Benard-Marangoni convection in a differentially heated cylindrical cavity

12 pagesThe work described in this paper concerns the study of a Bénard–Marangoni convection problem in a differentially heated cylindrical cavity. The study had two main aims; first to justify from a numerical point of view the transitions that have been reported in several experiments as the aspect ratio is varied and, second, to study both theoretically and experimentally the role of vertical and horizontal temperature differences in lateral heating convection. Initially, we analyzed the role of the aspect ratio in layers where a dynamic flow is imposed through a nonzero temperature gradient at the bottom. The basic solutions are linear or return flows depending on different parameters. Depending on the vertical temperature difference and other heat-related parameters, the problem bifurcates either to stationary or oscillatory structures. Competing solutions at codimension two bifurcation points were found: stationary radial rolls with different wavenumbers and radial rolls together with hydrothermal waves. For small aspect ratios it was found that the Biot number does not influence the bifurcations, whereas for large aspect ratios it does. In the second part we present experimental results obtained at larger aspect ratios and for stronger surface tension effects. The role of horizontal gradients to determine the type of bifurcation both in experiments and in numerics approaching experimental conditions are discussed along with the role of vertical temperature gradients in comparison with previous theoretical works. Good agreement was obtained in terms of patterns, bifurcation sequences, and thresholds between theory, where eigenfunctions are obtained by tuning two parameters in a linear stability analysis, and experiments, where patterns are due to a nonlinear secondary bifurcation sequence caused by increasing one of the parameters