Inverse energy cascade in stationary two-dimensional homogeneous turbulence

Direct numerical simulations with up to ${1024}^2$ resolution are performed to study statistical properties of the inverse energy cascade in stationary homogeneous two-dimensional turbulence driven by small-scale Gaussian white-in-time noise. The energy spectra for the inverse energy cascade deviate strongly from the expected ${\mathit{k}}^{\mathrm{-}5/3}$ law and are close (somewhat flatter) to ${\mathit{k}}^{\mathrm{-}3}$. The reason for the deviation is traced to the emergence of strong vortices distributed over all scales. Statistical properties of the vortices are explored.