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Intercomponent energy transfer in incompressible homogeneous turbulence: multi-point physics and amenability to one-point closures

Published online by Cambridge University Press:  28 August 2013

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: [email protected]
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Abstract

Intercomponent energy transfer (IET) is a direct consequence of the incompressibility-preserving action of pressure. This action of pressure is inherently non-local, and consequently its modelling must address multi-point physics. However, in second moment closures, pragmatism mandates a single-point closure model for the pressure–strain correlation, that is, the source of IET. In this study, we perform a rapid distortion analysis to demonstrate that for a given mean-flow gradient, IET is strongly dependent on fluctuation modes and critically influences the flow stability, asymptotic states and their bifurcations. The inference is that multi-point physics must be characterized and appropriately incorporated into pressure–strain correlation closures. To this end, we analyse and categorize various multi-point characteristics such as: (i) the fluctuation mode wavevector dynamics; (ii) the spectral space topology of dominant modes; and (iii) the range of IET behaviour and statistically most likely (SML) outcomes. Thence, this characterization is used to examine the validity and limitations of current one-point closures and to propose directions for improving the fidelity of future models.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence theory Turbulent Flows: Rotating turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , pp. 639 - 681
Copyright
©2013 Cambridge University Press 

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References

Bayly, B. J. 1986 Three-dimensional instability of elliptical flow. Phys. Rev. Lett. 57 (17), 2160–2163.CrossRefGoogle ScholarPubMed
Blaisdell, G. A. & Shariff, K. 1994 Homogeneous turbulence subjected to mean flow with elliptic streamlines. In Studying Turbulence Using Numerical Simulation Databases: Proceedings of the 1994 Summer Program, pp. 355–371.Google Scholar
Blaisdell, G. A. & Shariff, K. 1994 Simulation and modeling of the elliptic streamline flow. In Studying Turbulence Using Numerical Simulation Databases. V: Proceedings of the 1994 Summer Program, vol. 1, pp. 433–446.Google Scholar
Brasseur, J. G. & Lee, M. J. 1987 Local structure of intercomponent energy transfer in homogeneous turbulent shear flow. In Studying Turbulence Using Numerical Simulation Databases, vol. 1, pp. 165–178.Google Scholar
Brasseur, J. G. & Lee, M. J. 1988 pressure–strain-rate events in homogeneous turbulent shear flow. pp. 143–156.Google Scholar
Cambon, C. 1990 Single and Double Point Modeling of Homogeneous Turbulence. NASA Annual Research Briefs.Google Scholar
Cambon, C., Benoit, J. P., Shao, L. & Jacquin, L. 1994 Stability analysis and large-eddy simulation of rotating turbulence with organized eddies. J. Fluid Mech. 278, 175–200.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 A 4, 812–824.CrossRefGoogle Scholar
Cambon, C. & Scott, J. F. 1999 Linear and nonlinear models of anisotropic turbulence. Annu. Rev. Fluid Mech. 31 (1), 1–53.Google Scholar
Caulfield, C. P. & Kerswell, R. R. 2000 The nonlinear development of three-dimensional disturbances at hyperbolic stagnation points: a model of the braid region in mixing layers. Phys. Fluids 12, 1032–1043.Google Scholar
Girimaji, S. S. 2000 Pressure–strain correlation modelling of complex turbulent flows. J. Fluid Mech. 422, 91–123.CrossRefGoogle Scholar
Girimaji, S. S., Jeong, E. & Poroseva, S. V. 2003 Pressure–strain correlation in homogeneous anisotropic turbulence subject to rapid strain-dominated distortion. Phys. Fluids 15, 3209–3222.Google Scholar
Godeferd, F. S., Cambon, C. & Scott, J. F. 2001 Two-point closures and their applications: report on a workshop. J. Fluid Mech. 436, 393–407.Google Scholar
Jacquin, L., Leuchter, O., Cambon, C. & Mathieu, J. 1990 Homogeneous turbulence in the presence of rotation. J. Fluid Mech. 220, 1–52.Google Scholar
Johansson, A. V. & Hallback, M. 1994 Modelling of 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
Kassinos, S. C., Reynolds, W. C. & Rogers, M. M. 2001 One-point turbulence structure tensors. J. Fluid Mech. 428, 213–248.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543.Google Scholar
Kraichnan, R. H. 1971 An almost-Markovian Galilean-invariant turbulence model. J. Fluid Mech. 47, 513–524.CrossRefGoogle Scholar
Launder, B. E., Reece, G. Jr & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537–566.Google Scholar
Malkus, W. 1989 An experimental study of global instabilities due to the tidal (elliptical) distortion of a rotating elastic cylinder. Geophys. Astrophys. Fluid Dyn. 48, 123–134.Google Scholar
Mishra, A. A. & Girimaji, S. S. 2010 Pressure–strain correlation modeling: towards achieving consistency with rapid distortion theory. Flow Turbul. Combust. 85, 593–619.CrossRefGoogle Scholar
Moffatt, H. K. 1967 The interaction of turbulence with a strong wind shear. In URSI-IUGG International Colloquim on Atmospheric Turbulence and Radio Wave Propagation, pp. 139–156.Google Scholar
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363–386.Google Scholar
Perot, B. & Moin, P. 1995 Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence. J. Fluid Mech. 295, 199–228.CrossRefGoogle Scholar
Pierrehumbert, R. T. 1986 Universal short-wave instability of two-dimensional eddies in an inviscid fluid. Phys. Rev. Lett. 57 (17), 2157–2159.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Ristorcelli, J. R., Lumley, J. L. & Abid, R. 1995 A rapid pressure covariance representation consistent with the Taylor–Proudman theorem materially frame indifferent in the two-dimensional limit. J. Fluid Mech. 292, 111–152.Google Scholar
Rogers, M. M. 1991 The structure of a passive scalar field with a uniform mean gradient in rapidly sheared homogeneous turbulent flow. Phys. Fluids A 3, 144–154.Google Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Cambridge University Press.Google 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.Google Scholar
Sjögren, 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.Google Scholar
Slo, P. R. Van & Pope, S. B. 1997 PDF modeling for inhomogeneous turbulence with exact representation of rapid distortions. Phys. Fluids 9, 1085–1105.Google Scholar
Speziale, C. G., Abid, R. & Blaisdell, G. A. 1996 On the consistency of Reynolds stress turbulence closures with hydrodynamic stability theory. Phys. Fluids 8 (3), 781–788.Google Scholar
Speziale, C. G., Gatski, T. B. & Mhuiris, N. M. G. 1990 A critical comparison of turbulence models for homogeneous shear flows in a rotating frame. Phys. Fluids 2 (9), 1678–1684.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.Google Scholar
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence. Springer.Google Scholar