Developed Turbulence: From Full Simulations to Full Mode Reductions

Developed Navier-Stokes turbulence is simulated with varying wave-vector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents ${\zeta }_p$ of the $p\mathrm{th}$ order velocity structure functions seem to depend mainly on the proper resolution of the inertial subrange. Universal scaling properties (i.e., independent of the degree of mode reduction) are found for the relative scaling exponents ${\rho }_{p,q}=({\zeta }_p-{\zeta }_{3}p/3\mathrm{})/({\zeta }_q-{\zeta }_{3}q/3\mathrm{})$.