Intermittency in two-dimensional turbulence with drag

Yue-Kin Tsang, Edward Ott, Thomas M. Antonsen, Parvez N. Guzdar
2005 Physical Review E  
We consider the enstrophy cascade in forced two-dimensional turbulence with a linear drag force. In the presence of linear drag, the energy wavenumber 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 a previous theory, we compare numerical simulation results with predictions for the power law exponent of the energy wavenumber spectrum and the scaling
more » ... ponents of the vorticity structure functions ζ_2q obtained in terms of the distribution of finite time Lyapunov exponents. 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 and singularity spectrum f(α). 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_rω, the difference between the vorticity at two points separated by a distance r. Our numerical simulations are done on a 4096 × 4096 grid.
doi:10.1103/physreve.71.066313 pmid:16089873 fatcat:utuk7c2u75dyvb7ezreo7rluvu