Intermittency in two-dimensional turbulence with drag

We consider the enstrophy cascade in forced two-dimensional turbulence with a linear drag force. In the presence of linear drag, the energy wave-number spectrum drops with a power law faster than in the case without drag, and the vorticity field becomes intermittent, as shown by the anomalous scaling of the vorticity structure functions. Using previous theory, we compare numerical simulation results with predictions for the power law exponent of the energy wave-number spectrum and the scaling exponents of the vorticity structure functions ζ_2q. We also study, both by numerical experiment and theoretical analysis, the multifractal structure of the viscous enstrophy dissipation in terms of its Rényi dimension spectrum D_q. We derive a relation between D_q and ζ_2q, and discuss its relevance to a version of the refined similarity hypothesis. In addition, we obtain and compare theoretically and numerically derived results for the dependence on separation r of the probability distribution of δ_r⃗ω, the difference between the vorticity at two points separated by a distance r. Our numerical simulations are done on a 4096×4096 grid.