Local and nonlocal pressure Hessian effects in real and synthetic fluid turbulence

The Lagrangian dynamics of the velocity gradient tensor A in isotropic and homogeneous turbulence depends on the joint action of the self-stretching term and the pressure Hessian. Existing closures for pressure effects in terms of A are unable to reproduce one important statistical role played by the anisotropic part of the pressure Hessian, namely the redistribution of the probabilities towards enstrophy production dominated regions. As a step towards elucidating the required properties of closures, we study several synthetic velocity fields and how well they reproduce anisotropic pressure effects. It is found that synthetic (1) Gaussian, (2) multifractal, and (3) minimal turnover Lagrangian map incompressible velocity fields reproduce many features of real pressure fields that are obtained from numerical simulations of the Navier Stokes equations, including the redistribution towards enstrophy-production regions. The synthetic fields include both spatially local, and nonlocal, anisotropic pressure effec...