Theoretical prediction of Reynolds stresses and velocity profiles for barotropic turbulent jets

Abstract: It is extremely uncommon to be able to predict the velocity profile of a turbulent flow. In two-dimensional flows, atmosphere dynamics, and plasma physics, large scale coherent jets are created through inverse energy transfers from small scales to the largest scales of the flow. We prove that in the limits of vanishing energy injection, vanishing friction, and small scale forcing, the velocity profile of a jet obeys an equation independent of the details of the forcing. We find another general relation for the maximal curvature of a jet and we give strong arguments to support the existence of an hydrodynamic instability at the point with minimal jet velocity. Those results are the first computations of Reynolds stresses and self consistent velocity profiles from the turbulent dynamics, and the first consistent analytic theory of zonal jets in barotropic turbulence.