Spontaneous suppression of the inverse energy cascade by the generation of shielded vortices 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. We vary a control parameter γ that measures the fraction of energy injected by the instability. As increases, the system undergoes two transitions. For growth rates below a first threshold γ < γ1, a regular large-scale vortex condensate forms. γ ≥ γ1, shielded vortices (SVs) emerge and coexist with the condensate. At a second, larger value γ2 of the control parameter, 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. It is observed that individual SVs are trapped in the lattice at small γ, up to a sharp threshold γ0, above which the mean square displacement of SVs increases linearly with time, i.e. the crystal melts, more rapidly as γ increases. Bi- and multistability is observed between the dense SV states (intact or molten SV crystal), the condensate and the mixed condensate-SV, over a wide range of  growth rates. Our findings provide new evidence for a strong dependence of two-dimensional turbulence phenomenology on the forcing.