Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 42: Turbulence

DY 42.1: Talk

Wednesday, March 14, 2018, 10:00–10:15, BH-N 128

On the small-scale structures of the turbulent velocity gradient and the resulting pressure field — •Dimitar G Vlaykov and Michael Wilczek — Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

The non-local nature of the pressure in incompressible flows is at the heart of the complexity of the turbulence problem. Through a Poisson equation it is intimately related to the non-linear structures of the velocity gradient field in fully developed turbulence. To address both issues, we present a statistical characterization of the spatial structure of the second invariant of the velocity gradient tensor in homogeneous and isotropic turbulence. We distinguish regions of different intensity and type -- vorticity or strain dominated, and provide estimates on their scales and relative separation. The results inform a comparative statistical study of the dependence of the pressure non-locality on the local conditions for a range of Taylor-based Reynolds numbers between 123 and 433. It is found that in strongly vorticity-dominated regions a shielding mechanism is responsible for localizing the dominant pressure contributions to a dissipation-scale neighborhood. Moreover, this neighborhood is smaller than the underlying vortex structure. In strain-dominated regions, on the other hand, the same mechanism leads to the pressure statistics being determined on inertial scales. Finally, the well-known long-range pressure correlations stem from the strong non-locality of the contributions to the pressure in regions of low velocity-gradient intensity.