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

Eric Woillez (1) , Freddy Bouchet (1)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

It is extremely uncommon to be able to predict analytically, from first principles, 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 and friction on one hand, and small scale forcing on the other hand, the velocity profile of a jet obeys a universal equation independent of the details of the forcing. We find an other universal 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 from first principle in a genuine turbulent flow, and the first consistent analytic theory of zonal jets in barotropic turbulence.

Domaines: Dynamique des Fluides [physics.flu-dyn]

Eric Woillez, Freddy Bouchet. Theoretical prediction of Reynolds stresses and velocity profiles for barotropic turbulent jets . EPL - Europhysics Letters, 2017. ⟨hal-01357478v2⟩