Role of pressure on formation of extreme velocity gradients in turbulence

Turbulent flows are characterized by intermittent generation of intense velocity gradients, which are important to study in both theory and modeling. Such intense gradients result from nonlinear self-amplification and are also influenced by the nonlocal pressure field via its Hessian tensor. Prior work on the subject has have been restricted to low Reynolds numbers. Here, using direct numerical simulations (DNS) of isotropic turbulence with Taylor-scale Reynolds number in the range 140-1300, we systematically investigate how pressure Hessian affects the amplification of vorticity and strain-rate and contrast it with other inviscid nonlinear mechanisms.

Overall, H inhibits vortex stretching (VS), although the inhibition is much weaker than the amplification induced by other nonlinear mechanisms. However, in regions of most intense vorticity, the contribution from H dominates over nonlinearity, leading to an overall depletion of VS. We also observe near-perfect alignment between vorticity and the eigenvector of H corresponding to the smallest eigenvalue, consistent with the presence of intense vortex-tubes. We discuss the connection between the VS-inhibiting role of pressure, and the recently identified self-attenuation mechanism [Buaria et al. Nat. Commun. 11:5852 (2020)], whereby intense vorticity is locally attenuated through inviscid effects. We also discuss the influence of pressure Hessian on strain amplification, which is substantially weaker.