contrast to the Prandtl-Kolmogorov, hypothesis, the effective viscosity is found to grow in proportion to the anisotropy of turbulence and the length scale based on the magnitude of the mean strain rate. Using invariant theory the effective viscosity is determined for the limiting states of turbulence. Additional analysis of the constitutive relations is supplemented for the dissipation and pressure-strain correlations. It is shown that analytical derivations are in excellent agreement with the data obtained from direct numerical simulations. [S0098-2202(00)02801-7]
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March 2000
Technical Papers
On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence
J. Jovanovic´, Senior Research Scientist,
J. Jovanovic´, Senior Research Scientist
Lehrstuhl fu¨r Stro¨mungsmechanik, Universita¨t Erlangen-Nu¨rnberg, Cauerstrasse 4, D-91058, Germany
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I. Otic´, Ph.D. Student
I. Otic´, Ph.D. Student
Lehrstuhl fu¨r Stro¨mungsmechanik, Universita¨t Erlangen-Nu¨rnberg, Cauerstrasse 4, D-91058, Germany
Search for other works by this author on:
J. Jovanovic´, Senior Research Scientist
Lehrstuhl fu¨r Stro¨mungsmechanik, Universita¨t Erlangen-Nu¨rnberg, Cauerstrasse 4, D-91058, Germany
I. Otic´, Ph.D. Student
Lehrstuhl fu¨r Stro¨mungsmechanik, Universita¨t Erlangen-Nu¨rnberg, Cauerstrasse 4, D-91058, Germany
Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division June 8, 1999; revised manuscript received December 8, 1999. Associate Technical Editor: P. Bradshaw.
J. Fluids Eng. Mar 2000, 122(1): 48-50 (3 pages)
Published Online: December 8, 1999
Article history
Received:
June 8, 1999
Revised:
December 8, 1999
Citation
Jovanovic´, J., and Otic´, I. (December 8, 1999). "On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence ." ASME. J. Fluids Eng. March 2000; 122(1): 48–50. https://doi.org/10.1115/1.483225
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