On the small-scale structure of turbulence and its impact on the pressure field

Dimitar G. Vlaykov, Michael Wilczek

Published 2018-10-15Version 1

Understanding the small-scale structure of incompressible turbulence and its implications for the non-local pressure field is one of the fundamental challenges in fluid mechanics. Intense velocity gradient structures tend to cluster on a range of scales which affects the pressure through a Poisson equation. Here we present a quantitative investigation of the spatial distribution of these structures conditional on their intensity for Taylor-based Reynolds numbers in the range [160, 380]. We find that the correlation length of $-\mathrm{Tr} \mathbf{A}^2/2$, the second invariant of the velocity gradient, is proportional to the Kolmogorov scale. It also is a good indicator for the spatial localization of intense enstrophy and strain-dominated regions, as well as the separation between them. We describe and quantify the differences in the two-point statistics of these regions and the impact they have on the non-locality of the pressure field as a function of the intensity of the regions. Specifically, across the examined range of Reynolds numbers, the pressure in strong rotation-dominated regions is governed by a dissipation-scale neighbourhood. In strong strain-dominated regions, on the other hand, it is determined primarily by a larger neighbourhood reaching inertial scales.