Understanding non-universal scaling for the direct cascade in 2D flows

For high-Re turbulent 2D flows, the Kraichnan-Leith-Batchelor theory predicts that the energy density scales as an integral power of the wavenumber, E(k) ~ k^-3, in the inertial range. However, experiments and numerical simulations generally find spectra exhibiting scaling with fractal exponents. In this work, we consider statistically stationary 2D turbulent flows on a domain with periodic boundary conditions where forcing is balanced by viscous dissipation. We explore how the folding and stretching of vorticity filaments by the large-scale flow (LSF) generates self-similar structures characterized by fractal spectra. We show that the fractal exponent depends on the properties of the LSF which, in turn, depend on the forcing and boundary conditions.