Minimal model for double diffusion and its application to Kivu, Nyos, and Powell Lake

Double diffusion originates from the markedly different molecular diffusion rates of heat and salt in water, producing staircase structures under favorable conditions. The phenomenon essentially consists of two processes: molecular diffusion across sharp interfaces and convective transport in the gravitationally unstable layers. In this paper, we propose a model that is based on the one-dimensional description of these two processes only, and—by self-organization—is able to reproduce both the large-scale dynamics and the structure of individual layers, while accounting for different boundary conditions. Two parameters characterize the model, describing the time scale for the formation of unstable water parcels and the optimal spatial resolution. Theoretical relationships allow for the identification of the influence of these parameters on the layer structure and on the mass and heat fluxes. The performances of the model are tested for three different lakes (Powell, Kivu, and Nyos), showing a remarkable agreement with actual microstructure measurements.