Multiple states in Rayleigh-Bénard convection: A triad interaction manipulation framework

Recently, multiple convection-roll states were identified in two-dimensional planar Rayleigh-Bénard convection (Wang et al. 2020, Phys. Rev. Lett., 125(7), 074501). Different convection-roll states in the initial condition yielded these multiple states in simulations. Herein, we propose a framework that intrusively suppresses select non-linear triad interactions to yield these multiple states irrespective of the initial state. The intrusive framework is based on the observation that convection-roll wavenumber mediates triadic scale interactions resulting in both kinetic and thermal energy cascades which are dominant energy transfer processes in statistically stationary roll states. Suppression of these cascades mediated by a candidate wavenumber hinders the formation of convection rolls at that wavenumber. As a consequence, another candidate wavenumber which is allowed to mediate energy to establish the cascade processes, forms the convection rolls. In case, no stable convection-roll states are possible, this technique does not yield any convection rolls making it a suitable method for discovery of multiple states. This forcing technique is able to yield accurate predictions of statistical quantities such as Nusselt number and volume-averaged Reynolds numbers. The convection-roll states yielded using this technique may be used as initial conditions for direct simulations quickly converging to the target roll state without taking long convergence routes involving state transitions.