On the role of heat source location and multiplicity in topographically controlled Marangoni–Rayleigh–Bénard convection

Abstract

Periodically distributed wall-mounted hot blocks with a cubic shape located at the bottom of a layer of liquid with a free top interface tend to create patterns in their surrounding fluid that are reminiscent of the classical modes of Marangoni–Rayleigh–Bénard convection. Through direct numerical solution of the governing equations in their complete three-dimensional unsteady and nonlinear formulation, we investigate this specific subject giving much emphasis to understanding how ensemble properties arise from the interplay of localized effects. Through the used numerical framework, we identify the emerging planforms and connect the statistics of the associated heat transport mechanisms with the spatially averaged behaviour of the underlying thermal currents. In some cases, all these features can be directly mapped into the topography at the bottom of the layer. In other circumstances, these systems contain their own capacity for transformation, i.e. intrinsic evolutionary mechanisms are enabled, by which complex steady or unsteady patterns are produced. It is shown that self-organization driven by purely surface-tension or mixed buoyancy–Marangoni effects can result in ‘quantized states’, i.e. aesthetically appealing solutions that do not depend on the multiplicity of wall-mounted elements.