Two-layer thermal convection in miscible viscous fluids

Abstract

The influence of a viscosity stratification on the interaction between thermal convection and a stable density discontinuity is studied, using laboratory experiments. Initially, two superposed isothermal layers of high-Prandtl-number miscible fluids are suddenly cooled from above and heated from below. By adjusting the concentrations of salt and cellulose, Rayleigh numbers between 300 and 3×107 were achieved for density contrasts between 0.45 % and 5 % and viscosity ratios between 1 and 6.4×104. Heat and mass transfer through the interface were monitored.Two-layer convection is observed but a steady state is never obtained since penetrative convection occurs. A new interfacial instability is reported, owing to the nonlinear interaction of the unstable thermal and stable chemical density gradients. As a result, the temperature condition at the interface is highly inhomogeneous, driving, on top of the classical small-scale thermal convection, a large-scale flow in each layer which produces cusps at the interface. Entrainment, driven by viscous coupling between the two layers, proceeds through those cusps. The pattern of entrainment is asymmetric: two-dimensional sheets are dragged into the more viscous layer, while three-dimensional conduits are produced in the less viscous layer. A simple entrainment model is proposed and scaling laws for the entrainment rate are derived; they explain the experimental data well.