Active suppression of finite amplitude Rayleigh-Bénard convection

(Received ?? and in revised form ??) We study by a fully nonlinear, three-dimensional pseudospectral, time-splitting simulation the feedback control of a layer of fluid heated from below. The initial condition corresponds to a steady, large-amplitude, preferred convection state obtained at Prandtl number of 7.0 and Rayleigh number of 10 4 , which is about six times the Rayleigh critical value. A robust controller based on the LQG (Linear-Quadratic-Gaussian) synthesis method is used. Both sensors and actuator are thermal-based, planar, and assumed to be continuously distributed. The simulated results show that large-amplitude steady-state convection rolls can be suppressed by the linear LQG controller action. The Green's function of the controller gives the shape of the control action corresponding to a point measurement. In addition, for Rayleigh numbers below the proportional feedback control stability limit, this controller appeared to be effective in damping out steady-state convection rolls as well. However, in a region very near the proportional control stability limit, proportional control action induces subcritical g-type hexagonal convection, which is obtained here through direct simulations. Note that well above this proportional control limit, the LQG still damps out all convection. Check cases to validate the nonlinear plant model are also performed by comparison with published results.