Unifying scaling theory for vortex dynamics in two-dimensional turbulence

We present a scaling theory for unforced inviscid two-dimensional turbulence. Our model unifies existing spatial and temporal scaling theories. The theory is based on a self-similar distribution of vortices of different sizes A. Our model uniquely determines the spatial and temporal scaling of the associated vortex number density which allows the determination of the energy spectra and the vortex distributions. We find that the vortex number density scales as n(A, t) similar to t(-2/3)/A, which implies an energy spectrum epsilon similar to k(-5), significantly steeper than the classical Batchelor-Kraichnan scaling. High-resolution numerical simulations corroborate the model.