Statistically steady turbulence in thin films: Direct numerical simulations with Ekman friction

We present a detailed direct numerical simulation (DNS) of the two-dimensional Navier–Stokes equation with the incompressibility constraint and air-drag-induced Ekman friction; our DNS has been designed to investigate the combined effects of walls and such a friction on turbulence in forced thin films. We concentrate on the forward-cascade regime and show how to extract the isotropic parts of velocity and vorticity structure functions and hence the ratios of multiscaling exponents. We find that velocity structure functions display simple scaling, whereas their vorticity counterparts show multiscaling, and the probability distribution function of the Weiss parameter ¿, which distinguishes between regions with centers and saddles, is in quantitative agreement with experiments.