Anomalous scalings in non-stationary turbulence (Sergey Nazarenko, University of Warwick)

We will discuss non-stationary turbulence at the stage prior (and leading to) formation of Kolmogorov cascade. We will consider several basic models of turbulence in which the energy spectrum obeys a nonlinear PDE or an integral equation. We will show that the specrum has a power-law asymptotic with an anomalous exponent which is less than the Kolmogorov value -5/3. By comparison with turbulence in Burgers equation and with numerical simulations of Navier-Stokes equations, we will speculate that the anomalous scaling is related to formation of a singularity, and that this scenario may be generic for turbulence systems.