High-resolution computation of local dissipation scales in turbulence

Abstract

The world record for the biggest numerical simulation of statistically stationary, homogene-ous and locally isotropic turbulence has been kept by a Japanese team over the last years. They performed their simulation run on the Earth Simulator for an equidistant mesh grid of 40963 points. A very large Reynolds number of 106 was accessible there at the cost of a poor resolution of the smallest turbulent scales. Recent investigations however indicate that these scales have to be resolved properly in simulations since they provide important information about the physics at larger scales, i.e. in the inertial cascade range of turbulence. We propose therefore a numerical simulation at half the resolution of the Earth Simulator run that is not aiming at such high Reynolds numbers, but resolves the finest scales of turbulence properly. The fine spectral resolution makes a reliable statistical study of velocity gradients and local dissipation scales possible. The well-resolved gradient fluctuations allow us to predict asymp-totic inertial range scaling exponents of the turbulent velocity field and to compare them with a recent theoretical approach.