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

Abstract

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, 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.

arXiv commentAccepted for publication by the Journal of Fluid Mechanics

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Cited by in corpus (5)

• On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade
• Gauge symmetry and dimensionality reduction of the anisotropic pressure Hessian
• Role of pressure in generation of intense velocity gradients in turbulent flows
• Reynolds number dependence of Lyapunov exponents of turbulence and fluid particles
• A length scale for non-local multi-scale gradient interactions in isotropic turbulence