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

TL;DR

This paper develops an analytical theory predicting Reynolds stresses and velocity profiles in barotropic turbulent jets, revealing universal behaviors and potential instabilities in large-scale atmospheric and plasma flows.

Contribution

It provides the first self-consistent analytical predictions of Reynolds stresses and velocity profiles in turbulent jets, independent of forcing details.

Findings

Velocity profile obeys a universal equation under certain limits.

Derived a relation for the maximal curvature of a jet.

Identified potential hydrodynamic instability points.

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.