Plume model for the boundary-layer dynamics in hard turbulence

‘‘Hard turbulence’’ has come to be associated with several features of high-Rayleigh-number Boussinesq convection: thermal plumes, intermittency, nonclassical Nu-Ra scaling (Nu∝${\mathrm{Ra}}^{2/7}$), large-scale circulation, and the strongly sheared thermal boundary layers that result. In this paper, we make use of one of these features, the plumes, to offer an explanation of recent measurements of ‘‘waves’’ propagating on the boundary layers. The measured ‘‘dispersion relation’’ is reproduced here by a scaling theory incorporating the drag force of buoyant plumes and the interaction of these plumes with the boundary layers.