Space-local Navier-Stokes turbulence

We investigate the physical-space locality of interactions in three-dimensional in- compressible turbulent flow. To that, we modify the nonlinear terms of the vorticity equation such that the vorticity field is advected and stretched by the locally induced velocity. This space-local velocity field is defined by the truncated Biot-Savart law, where only the neighboring vorticity field in a sphere of radius R is integrated. We conduct direct numerical simulations of the space-local system to investigate its statistics in the inertial range. We observe a standard E(k) alpha k(-5/3) scaling of the energy spectrum associated with an energy cascade for scales smaller than the space-local domain size k >> R-1. This result is consistent with the assumption [Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941)] made for the space locality of the nonlinear interactions. The enstrophy amplification is suppressed for larger scales k << R-1, and for these scales, the system exhibits a scaling consistent with a conservative enstrophy cascade.