6 Concluding remarks

Both the experimental and numerical investigations indicate that the free surface boundary condition has a relatively small effect on the bulk flow structure. The main differences appear for both the velocity and temperature fields in the upper part of the cavity. The numerical models proved their ability to describe most of the experimental features. The main result of this work is the empirical evidence of a two-dimensional recirculating flow present at the free surface. The physical interpretation of this flow is rather intuitive, exploring the idea of a molecular surface layer. The structure and properties of surface monolayers are functions of the molecular arrangement and their interactions. Surface active agents may significantly modify the physical structure of the surface and hence its mechanical properties. However, our experiments showed that there was no effect on the anomalous surface flow. Absent any physical explanation, the observed surface effect is nevertheless reproducible in our experiments and presumably can be found in many other free surface flow configurations. Hence, our present attempt to explore this phenomenon through a computational model of a thin surface layer may be useful. Our simple model does not pretend to describe the physics at the surface. For this purpose, a reliable description of intermolecular forces for a given physical surface structure must be known a priori, to provide values for the surface access energy, surface viscosity, and molecular depth of the layer. Our present aim is rather to indicate that the proper interpretation of some free surface flow patterns may need a reassessment of the standard boundary conditions. Experimental and numerical investigation of natural convection in a cube with two heated side walls, Topological Fluid Mech., eds. visible when viewed from the side of the cavity, but was clearly visible from above. To explore this model, some numerical computations were performed in which the free surface was represented as an impermeable but mobile layer three nodes thick in which the vertical velocity component u y was artificially suppressed. The bulk 3D motion below the surface drives a 2D motion in the layer. To simulate the thin but finite thickness of this layer, a non-uniform mesh was used with the three points located at dimensionless distances of 0.00167, 0.00333 and 0.006 below the surface (compared with a cavity depth of 0.9). These dimensions are far from the molecular scale and were chosen only to ensure code stability. The kinematic boundary …