Dynamics of large-scale flow states in turbulent Rayleigh-Bénard convection in a cubic container: A low-dimensional transition manifold approach

We investigated the transitions between large-scale circulations (LSC) in a closed cubic Rayleigh-Bénard cell, with no-slip velocity boundaries. The simulations were performed at a fluid of Prandtl number Pr = 0.7 and Rayleigh numbers Ra = 10⁶ and 10⁷, assuming thermally insulated sidewalls. We observed that the system bounces between four long-lived LSC (LL-LSC) state aligned along the diagonals, via short-lived LSC (SL-LSC) state aligned along the edges, and the decoherent state. The transitions between the states are induced by the destabilizing action of intense vortices, which are found on both sides of the LSC. The frequency of transitions is higher for the lower Ra due to larger values of vorticity fluctuations in the system. We, thereafter, applied time lagged independent coordinate analysis technique (TICA) for dimensionality reduction of the data aiming for a more energy and time efficient analysis. The TICA analysis confirmed the presence of four prominent clusters corresponding to the four LL-LSC states. Further application of low-dimensional transition manifold analysis, faithfully captures the transition pathways between the states.