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On the realizability of pressure–strain closures

Published online by Cambridge University Press:  20 August 2014

Aashwin A. Mishra  and
Sharath S. Girimaji
Aashwin A. Mishra*
Affiliation:
Aerospace Engineering Department, Texas A&M University, College Station, TX 77840, USA
Sharath S. Girimaji
Affiliation:
Aerospace Engineering Department, Texas A&M University, College Station, TX 77840, USA
*
†Email address for correspondence: aashwin@neo.tamu.edu
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Abstract

The realizability condition for statistical models of turbulence is augmented to ensure that not only is the Reynolds stress tensor positive semi-definite, but the process of its evolution is physically attainable as well. The mathematical constraints due to this process realizability requirement on the rapid pressure strain correlation are derived. The resulting constraints reveal important limits on the inter-component energy transfer and the consequent flow stability characteristics, as a function of the mean flow. For planar mean flows, the realizability constraints are most stringent for the case of purely sheared flows rather than elliptic flows. The relationship between the constraints and flow stability is explained. Process realizability leads to closure model guidance not only at the two-component (2C) limit of turbulence (as in the classical realizability approach) but throughout the anisotropy space. Consequently, the domain of validity and applicability of current models can be clearly identified for different mean flows. A simple framework for incorporating these process realizability constraints in model formulation is outlined.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 755 , 25 September 2014 , pp. 535 - 560
Copyright
© 2014 Cambridge University Press 

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References

Cambon, C.1982 Étude spectrale d’un champ turbulent incompressible, soumis à des effets couplés de déformation et de rotation, imposés extérieurement. Thèse de Doctorat d’État, Université de Lyon, France.Google Scholar
Cambon, C. & Jacquin, L. 1989 Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295–317.CrossRefGoogle Scholar
Cambon, C., Jacquin, L. & Lubrano, J. L. 1992 Toward a new Reynolds stress model for rotating turbulent flows. Phys. Fluids 4 (4), 812–824.CrossRefGoogle Scholar
Cambon, C. & Rubinstein, R. 2006 Anisotropic developments for homogeneous shear flows. Phys. Fluids 18, 085106.CrossRefGoogle Scholar
Cambon, C. & Scott, J. F. 1999 Linear and nonlinear models of anisotropic turbulence. Annu. Rev. Fluid Mech. 31 (1), 1–53.CrossRefGoogle Scholar
Crow, S. C. 1968 Viscoelastic properties of fine-grained incompressible turbulence. J. Fluid Mech. 33, 1–20.CrossRefGoogle Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.CrossRefGoogle Scholar
Girimaji, S. S. 2000 Pressure strain correlation modelling of complex turbulent flows. J. Fluid Mech. 422, 91–123.CrossRefGoogle Scholar
Girimaji, S. S. 2004 A new perspective on realizability of turbulence models. J. Fluid Mech. 512, 191–210.CrossRefGoogle Scholar
Hanjalic, K. & Launder, B. 2011 Modelling Turbulence in Engineering and the Environment: Second-Moment Routes to Closure. Cambridge University Press.CrossRefGoogle Scholar
Johansson, A. V. & Hallback, M. 1994 Modeling the rapid pressure–strain in Reynolds stress closures. J. Fluid Mech. 269, 143–168.CrossRefGoogle Scholar
Kassinos, S. C. & Reynolds, W. C.1994 A structure-based model for the rapid distortion of homogeneous turbulence. Report TF 61, Thermosciences Division, Department of Mechanical Engineering, Stanford University.Google Scholar
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68 (03), 537–566.CrossRefGoogle Scholar
Lee, M. J. 1990 Distortion of homogeneous turbulence by axisymmetric strain and dilation. Phys. Fluids A 2, 630–633.CrossRefGoogle Scholar
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123–176.CrossRefGoogle Scholar
Meyer, C. D. 2001 Matrix Analysis and Applied Linear Algebra. Society for Industrial and Applied Mathematics.Google Scholar
Mishra, A. A. & Girimaji, S. S. 2010 Pressure–strain correlation modeling: towards achieving consistency with rapid distrotion theory. Flow Turbul. Combust. 85, 593–619.CrossRefGoogle Scholar
Mishra, A. A. & Girimaji, S. S. 2013 Intercomponent energy transfer in incompressible homogeneous turbulence: multi-point physics and amenability to one-point closures. J. Fluid Mech. 731, 639–681.CrossRefGoogle Scholar
Pope, S. B. 1985 PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Rotta, J. 1951 Statistische Theorie nichthomogener Turbulenz. Z. Phys. 129, 547–572.CrossRefGoogle Scholar
Rubinstein, R. & Girimaji, S. S. 2006 Second moment closure near the two-component limit. J. Fluid Mech. 548 (1), 197–206.CrossRefGoogle Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Salhi, A., Cambon, C. & Speziale, C. G. 1997 Linear stability analysis of plane quadratic flows in a rotating frame with applications to modeling. Phys. Fluids 9 (8), 2300–2309.CrossRefGoogle Scholar
Sambasivam, A., Girimaji, S. S. & Poroseva, S. V. 2004 Realizability of Reynolds stress and rapid pressure strain correlation in turbulence modelling. J. Turbul. 5 (6), 1–22.CrossRefGoogle Scholar
Schumann, U. 1977 Realizability of Reynolds stress turbulence models. J. Fluid Mech. 20, 721–725.Google Scholar
Shih, T. H., Mansour, N. N. & Chen, J. Y.1987 Reynolds stress models of homogeneous turbulence. In Proceedings of the 1987 Summer Program. Center for Turbulence Research, Stanford University.Google Scholar
Shih, T. H., Reynolds, W. C. & Mansour, N. N. 1990 A spectrum model for weakly anisotropic turbulence. Phys. Fluids A 2, 1500–1502.CrossRefGoogle Scholar
Sjogren, T. & Johansson, A. V. 2000 Development and calibration of algebraic nonlinear models for terms in the Reynolds stress transport equations. Phys. Fluids 12 (6), 1554–1572.CrossRefGoogle Scholar
Speziale, C. G., Abid, R. & Durbin, P. A. 1994 On the realizability of Reynolds stress turbulence closures. J. Sci. Comput. 9, 369–403.CrossRefGoogle Scholar
Speziale, C. G. & Durbin, P. A. 1994 Realizability of second-moment closure via stochastic analysis. J. Fluid Mech. 280, 395–407.Google Scholar
Speziale, C. G., Sarkar, S. & Gatski, T. B. 1991 Modelling the pressure strain correlation of turbulence: an invariant dynamical systems approach. J. Fluid Mech. 227, 245–272.CrossRefGoogle Scholar