Dynamics of three-dimensional turbulence from Navier-Stokes equations

Turbulent flows contain occasional, well-separated sharp features, as illustrated in this picture by Bonn et al. (1993), reproduced with permission, surrounded mostly by low levels of activity. Both interacting structures contribute to the complexity of turbulence. A full theory requires the understanding of both, which is what our paper attempts to do. We predict quantitatively the multi-scaling exponents for these singular-like features of different strengths, while also showing that the background flow is Gaussian. The large spatial separation between the sharp structures enables one to treat them as a ``weakly interacting gas''.