×

Statistical analysis of the deviation of the Reynolds stress from its eddy-viscosity representation. (English) Zbl 0572.76048

An improvement of the eddy-viscosity representation for Reynolds stress is made from the statistical viewpoint. The Reynolds stress is calculated with the aid of the two-scale direct-interaction formalism, and its deviation from the eddy-viscosity representation is found under general mean flows. This result theoretically elucidates the noncoincidence of the zeros of Reynolds stress and mean strain, which is frequently observed in asymmetric turbulent shear flows.

MSC:

76F10 Shear flows and turbulence
82D15 Statistical mechanics of liquids
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
76D05 Navier-Stokes equations for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] P. Bradshaw, T. Cebeci, and J. H. Whitelaw,Engineering Calculation Methods for Turbulent Flow(Academic, London, 1981). · Zbl 0646.76004
[2] Deardorff, J. Fluid Mech. 41 pp 453– (1970)
[3] Schumann, J. Comput. Phys. 18 pp 376– (1975)
[4] Horiuti, Theor. and Appl. Mech. 31 pp 407– (1982)
[5] Moin, J. Fluid Mech. 118 pp 341– (1982)
[6] M. Ohji,Turbuence, edited by I. Tani (Maruzen, Tokyo, 1979), Chap. 4.
[7] Hanjalić, J. Fluid Mech. 51 pp 301– (1972)
[8] Launder, J. Fluid Mech. 68 pp 537– (1975)
[9] Lumley, Adv. Appl. Mech. 18 pp 123– (1978)
[10] Kraichnan, Phys. Fluids 7 pp 1048– (1964)
[11] Kraichnan, J. Fluid Mech. 5 pp 497– (1959)
[12] Kraichnan, J. Fluid Mech. 83 pp 349– (1977)
[13] A. H. Neyfeh,Perturbation Methods(Wiley, New York, 1973), p. 243.
[14] Yoshizawa, J. Phys. Soc. Jpn. 47 pp 1665– (1979)
[15] Yoshizawa, J. Phys. Soc. Jpn. 51 pp 658– (1982)
[16] Yoshizawa, J. Phys. Soc. Jpn. 51 pp 2326– (1982)
[17] Yoshizawa, Phys. Fluids 25 pp 1532– (1982)
[18] Yoshizawa, J. Phys. Soc. Jpn. 52 pp 1194– (1983)
[19] D. C. Leslie,Developments in the Theory of Turbulence(Clarendon, Oxford, 1973), p. 326. · Zbl 0273.76034
[20] Kraichnan, Phys. Fluids 8 pp 575– (1968)
[21] Kraichnan, Phys. Fluids 9 pp 1728– (1969)
[22] Kraichnan, J. Fluid Mech. 47 pp 513– (1971)
[23] Kraichnan, J. Fluid Mech. 47 pp 525– (1971)
[24] Nakano, Ann. Phys. (USA) 73 pp 326– (1972)
[25] Yoshizawa, J. Phys. Soc. Jpn. 45 pp 1734– (1978)
[26] Kraichnan, J. Atmos. Sci. 33 pp 521– (1976)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.