Critical transition in fast-rotating turbulence within highly elongated domains

We study rapidly rotating turbulent flows in a highly elongated domain using an asymptotic expansion at simultaneously low Rossby number Ro << 1 and large domain height compared with the energy injection scale, h = H/l(in) >> 1. We solve the resulting equations using an extensive set of direct numerical simulations for different parameter regimes. As the parameter lambda = (hRo)(-1) is increased beyond a threshold lambda(c), a transition is observed from a state without an inverse energy cascade to a state with an inverse energy cascade. For large Reynolds number and large horizontal box size, we provide evidence for criticality of the transition in terms of the large-scale energy dissipation rate.