Energy spectra of steady two-dimensional turbulent flows

The power spectrum is measured in direct numerical simulations of the two-d imensional Navier-Stokes equation and other two-dimensional flows with whit e-in-time forcing at large scales. For the Navier-Stokes equation the energ y spectrum in the inertial range approaches k(-3) with increasing Reynolds number, with possible logarithmic corrections. A family of two-dimensional hows, including the surface quasigeostrophic equation, allows us to vary th e locality of the "enstrophy" transfer, where enstrophy is the mean square of the convected quantity. Dimensional analysis based on the enstrophy diss ipation correctly predicts the energy spectrum, whenever the enstrophy tran sfer can be assumed to be spectrally local. Otherwise, the enstrophy spectr um is steeper than would be expected on the basis of local transfer. In thi s case the data suggest a k(-1) passive scalar spectrum.