Transitions between turbulent states in a two-dimensional shear flow

TL;DR

This study investigates how large-scale jets in turbulent shear flow undergo bifurcations as the Reynolds number increases, revealing transitions from Gaussian to bimodal and then to unimodal flow states, with a minimal model capturing these dynamics.

Contribution

The paper introduces a minimal 15-mode model that replicates bifurcation behavior of large-scale jets observed in direct numerical simulations of Navier-Stokes equations.

Findings

PDF bifurcates from Gaussian to bimodal with increasing Reynolds number

Reversals of large-scale flow disappear at higher Reynolds numbers

Minimal model successfully reproduces bifurcation phenomena

Abstract

We study the bifurcations of the large scale jets in the turbulent regime of a forced shear flow using direct numerical simulations of the Navier-Stokes equations. The bifurcations are seen in the probability density function (PDF) of the largest scale mode with the control parameter being the Reynolds number based on the friction coefficient denoted as $Rh$. As one increases $Rh$ in the turbulent regime, the PDF of the large scale mode first bifurcates from a Gaussian to a bimodal behaviour, signifying the emergence of reversals of the large scale flow where the flow fluctuates between two distinct turbulent states. Further increase in $Rh$ leads to a bifurcation from bimodal to unimodal PDF which denotes the disappearance of the reversals of the largest scale mode. We attribute the latter transition to the long-time memory that the large scale flow exhibits related to low frequency $1/f^\alpha$ type of noise with $0 < \alpha < 2$. We also demonstrate that a minimal model with 15 modes, obtained from the truncated Euler equation, is able to capture the bifurcations of the large scale jets exhibited by the Navier-Stokes equations.