Subgrid-scale stresses and their modelling in a turbulent plane wake

John O'Neil and Charles Meneveau
Department of Mechanical Engineering
The Johns Hopkins University
Baltimore MD 21218

ABSTRACT: Velocity measurements using hot-wires are performed across a high Reynolds number, turbulent plane wake, with the aim of studying the subgrid-scale (SGS) stress and its modeling. This quantity is needed to close the filtered Navier-Stokes equations used for Large Eddy Simulation (LES) of turbulent flows. Comparisons of various globally time-averaged quantities involving the measured and modeled SGS stress are made, with special emphasis on the SGS energy dissipation rate. Experimental constraints require the analysis of a one-dimensional surrogate of the SGS dissipation. Broadly, the globally averaged results show that all models considered, namely the Smagorinsky and similarity models, as well as the dynamic Smagorinsky model, approximately reproduce profiles of the surrogate SGS dissipation. Some discrepancies near the outer edge of the wake are observed, where the Smagorinsky model slightly overpredicts, and the similarity model underpredicts, energy dissipation unless the filtering scale is about two orders of magnitude smaller than the integral length scale. A more detailed comparison between real and modeled SGS stresses is achieved by conditional averaging based on particular physical phenomena: (i) the outer-intermittency of the wake, and (ii) large-scale coherent structures of the turbulent wake. Thus, the interaction of the subgrid-scales with the resolved flow and model viability can be individually tested in regions where isolated mechanisms such as outer-intermittency, vortex stretching, rotation, etc., are dominant. Conditioning on outer-intermittency did not help to clarify observed features of the measurements. Alternatively, the large scale organized structures are found to have a strong impact upon the distribution of surrogate SGS energy dissipation, even at filter scales well inside the inertial range. The similarity model is able to capture this result, while the Smagorinsky model gives a more uniform (i.e. unrealistic) distribution. Both dynamic Smagorinsky and similarity models reproduce realistic distributions, but only if all filter levels are well contained inside the inertial range.

J. Fluid Mech. 349 (1997), p. 253

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