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The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study

The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study
The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study
The influence of compressibility upon the structure of homogeneous sheared turbulence is investigated. For the case in which the rate of shear is much larger than the rate of nonlinear interactions of the turbulence, the modification caused by compressibility to the amplification of turbulent kinetic energy by the mean shear is found to be primarily reflected in pressure-strain correlations and related to the anisotropy of the Reynolds stress tensor, rather than in explicit dilatational terms such as the pressure-dilatation correlation or the dilatational dissipation. The central role of a 'distortion Mach number' Md = Sℓ/a, where S is the mean strain or shear rate, ℓ a length scale of energetic structures, and a the sonic speed, is demonstrated. This parameter has appeared in previous rapid-distortion-theory (RDT) and direct-numerical-simulation (DNS) studies; in order to generalize the previous analyses, the quasi-isentropic compressible RDT equations are numerically solved for homogeneous turbulence subjected to spherical (isotropic) compression, one-dimensional (axial) compression and pure shear. For pure-shear flow at finite Mach number, the RDT results display qualitatively different behaviour at large and small non-dimensional times St: when St < 4 the kinetic energy growth rate increases as the distortion Mach number increases; for St > 4 the inverse occurs, which is consistent with the frequently observed tendency for compressibility to stabilize a turbulent shear flow. This 'crossover' behaviour, which is not present when the mean distortion is irrotational, is due to the kinematic distortion and the mean-shear-induced linear coupling of the dilatational and solenoidal fields. The relevance of the RDT is illustrated by comparison to the recent DNS results of Sarkar (1995), as well as new DNS data, both of which were obtained by solving the fully nonlinear compressible Navier-Stokes equations. The linear quasi-isentropic RDT and nonlinear non-isentropic DNS solutions are in good general agreement over a wide range of parameters; this agreement gives new insight into the stabilizing and destabilizing effects of compressibility, and reveals the extent to which linear processes are responsible for modifying the structure of compressible turbulence.
0022-1120
307-338
Simone, A.
fa358dad-4389-4469-a66a-82d5253b12e3
Coleman, G.N.
ea3639b9-c533-40d7-9edc-3c61246b06e0
Cambon, C.
2dd3f8ef-d5ef-4ed5-a522-8ead009eb032
Simone, A.
fa358dad-4389-4469-a66a-82d5253b12e3
Coleman, G.N.
ea3639b9-c533-40d7-9edc-3c61246b06e0
Cambon, C.
2dd3f8ef-d5ef-4ed5-a522-8ead009eb032

Simone, A., Coleman, G.N. and Cambon, C. (1997) The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study. Journal of Fluid Mechanics, 330, 307-338. (doi:10.1017/S0022112096003837).

Record type: Article

Abstract

The influence of compressibility upon the structure of homogeneous sheared turbulence is investigated. For the case in which the rate of shear is much larger than the rate of nonlinear interactions of the turbulence, the modification caused by compressibility to the amplification of turbulent kinetic energy by the mean shear is found to be primarily reflected in pressure-strain correlations and related to the anisotropy of the Reynolds stress tensor, rather than in explicit dilatational terms such as the pressure-dilatation correlation or the dilatational dissipation. The central role of a 'distortion Mach number' Md = Sℓ/a, where S is the mean strain or shear rate, ℓ a length scale of energetic structures, and a the sonic speed, is demonstrated. This parameter has appeared in previous rapid-distortion-theory (RDT) and direct-numerical-simulation (DNS) studies; in order to generalize the previous analyses, the quasi-isentropic compressible RDT equations are numerically solved for homogeneous turbulence subjected to spherical (isotropic) compression, one-dimensional (axial) compression and pure shear. For pure-shear flow at finite Mach number, the RDT results display qualitatively different behaviour at large and small non-dimensional times St: when St < 4 the kinetic energy growth rate increases as the distortion Mach number increases; for St > 4 the inverse occurs, which is consistent with the frequently observed tendency for compressibility to stabilize a turbulent shear flow. This 'crossover' behaviour, which is not present when the mean distortion is irrotational, is due to the kinematic distortion and the mean-shear-induced linear coupling of the dilatational and solenoidal fields. The relevance of the RDT is illustrated by comparison to the recent DNS results of Sarkar (1995), as well as new DNS data, both of which were obtained by solving the fully nonlinear compressible Navier-Stokes equations. The linear quasi-isentropic RDT and nonlinear non-isentropic DNS solutions are in good general agreement over a wide range of parameters; this agreement gives new insight into the stabilizing and destabilizing effects of compressibility, and reveals the extent to which linear processes are responsible for modifying the structure of compressible turbulence.

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Published date: 1997

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Local EPrints ID: 71969
URI: http://eprints.soton.ac.uk/id/eprint/71969
ISSN: 0022-1120
PURE UUID: 057ff201-846f-42ed-840c-15c2f6426305

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Date deposited: 13 Jan 2010
Last modified: 13 Mar 2024 20:54

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Contributors

Author: A. Simone
Author: G.N. Coleman
Author: C. Cambon

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