Stochastic and deterministic dynamics of free boundaries atop turbulent convection

We present a low-dimensional model that explains the coupled dynamics of floating boundaries that interact with turbulent flows in thermal convection. The model consists of Langevin-type, stochastic differential equations, which captures the deterministic and stochastic movements of boundaries shown in an earlier experiment J.-Q. Zhong et al. [ Phys. Rev. E 75, 055301(R) (2007)1539-3755 10.1103/PhysRevE.75.055301 ]. From the displacement, speed, and acceleration of the boundaries, we construct the force potentials that underlie two distinct boundary-size-dependent behaviors. Namely, we find a repulsive potential (when the boundary is small) that leads to an oscillatory state and an attractive potential (when the boundary is large) that leads to a trapped state. The boundary movements, which are subject to thermal convection underneath, also inform us of the mean speed and turbulent fluctuations of the flows.