Double-diffusive convection at high and low Prandtl numbers.

摘要

Double-diffusive convection takes place in stably-stratified fluids where two or more components (most commonly temperature and chemical composition) control the density of the fluid and diffuse at different rates. This instability can occur in one of two regimes, the "fingering" or "diffusive" case. In such systems, the presence of double-diffusive convection can greatly enhance vertical mixing of the fluid, and often leads to modification of the density profile into a striking "staircase" of well-mixed layers. Applications of the fundamental mechanism have been noted for areas as diverse as the Earth's atmosphere and the interiors of stars, and formulated more generally as "multi-component convection." In the present work, I will focus on two regimes: the oceanographic case where the instability was first discovered and where its effects have been most studied, and the astrophysical case, where both the fingering and diffusive forms of the instability have been suggested as important transport-controlling processes in stellar and planetary interiors.;Since the discovery of the instability some fifty years ago, its effects have been studied in the laboratory and the ocean, but some discrepancies between these results have rendered a detailed understanding of double-diffusive transport and staircases elusive. Numerical studies allow detailed evaluation of the assorted secondary instability theories that would resolve these discrepancies; but the computational challenges of the problem have made extended three-dimensional simulations only recently tractable. The work collected here employs advances in computational power of the last few years to compare high-quality numerics with the state of the art of theory. Part I focuses on the oceanic fingering case. In it, we present the first three-dimensional simulations of oceanic fingering, derive a unified theory for large-scale structure formation in this regime, and then apply the theory to a numerical simulation showing spontaneous staircase formation. Part II treats the astrophysical regime. There we discuss preliminary results in hot the fingering and diffusive regimes, where the fluid properties present difficult numerical challenges, but our simulations combined with the theory of Part I show important implications for double-diffusion in these systems.