Statistics of local Reynolds number in box turbulence: Ratio of inertial to viscous forces

In high-Reynolds-number turbulence the spatial distribution of velocity fluctuation at small scales is strongly non-uniform. In accordance with the non-uniformity, the distributions of the inertial and viscous forces are also non-uniform. According to direct numerical simulation (DNS) of forced turbulence of an incompressible fluid obeying the Navier-Stokes equation in a periodic box at the Taylor microscale Reynolds number Rλ ≈ 1100, the average 〈Rloc〉 over the space of the 'local Reynolds number' Rloc, which is defined as the ratio of inertial to viscous forces at each point in the flow, is much smaller than the conventional 'Reynolds number' given by Re ≡ UL/ν, where U and L are the characteristic velocity and length of the energy-containing eddies, and ν is the kinematic viscosity. While both conditional averages of the inertial and viscous forces for a given squared vorticity ω2 increase with ω2 at large ω2, the conditional average of Rloc is almost independent of ω2. A comparison of the DNS field with a random structureless velocity field suggests that the increase in the conditional average of Rloc with ω2 at large ω2 is suppressed by the Navier-Stokes dynamics. Something similar is also true for the conditional averages for a given local energy dissipation rate per unit mass. Certain features of intermittency effects such as that on the Re dependence of 〈Rloc〉 are explained by a multi-fractal model by Dubrulle (J. Fluid Mech., vol. 867, 2019, P1).