Effects of SGS stresses on velocity gradient dynamics

The effects of small-scale motions on the inertial range structure of turbulence are investigated by considering the dynamics of the velocity gradient tensor filtered at inertial-range scales. In addition to self-interactions and the filtered pressure Hessian, the evolution of the filtered velocity gradient tensor is determined by the subgrid-scale stress tensor. As in so-called Restricted Euler dynamics, the evolution equations can be simplified by considering two invariants R and Q. The effects of the subgrid-scale stress tensor on them can be quantified unambiguously by evaluating conditional averages that appear in the evolution equation for the joint PDF of the invariants. The required conditional averages are computed from three-dimensional HPIV measurements of fully developed turbulence in a square duct, at a friction Reynolds number of about 2300. The results show that the SGS stresses have significant effects, e.g. along the so-called Vieillefosse tail they oppose the formation of a finite-time singularity that occurs in Restricted Euler dynamics. A-priori tests of the Smagorinsky, nonlinear, and mixed models show that all reproduce the real SGS stress effect along the Vieillefosse tail, but that they fail in several other regions. An attempt is made to optimize the mixed model by letting the two coefficients be functions of the two invariants R and Q.