Turbulence screening suppresses long-range pressure contributions

The complexity in turbulence can be seen to stem from the non-linearity and non-locality of the governing Navier-Stokes equations. The non-linearity gives rise to structures on many scales with varying topologies -- from strain sheets to vortex tubes. In incompressible flows, these structures determine the pressure field through a Poisson relation. This in turn describes the non-locality of incompressible flows -- formally the pressure at any point is determined by the competition of strain and enstrophy over the entire flow. We show how due to the relative compactness and close proximity of extreme strain and vortex regions a type of effective turbulence screening emerges. We characterize this effect in statistically stationary homogeneous and isotropic turbulence by considering the spatial (two-point) statistics of the velocity gradient fields. This clarifies the observation from both experiments and numerical simulations that a relatively small neighbourhood -- comparable with the small turbulence scales, contains the large majority of the information about the pressure at a given point. We characterize the properties of this neighbourhood as a function of global flow parameters, like Reynolds number, as well as local flow properties, e.g. local topology and dissipation.