Alongside classical effects driven by gravity or surface tension in non-isothermal fluids, the present experimental study concentrates on other exotic (poorly known) modes of convection, which are enabled in a fluid layer delimited from below by a hot plate and unbounded from above when its container is inclined to the horizontal direction. By means of a concerted approach based on the application of a thermographic visualization technique, multiple temperature measurements at different points and a posteriori computer-based reconstruction of the spatial distribution of wavelengths, it is shown that this fluid-dynamic system is prone to develop a rich set of patterns. These include (but are not limited to), spatially localized (compact) cells, longitudinal wavy rolls, various defects produced by other instabilities and finger-like structures resulting from an interesting roll pinching mechanism (by which a single longitudinal roll can be split into two neighboring rolls with smaller wavelength). Through parametric variation of the tilt angle, the imposed temperature difference and the volume of liquid employed, it is inferred that the observable dynamics are driven by the ability of gravity-induced shear flow to break the in-plane isotropy of the system, the relative importance of surface-tension-driven and buoyancy effects, and the spatially varying depth of the layer. Some effort is provided to identify universality classes and similarities with other out-of-equilibrium thermal systems, which have attracted significant attention in the literature.

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.

Convection induced in a layer of liquid with a top free surface by a distribution of heating elements at the bottom can be seen as a variant of standard Marangoni–Rayleigh–Bénard Convection where in place of a flat boundary at constant temperature delimiting the system from below, the underlying thermal inhomogeneity reflects the existence of a topography. In the present work, this problem is investigated numerically through solution of the governing equations for mass, momentum and energy in their complete, three-dimensional time-dependent and non-linear form. Emphasis is given to a class of liquids for which thermal diffusion is expected to dominate over viscous effects (liquid metals). Fixing the Rayleigh and Marangoni number to 104 and 5 × 103, respectively, the sensitivity of the problem to the geometrical, kinematic and thermal boundary conditions is investigated parametrically by changing: the number and spacing of heating elements, their vertical extension, the nature of the lateral boundary (solid walls or periodic boundary) and the thermal behavior of the portions of bottom wall between adjoining elements (assumed to be either adiabatic or at the same temperature of the hot blocks). It is shown that, like the parent phenomena, this type of thermal flow is extremely sensitive to the specific conditions considered. The topography can be used to exert a control on the emerging flow in terms of temporal response and patterning behavior.