Dynamics of reversals and condensates in 2D Kolmogorov flows

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 $6\times 6$ 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.

Submitted to Physical Review E

References in corpus (4)

• Growing condensate in two-dimensional turbulence
• Dynamo regimes and transitions in the VKS experiment
• Turbulence-condensate interaction in two dimensions
• Flow reversals in turbulent convection with free-slip walls

Cited by in corpus (6)

• Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence
• Statistical theory of reversals in two-dimensional confined turbulent flows
• Bifurcations of a large scale circulation in a quasi-bidimensional turbulent flow
• Intermittent direction reversals of moving spatially-localized turbulence observed in two-dimensional Kolmogorov flow
• Kolmogorov flow: Linear Stability and Energy Transfers in a minimal low-dimensional model
• Discrete Symmetries in Dynamo Reversals