Effects of small-scale turbulent motions on the filtered velocity gradient tensor as deduced from holographic particle image velocimetry measurements

The effects of small-scale motions on the inertial range structure of turbulence are investigated by considering the dynamics of the velocity gradient tensor (Aij) filtered at scale Δ. In addition to self-interactions and the filtered pressure Hessian, the evolution of Aij is determined by the subgrid-scale stress tensor. As in the so-called restricted Euler dynamics, the evolution equations can be simplified by considering the invariants RΔ and QΔ of Aij. The effects of the subgrid-scale stress tensor on RΔ and QΔ can be quantified unambiguously by evaluating conditional averages that appear in the evolution equation for the joint probability distribution function of these invariants. The required conditional averages are computed from three-dimensional measurements of fully developed turbulence in a square duct, at Reτ≈2360. The measurements are performed using holographic particle image velocimetry [Tao et al., Phys. Fluids 12, 941 (2000); Tao et al., J. Fluid Mech. 457, 35 (2002)]. The velocity distri...