Thermal coupling in layered convection: evidence for an interface viscosity control from mechanical experiments and marginal stability analysis

Abstract

Convection in a two-layer system (silicone oil over glycerol, in particular) is studied. Two types of studies have been performed. (1) In the laboratory, we analyse the dynamical role of the interface, by inducing roll-like motions in one of the liquid layers, using a system of two inversely rotating cylinders. Streamlines and velocities on both sides of the interface are measured, by observing suspended aluminum particles. The results strongly depend upon the sense of rotation of the cylinders (convergence or divergence), and upon the amplitude of the imposed velocity. This implies an interface strength, which is of the same order as the volume viscous strength, and that can be associated to a large interface viscosity. (2) A numerical study of convective marginal stability in a two-layer system has been performed. The physical properties of the silicone oil/glycerol system are used, and special attention is given to the influence of interface viscosity. The role of varying the depth ratio, the deformation of the interface, the temperature-dependence of interface tension, and the density ratio is reviewed. It is shown that none of these effects, when realistic values are taken, is able to modify the preferred type of coupling at the threshold: it remains “mechanical” coupling (downwellings in the upper layer remain above uprisings in the lower layer). However, the type of coupling is changed when the interface viscosity is introduced, with values compatible with the experimental observations: “thermal” coupling (uprisings above uprisings) becomes the preferred convective mode. This result removes the contradiction there was until now between the observation of “thermal” coupling in laboratory convection experiments, and the prediction of “mechanical” coupling obtained from marginal stability analysis and numerical experiments.