Diffusion in laminar Rayleigh–Bénard convection: Boundary layers versus boundary tubes

Abstract

New results on the advection–diffusion of a passive tracer in a periodic system of hexagonal Rayleigh–Bénard convection cells at high Péclet number P=Lv/D0≫1 are presented, where L is the characteristic length scale of the flow, v is the velocity amplitude, and D0 is the molecular diffusivity. It is shown that the transport properties of this three-dimensional (3-D) laminar flow are drastically different from those of the well-studied two-dimensional convection rolls. The 3-D topology of the streamlines in the hexagonal convection leads to the formation of boundary tubes near the axes and the edges of the hexagons, in addition to the standard boundary layers found near the faces and the bases. A scaling theory is given and confirmed by test-particle simulations that show that the transport enhancement due to the hexagonal cells is controlled by the boundary tubes and scales only logarithmically with P. On the other hand, it is found that the subdiffusive regimes of transport in hexagons are similar to those found in other flows with constrained streamlines. The described effects can be used for the experimental investigation of structures in thermal convection.