Multiscale correlations and conditional averages in numerical turbulence

The equations of motion for the $n\mathrm{th}$ order velocity differences raise the interest in correlation functions containing both large and small scales simultaneously. We consider the scaling of such objects and also their conditional average representation with emphasis on the question of whether they behave differently in the inertial or the viscous subranges. The turbulent flow data are obtained by Navier-Stokes solutions on a ${60}^3$ grid with periodic boundary conditions and ${\mathrm{Re}}_{\lambda }=70.\mathrm{}$ Our results complement previous high Re data analysis based on measured data [A. L. Fairhall, V. S. L’vov, and I. Procaccia, Europhys. Lett 43, 277 (1998)] whose preference were the larger scales, and the analysis of both experimental and synthetic turbulence data by [R. Benzi and co-workers, Phys. Rev. Lett. 80, 3244 (1998); Phys. Fluids 11, 2215 (1999)]. The inertial range fusion rule is confirmed and insight is obtained for the conditional averages (the local dissipation rate conditioned on the velocity fluctuations).