Dynamics of reversals and condensates in two-dimensional Kolmogorov flows

Abstract

We present 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 × 6 square array of counterrotating 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.