Published online by Cambridge University Press: 12 September 2018
The motion of a free-moving plate atop turbulent thermal convection exhibits diverse dynamics that displays characteristics of both deterministic and chaotic motions. Early experiments performed by Zhong & Zhang (Phys. Rev. E, vol. 75 (5), 2007, 055301) found an oscillatory and a trapped state existing for a plate floating on convective fluid in a rectangular tank. They proposed a piecewise smooth physical model (ZZ model) that successfully captures this transition of states. However, their model was deterministic and therefore could not describe the stochastic behaviours. In this study, we combine the ZZ model with a novel approach that models the stochastic aspects through a variational inequality structure. With the powerful mathematical tools for stochastic variational inequalities, the properties of the Markov process and corresponding Kolmogorov equations could be studied both numerically and analytically. Moreover, this framework also allows one to compute the transition probabilities. Our present work captures the stochastic aspects of the two aforementioned boundary–fluid coupling states, predicts the stochastic behaviours and shows excellent qualitative and quantitative agreements with the experimental data.