Abrupt transitions of zonal jets in two-dimensional turbulent shear flow

Vassilios Dallas, Kannabiran Seshasayanan, Stephan Fauve

Published 2019-11-02Version 1

We study the complex transitions of zonal jets in the turbulent regime of a forced shear flow using direct numerical simulations of the Navier-Stokes equations. The behaviour of the zonal mean flow involves bifurcations of the probability density function (PDF) of the largest scale mode which exhibits two types of transitions over the turbulent regime. One transition is from Gaussian to bimodal PDF which signifies the emergence of reversals of the zonal mean flow where the flow fluctuates between two turbulent states. The other transition is from bimodal to unimodal PDF which designates the disappearance of the reversals of the largest scale mode. We attribute the later bifurcation to the long-time memory that the large scale flow exhibits related to low frequency $1/f$ type of noise. We also demonstrate the a minimal model with 15 modes, that was devised using the truncated Euler equations, is able to capture the large scale dynamics of the Navier-Stokes equations.