Structure and role of the pressure Hessian in regions of strong vorticity in turbulence

Amplification of velocity gradients, a key feature of turbulent flows, is affected by the non-local character of the incompressible fluid equations expressed by the second derivative (Hessian) of the pressure field. By analysing the structure of the flow in regions where the vorticity is the highest, we propose an approximate expression for the pressure Hessian in terms of the local vorticity, consistent with the existence of intense vortex tubes. Contrary to the often used simplification of an isotropic form for the pressure Hessian, which in effect inhibits vortex stretching, the proposed approximate form of the pressure Hessian enables much stronger vortex stretching. The prediction of the approximation proposed here is validated with results of direct numerical simulations of turbulent flows.