Testing Batchelor's similarity hypotheses for decaying two-dimensional turbulence

We carry out three high resolution direct numerical simulations of the two-dimensional Navier-Stokes equation to test Batchelor's similarity hypotheses of an equilibrium spectral range and an inertial subrange where the enstrophy wave number spectrum has the form Phi(k)=C chi(2/3)k(-1), where chi is the mean enstrophy dissipation rate and C is a constant. We use very different initial conditions in the three simulations and find that Batchelor's hypotheses are well satisfied in each simulation. However, there is a small but significant difference between the equilibrium range spectrum of one of the simulations as compared to the spectra of the other two. We suggest that the difference is linked to the stronger degree of large scale variation of the enstrophy dissipation which is observed in this simulation as compared to the other two. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3488997]