Fluctuation-induced transitions in anisotropic two-dimensional turbulence

Two-dimensional (2D) turbulence features an inverse energy cascade that produces large-scale flow structures such as large-scale vortices (LSVs) and unidirectional jets. We investigate the dynamics of such large-scale structures using extensive direct numerical simulations (DNS) of stochastically forced, viscously damped 2D turbulence within a periodic rectangular (Cartesian) domain [0,Lx]×[0,Ly]. LSVs form and dominate the system when the domain aspect ratio δ=Lx/Ly≈1, while unidirectional jets predominate at δ≳1.1. At intermediate values of δ, both structures are metastable, and fluctuation-induced transitions between LSVs and jets are observed. Based on large-scale energy balance in the condensate, we derive and verify predictions for the dependence of the total kinetic energy and the flow polarity on the nondimensional control parameters. We further collect detailed statistics on the lifetimes of LSVs and jets from DNS runs of up to 10738 viscous diffusive time units in length. The distribution of the lifetimes is consistent with that of a memoryless Poisson process. The data are compatible with an exponential dependence of the mean lifetime on the aspect ratio δ. In addition, the mean lifetimes depend sensitively on the Reynolds number Re: As Re increases, the energy gap between LSV (lower energy) and jet states (higher energy) arising from anisotropic dissipation increases, leading to an increase in lifetimes that is approximately exponential in Re for both LSVs and jets. Similarly, as the ratio of the forcing scale to the domain size increases, the transition rates increase sharply, confirming earlier findings. We investigate the transition dynamics in terms of kinetic energy, flow polarity, modal amplitude, and 2D phase-space diagrams, revealing that the transitions occur in two stages: In the initial stage, an efficient redistribution of kinetic energy by nonlinear triadic interactions facilitates a rapid transition from LSVs to jets and vice versa. In the second stage, the kinetic energy of the newly formed structure slowly adjusts to its associated (higher or lower) equilibrium value on a longer, viscous timescale, leading to a time delay that results in hysteretic transition behavior. Fluctuation-induced transitions may also occur between different numbers of jets. Our findings shed new light on the dynamics of coherent large-scale structures in anisotropic turbulence.