Spontaneous suppression of the inverse energy cascade and formation of vortex crystals in instability-driven two-dimensional turbulence*

Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a  wavenumber-localised instability superposed on stochastic forcing, in contrast to previous studies of state-independent forcing. As the instability growth rate $\gamma$ increases, the system undergoes two transitions. For growth rates below a first threshold $\gamma<\gamma_1$, a regular large-scale vortex condensate (LSC) forms. For $\gamma \geq \gamma_1$, shielded vortices (SVs) emerge and coexist with the condensate. At a second, larger value $\gamma_2$ of the growth rate, the condensate breaks down, and a gas of weakly interacting vortices with broken symmetry spontaneously emerges,  characterised by preponderance of vortices of one sign only and suppressed inverse energy cascade. The number density of SVs in this broken symmetry state slowly increases via a random nucleation process. In the late-time limit a dense SV gas emerges, which persists down to small growth rates, where it  crystallises to form a hexagonal lattice. Bi- and multistability is observed between the LSC, the mixed LSC-SV and the dense SV states over a wide range of  growth rates. Our findings provide new evidence for a strong dependence of two-dimensional turbulence phenomenology on the forcing.