Discontinuous Transitions Towards Vortex Condensates in Buoyancy-Driven Rotating Turbulence: Analogies with First-Order Phase Transitions.

Employing immediate analogies with phase transitions in equilibrium statistical mechanics, we explore the transitions between turbulent states from a 3D flow state towards a quasi-2D condensate known as the large-scale vortex (LSV). Using direct numerical simulations of rotating Rayleigh-Benard convection, we vary the Rayleigh number Ra as control parameter and study the system response (strength of the LSV) in terms of order parameters assessing the energetic content in the flow and the upscale energy flux. By sensitively probing the boundaries of the domain of existence of the LSV, we find discontinuous transitions and we identify the presence of a hysteresis loop as well as nucleation & growth type of dynamics, manifesting the striking correspondence with first-order phase transitions in equilibrium statistical mechanics. We show furthermore that the creation of the condensate state coincides with a discontinuous transition of the energy transport into the largest mode of the system.