Dynamics of reversals and condensates in 2D Kolmogorov flows

TL;DR

This paper uses direct numerical simulations to explore how 2D Kolmogorov flows transition between different flow regimes, including stable vortices, chaos, and large-scale circulation reversals, as the Reynolds number and damping rate vary.

Contribution

It identifies the bifurcation sequence leading to chaos and characterizes the flow regime transitions, especially the reversals of large-scale circulation in 2D flows.

Findings

Stable vortex array at low Re and Rh

Transition to chaos with increasing Re and Rh

Reversals of large-scale circulation at lower Rh

Abstract

We present direct numerical simulations of the different two-dimensional flow regimes generated by a constant spatially periodic forcing balanced by viscous dissipation and large scale drag with a dimensionless damping rate $1/Rh$. The linear response to the forcing is a $6\times6$ square array of counter-rotating vortices, which is stable when the Reynolds number $Re$ or $Rh$ are small. After identifying the sequence of bifurcations that lead to a spatially and temporally chaotic regime of the flow when $Re$ and $Rh$ are increased, we study the transitions between the different turbulent regimes observed for large $Re$ by varying $Rh$. A large scale circulation at the box size (the condensate state) is the dominant mode in the limit of vanishing large scale drag ($Rh$ large). When $Rh$ is decreased, the condensate becomes unstable and a regime with random reversals between two large scale circulations of opposite signs is generated. It involves a bimodal probability density function of the large scale velocity that continuously bifurcates to a Gaussian distribution when $Rh$ is decreased further.