Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields

摘要

Understanding the non-local pressure contributions and viscous effects on thesmall-scale statistics remains one of the central challenges in the study ofhomogeneous isotropic turbulence. Here we address this issue by studying theimpact of the pressure Hessian as well as viscous diffusion on the statisticsof the velocity gradient tensor in the framework of an exact statisticalevolution equation. This evolution equation shares similarities with earlierphenomenological models for the Lagrangian velocity gradient tensor evolution,yet constitutes the starting point for a systematic study of the unclosedpressure Hessian and viscous diffusion terms. Based on the assumption ofincompressible Gaussian velocity fields, closed expressions are obtained as theresults of an evaluation of the characteristic functionals. The benefits andshortcomings of this Gaussian closure are discussed, and a generalization isproposed based on results from direct numerical simulations. This enhancedGaussian closure yields, for example, insights on how the pressure Hessianprevents the finite-time singularity induced by the local self-amplificationand how its interaction with viscous effects leads to the characteristic strainskewness phenomenon.