1 research outputs found
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 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 exponents of the vorticity structure
functions 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 R\'{e}nyi dimension spectrum and singularity spectrum
. We derive a relation between and , 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 of the probability distribution of
\delta_{\V{r}}\omega, the difference between the vorticity at two points
separated by a distance . Our numerical simulations are done on a grid.Comment: 18 pages, 17 figure