Discontinuous transitions towards vortex condensates in buoyancy-driven rotating turbulence

Abstract

Using direct numerical simulations of rotating Rayleigh–Bénard convection, we explore the transitions between turbulent states from a three-dimensional (3-D) flow state towards a quasi-2-D condensate known as the large-scale vortex (LSV). 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 region of existence of the LSV in parameter space, we find discontinuous transitions and we identify the presence of a hysteresis loop as well as a memoryless abrupt growth dynamics. 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.