Role of pressure in generation of intense velocity gradients in turbulent flows

Abstract

We investigate the role of pressure, via its Hessian tensor $\mathbf{H}$, on amplification of vorticity and strain-rate and contrast it with other inviscid nonlinear mechanisms. Results are obtained from direct numerical simulations of isotropic turbulence with Taylor-scale Reynolds number in the range $140-1300$. Decomposing $\mathbf{H}$ into local isotropic ($\mathbf{H}^{\rm I}$) and nonlocal deviatoric ($\mathbf{H}^{\rm D}$) components reveals that $\mathbf{H}^{\rm I}$ depletes vortex stretching (VS), whereas $\mathbf{H}^{\rm D}$ enables it, with the former slightly stronger. The resulting inhibition is significantly weaker than the nonlinear mechanism which always enables VS. However, in regions of intense vorticity, identified using conditional statistics, contribution from $\mathbf{H}$ dominates over nonlinearity, leading to overall depletion of VS. We also observe near-perfect alignment between vorticity and the eigenvector of $\mathbf{H}$ corresponding to the smallest eigenvalue, which conforms with well-known vortex-tubes. We discuss the connection between this depletion, essentially due to (local) $\mathbf{H}^{\rm I}$, and recently identified self-attenuation mechanism [Buaria et al. {\em Nat. Commun.} 11:5852 (2020)], whereby intense vorticity is locally attenuated through inviscid effects. In contrast, the influence of $\mathbf{H}$ on strain-amplification is weak. It opposes strain self-amplification, together with VS, but its effect is much weaker than VS. Correspondingly, the eigenvectors of strain and $\mathbf{H}$ do not exhibit any strong alignments. For all results, the dependence on Reynolds number is very weak. In addition to the fundamental insights, our work provides useful data and validation benchmarks for future modeling endeavors, for instance in Lagrangian modeling of velocity gradient dynamics, where conditional $\mathbf{H}$ is explicitly modeled.