Statistically Steady Turbulence in Soap Films: Direct Numerical Simulations with Ekman Friction

We present a detailed direct numerical simulation (DNS) designed to investigate the combined effects of walls and Ekman friction on turbulence in forced soap films. We concentrate on the forward-cascade regime and show how to extract the isotropic parts of velocity and vorticity structure functions and thence 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 $\Lambda$, which distinguishes between regions with centers and saddles, is in quantitative agreement with experiments.Comment: 4 pages, 6 figure

Persistence Problem in Two-Dimensional Fluid Turbulence

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter $\Lambda$ to distinguish between vortical and extensional regions. We then use a direct numerical simulation (DNS) of the two-dimensional, incompressible Navier--Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent $\theta=2.9\pm0.2$.Comment: consistent with the published versio