Analysis of subgrid-scale torque for large-eddy simulation of turbulence

A study is performed of the vorticity source induced by filtering the nonlinear terms of the Navier-Stokes equation, as used in large-eddy simulation of turbulent flows. In analogy to the subgrid-scale (SGS) stress, this vorticity source is referred to as the subgrid-scale torque. The SGS torque results from derivatives of the part of the SGS stress and force terms that play a role in modifying the filtered velocity field. Other parts of the SGS stress and force modify pressure but have no influence on velocity field in a constant-density flow and are, therefore, not dynamically significant. The total dissipation rate due to the SGS flow is shown to depend only on the part of the SGS force induced by the SGS torque. With a series of examples with increasing complexity, it is shown that the SGS stress and force are often dominated by terms that generate no SGS torque. With use of the scale-similarity model, both for isotropic turbulence and for turbulence near a large-scale vortex structure, it is demonstrated that LES closure models can sometimes yield reasonably good results in a priori tests for prediction of SGS stress and force, while yielding poor predictions for SGS torque. This conclusion is consistent with the common observation that the scale-similarity model yields good results in a priori tests (when only the SGS stress is examined) but nevertheless has insufficient dissipation in a posteriori tests.