  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 $\delta = L_x/L_y \approx 1$, while unidirectional jets
predominate at $\delta \gtrsim 1.1$. At intermediate $\delta$, 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 $\delta$. 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.
