We investigate the physical-space locality of interactions in
three-dimensional incompressible 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)βkβ5/3
scaling of the energy spectrum associated with an energy cascade for scales
smaller than the space-local domain size kβ«Rβ1. This result is
consistent with the assumption Kolmogorov's 1941 paper made for the
space-locality of the nonlinear interactions. The enstrophy production is
suppressed for larger scales kβͺRβ1, and for these scales, the system
exhibits a scaling consistent with a conservative enstrophy cascade.Comment: 22 pages, 8 figure