The diffusive interface in double-diffusive convection

Abstract

A model of the diffusive interface in double-diffusive convection at high Rayleigh number is proposed. The interface is assumed to have a double structure: two marginally stable boundary layers from which blobs or thermals arise on the outer edges of the interface, separated by a diffusive core across which all transport takes place by molecular diffusion. The model is time-independent and comparison is made with unsteady ‘run-down’ experiments on the assumption that the experiments run down through a sequence of equilibrium states each of which can be considered separately. The model predicts a constant ratio of the buoyancy fluxes of the two components at a value equal to the square root of the ratio of their molecular diffusivities, and individual fluxes in reasonable agreement with the available experimental data. Some time-dependent features of the model are also examined.

Simulations of a double-diffusive interface in the diffusive convection regime

“…In contrast to the Kelley (1990) model of steady large-scale circulations driven by plumes from the boundary layers, Linden & Shirtcliffe (1978) breaking away of this unstable layer through a convective instability. The present simulations display elements of both theories, with a persistent unstable boundary layer present (figure 6c,d) that feeds quasi-steady plumes in support of the Kelley (1990) description, as well as periodically fluctuating flow and plume strength due to the formation of instabilities in the boundary layer also leading to shifts in the large-scale circulation in support of Linden & Shirtcliffe (1978). It should be noted that since the convection usually consists of only a single cell the small domain size is likely to be exerting an influence on the flow.…”

“…Linden & Shirtcliffe 1978;Newell 1984;Fernando 1989;Kelley 1990;Worster 2004). Convection begins at t ≈ 2 h when the gravitationally unstable boundary layers break away from the stable interface core.…”

“…In § 6, we shall provide a possible explanation in terms of the interface stability. Worster (2004) has formulated an extension of the Linden & Shirtcliffe (1978) model of the diffusive interface that includes time dependence. The application of this model to laboratory experiments has found good agreement, and shows that the evolution of the diffusive interface is often dependent on the initial conditions.…”

“…This can be seen in figure 1, and results in gravitationally unstable boundary layers above and below the stable interface core. This boundary layer is ultimately responsible for producing turbulence and mixing in the mixed layers, and a number of previous studies have proposed mechanisms to describe the coupling between the boundary layer and the mixed layer (Linden & Shirtcliffe 1978;Fernando 1989;Kelley 1990). Kelley (1990) describes a model that is based on a large-scale circulation within the mixed layers.…”

“…The formulation of many phenomenological models of the diffusive interface from previous studies has been based on the assumption of molecular fluxes through the interface core (Linden & Shirtcliffe 1978;Newell 1984;Kelley 1990). Furthermore, the field observations of Padman & Dillon (1987) and Timmermans et al (2008) have shown a close agreement between F mol T and the F T predicted by different laboratorybased flux laws.…”