Fluctuation-Induced Transitions in Anisotropic Two-Dimensional Turbulence

Abstract

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 structures using extensive direct numerical simulations (DNS) of randomly forced, viscously damped 2D turbulence within a periodic rectangular (Cartesian) domain $[0,L_x]\times[0,L_y]$. LSVs form and dominate the system when the domain aspect ratio $δ= L_x/L_y \approx 1$, while unidirectional jets predominate at $δ\gtrsim 1.1$. At intermediate $δ$, both structures are metastable, with noise-induced transitions between LSVs and jets. We derive and verify predictions for the dependence of kinetic energy E and flow polarity on the nondimensional control parameters. We further collect detailed statistics on the lifetimes of LSVs and jets from DNS runs that are up to 10738 viscous diffusive times long. The distribution of the lifetimes is consistent with that of a memoryless process. Our DNS show an exponential dependence of the mean lifetime on $δ$. Mean lifetimes depend sensitively on the Reynolds number Re: as Re increases, the energy gap between LSV (lower E) and jet states (higher E) arising from anisotropic dissipation increases, leading to an approximately exponential increase in lifetimes with Re for both LSVs and jets. Similarly, as the forcing scale decreases, transitions become less frequent. We study the transitions in detail, revealing that they occur in two stages: an initial, rapid redistribution of kinetic energy by nonlinear triadic interactions deforms LSVs into jets or vice versa. In the second stage, the energy of the newly formed structure slowly adjusts to its associated equilibrium value on a longer, viscous timescale, producing hysteresis. Our findings shed new light on the dynamics of coherent large-scale structures in anisotropic turbulence.