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Stochastic estimation of organized turbulent structure: homogeneous shear flow

Published online by Cambridge University Press:  21 April 2006

Ronald J. Adrian  and
Parviz Moin
Ronald J. Adrian
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801, USA
Parviz Moin
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford CA 94305 USA and NASA Ames Research Center, Moffett Field, CA 94035, USA
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Abstract

The large-scale organized structures of turbulent flow can be characterized quantitatively by a conditional eddy, given the local kinematic state of the flow as specified by the conditional average of u(x’, t) given the velocity and the deformation tensor at a point x: 〈u(x’, t)|u(x, t), d(x, t)〉. By means of linear mean-square stochastic estimation, 〈u’|u, d〉 is approximated in terms of the two-point spatial correlation tensor, and the conditional eddy is evaluated for arbitrary values of u(x, t) and d(x, t), permitting study of the turbulent field for a wide range of local kinematic states. The linear estimate is applied to homogeneous turbulent shear flow data generated by direct numerical simulation. The joint velocity-deformation probability density function is used to obtain conditions corresponding to those events that contribute most to the Reynolds shear stress. The primary contributions to the second-quadrant and fourth-quadrant Reynolds-stress events in homogeneous shear flow come from flow induced through the ‘legs’ and close to the ‘heads’ of upright and inverted ‘hairpins’, respectively.

The equation governing the joint probability density function of fu,d (u, d) is derived. It is shown that this equation contains 〈u’/u, d〉 and that the equations for second-order closure can be derived from it. Closure requires approximation of 〈u’/u, d〉.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 190 , May 1988 , pp. 531 - 559
Copyright
© 1988 Cambridge University Press

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References

Adrian, R. J. 1975 On the role of conditional averages in turbulence theory. In Proc. Fourth Biennial Symp. on Turbulence in Liquids, Sept. 1975. University of Missouri-Rolla. Also in Turbulence in Liquids (1977), p. 323. Science.
Adrian, R. J. 1978 Structural information obtained from analysis using conditional vector events: A potential tool for the study of coherent structures. In Coherent Structure of Turbulent Boundary Layers (ed. C. R. Smith & D. E. Abbott), pp. 416–421. Lehigh Univ., Bethlehem, PA.
Adrian, R. J. 1979 Conditional eddies in isotropic turbulence. Phys. Fluids 22, 2065.Google Scholar
Adrian, R. J., Jones, B. G. & Hassan, Y. A. R. 1979 Conditional Eddies in Turbulent Pipe Flow. 8 mm film. University of Illinois, Urbana.
Antonia, R. A. 1981 Conditional sampling in turbulence measurement. Ann. Rev. Fluid Mech. 13, 131.Google Scholar
Bakewell, H. P. & Lumley, J. L. 1967 Viscous sublayer and adjacent wall region in turbulent pipe flow. Phys. Fluids 10, 1880.Google Scholar
Blackwelder, R. F. & Kaplan, R. E. 1976 On the wall structure of the turbulent boundary layer. J. Fluid Mech. 76, 89.Google Scholar
Bradshaw, P. & Koh, Y. M. 1981 A note on Poisson's equation for pressure in a turbulent flow. Phys. Fluids 24, 777.Google Scholar
Cantwell, B. 1981 Organized motion in turbulent flow, Ann. Rev. Fluid Mech. 13, 457.Google Scholar
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 Experiments on nearly homogeneous shear flow. J. Fluid Mech. 41, 81.Google Scholar
Chang, P., Adrian, R. J. & Jones, B. G. 1985 Fluctuating pressure and velocity fields in the near field of a round jet. Theor. and Appl. Mech. Dept, University of Illinois, Rep. 475. UILU-ENG 85-6006.
Ditter, J. L. 1987 Stochastic estimation of eddies conditioned on local kinematics: isotropic turbulence. M.S. thesis, Dept of Theor. and Appl. Mech., University of Illinois, Urbana, Illinois.
Falco. R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids, 20, S124.Google Scholar
Hassan, Y. A. R. 1980 Experimental and modeling studies of two-point stochastic structure in turbulent pipe flow. Ph.D. Thesis, Nuclear Engr. Prog., University of Illinois, Urbana.
Hassan, Y. A. R., Jones, B. G. & Adrian, R. J. 1987 Two-point stochastic structure in turbulent pipe flow. Nuclear Thermal-Hydraulics Rep. 2. UILU-ENG, 87-5302, University of Illinois, Urbana, IL.
Hussain, A. K. M. F. 1983 Coherent structures - reality and myth. Phys. Fluids 26, 2816.Google Scholar
Kim, J. & Moin, P. 1986 The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields. J. Fluid Mech. 162, 339.Google Scholar
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic.
Lumley, J. L. 1981 Coherent structures in turbulence. In Transition and Turbulence (ed. R. E. Meyer), pp. 215–241. Academic.
Lundgren, T. S. 1967 Distribution functions in the statistical theory of turbulence. Phys. Fluids 10, 969.Google Scholar
Moin, P. 1984 Probing turbulence via large eddy simulation. AIAA Paper 84–0174.
Moin, P. & Kim, J. 1985 The structure of the vorticity field in turbulent channel flow. Part 1. Analysis of instantaneous fields and statistical correlations. J. Fluid Mech. 155, 441.Google Scholar
Moin, P., Leonard, A. & Kim, J. 1986 Evolution of a curved vortex filament into a vortex ring. Phys. Fluids 29, 955.Google Scholar
Nithianandan, C. K. 1980 Fluctuating velocity pressure field structure in a round jet turbulent mixing region. Ph.D. Thesis, Nuclear Engr. Prog., University of Illinois, Urbana, IL.
Nithianandan, C. K., Jones, B. G. & Adrian, R. J. 1987 Turbulent velocity pressure field structures in an axisymmetric mixing layer. Nuclear Thermal Hydraulics Rep. 1. UILU-ENG 87–5301, University of Illinois, Urbana, IL.
Papoulis, A. 1984 Probability, Random Variables and Stochastic Theory, 2nd Edn, McGraw-Hill.
Payne, F. R. & Lumley, J. L. 1967 Large eddy structure of the turbulent wake behind a circular cylinder. Phys. Fluids 10, S194.Google Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA TM 81315.
Rogers, M. M. & Moin, P. 1987 The structure of the vorticity field in homogeneous turbulent flows, J. Fluid Mech. 176, 33.Google Scholar
Theodorsen, T. 1952 Mechanism of turbulence. In Proc. 2nd Midwestern Conf. on Fluid Mech. Ohio State University, Columbus, Ohio.
Tung, A. T. C. 1982 Properties of conditional eddies in free shear flows. Ph.D. Thesis, Dept. of Theor. and Appl. Mech., University of Illinois, Urbana, IL.
Tung, T. C. & Adrian, R. J. 1980 Higher-order estimates of conditional eddies in isotropic turbulence. Phys. Fluids 23, 1469.Google Scholar
Tung, A. T. C., Adrian, R. J. & Jones, B. G. 1987 Theor. and Appl. Mechanics Rep. 483, UILU-ENG 87-6001, University of Illinois, Urbana, IL.
Willmarth, W. W. 1978 Survey of multiple sensor measurements and correlations in boundary layers. In Coherent Structure of Turbulent Boundary Layers (ed. C. R. Smith & D. E. Abbott), pp. 130–167. AFOSR/Lehigh University Workshop, Dept Mech. Engng & Mech., Bethlehem, PA.
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65.Google Scholar