Double-diffusive instability in a thin vertical channel

Abstract

Double-diffusive convection in the finger regime is studied using direct numerical simulations in a confined domain. For narrow (1–4 mm horizontal extent) domains, we demonstrate active instabilities that are uniquely double-diffusive, or in other words that no instabilities develop when differential diffusion is not present. The novel double-diffusive instabilities are influenced by the boundaries, but demonstrate complex time-dependent evolution down to lateral extents of 1.25 mm. We quantify the energetics, the horizontal asymmetry, and the buoyancy flux due to the instability. We utilize these results to characterize the instability within regimes and point out that while coherent instabilities associated with larger gaps are well characterized by the ratio of diffusive effects to buoyancy forces (the time dependent Grashof number), for smaller gap widths, regime characterization is more difficult. Nevertheless, even at a gap of 1.25 mm, the instability remains robust, and thus it can be concluded that double diffusion can be employed to drive localized mixing in highly confined settings for which single constituent Rayleigh–Taylor does not manifest.