On the role of roughness valleys in turbulent Rayleigh–Bénard convection

Three-dimensional direct numerical simulations are used to characterize turbulent buoyant convection in a box-shaped Rayleigh–Bénard cavity with a rough bottom plate made of a series of square based blocks separated by valleys. The cavity is filled with water. The Rayleigh number varies over five decades up to $10^{10}$. As mentioned in the literature, three successive heat transfer regimes are identified: from inactive roughness (I) to a regime (III) where the heat transfer increase is larger than that expected from only surface increase due to roughness. The heat transfers of the transitional regime II are particularly intense. After validation against experimental and numerical data from the literature, we highlight the role of the fluid retained within valleys (the inner fluid). It is shown that only the heat transfer across the fluid interface between the cavity bulk and the inner fluid is responsible for changes in the overall heat transfer at the rough plate, with an exponent of the heat transfer scaling law close to $1/2$ in regime II. The valley flow typifies the limits of this regime: the blocks protrude from the thermal boundary layer while remaining within the kinetic boundary layer. As compared with regimes I and III, regime II is characterized by larger temperature fluctuations, especially near the rough plate, and a larger friction coefficient. A fluctuating rough fluid layer overlaying both blocks and valleys appears in regime III, in addition to the classic boundary layers formed along the plate geometry.