Evolution and modelling of subgrid scales during rapid straining of turbulence

Abstract

The response, evolution, and modelling of subgrid-scale (SGS) stresses during rapid straining of turbulence is studied experimentally. Nearly isotropic turbulence with low mean velocity and Rλ˜290 is generated in a water tank by means of spinning grids. Rapid straining (axisymmetric expansion) is achieved with two disks pushed towards each other at rates that for a while generate a constant strain rate. Time-resolved, two-dimensional velocity measurements are performed using cinematic PIV. The SGS stress is subdivided to a stress due to the mean distortion, a cross-term (the interaction between the mean and turbulence), and the turbulent SGS stress τ(T)ij. Analysis of the time evolution of τ(T)ij at various filter scales shows that all scales are more isotropic than the prediction of rapid distortion theory, with increasing isotropy as scales decrease. A priori tests show that rapid straining does not affect the high correlation and low square-error exhibited by the similarity model. Analysis of the evolution of total SGS energy dissipation reveals, surprisingly, that the Smagorinsky model with a constant coefficient (determined from isotropic turbulence data) underpredicts the dissipation during rapid straining. While the partial dissipation −〈τ(T)ijS˜ij〉 (due only to the turbulent part of the stress) is overpredicted by the Smagorinsky model, addition of the cross-terms reverses the trend. The similarity model with a constant coefficient appropriate for isotropic turbulence, on the other hand, overpredicts SGS dissipation. Owing to these opposite trends a linear combination of both models (mixed model) provides better prediction of SGS dissipation during rapid straining. However, the mixed model with coefficients determined from dissipation balance underpredicts the SGS stress.