Interface structure and flux laws in a natural double-diffusive layering

Abstract

The diffusive regime of double‐diffusive convection generates staircases consisting of thin high‐gradient interfaces sandwiched between convectively mixed layers. Simultaneous microstructure measurements of both temperature and conductivity from the staircases in Lake Kivu are used to test flux laws and theoretical models for double diffusion. Density ratios in Lake Kivu are between one and ten and mixed layer thicknesses on average 0.7 m. The larger interface thickness of temperature (average 9 cm) compared to dissolved substances (6 cm) confirms the boundary‐layer structure of the interface. Our observations suggest that the boundary‐layer break‐off cannot be characterized by a single critical boundary‐layer Rayleigh number, but occurs within a range of O(102) to O(104). Heat flux parameterizations which assume that the Nusselt number follows a power law increase with the Rayleigh number Ra are tested for their exponent η. In contrast to the standard estimate η = 1/3, we found η = 0.20 ± 0.03 for density ratios between two and six. Therefore, we suggest a correction of heat flux estimates which are based on η = 1/3. The magnitude of the correction depends on Ra in the system of interest. For Lake Kivu (average heat flux 0.10 W m−2) with Ra = O(108), corrections are marginal. In the Arctic Ocean with Ra = O(108) to O(1012), however, heat fluxes can be overestimated by a factor of four.

Double‐diffusive interfaces in Lake Kivu reproduced by direct numerical simulations

“…Double-diffusive staircases are found below~100 m depth containing up to 300 interfaces and mixed layers [Newman, 1976;Schmid et al, 2010;Sommer et al, 2013a]. An algorithm was used to extract the T and S properties of 9401 interfaces and adjacent mixed layers from the temperature and conductivity profiles.…”

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

“…It follows that the density flux ratio can also be rewritten as R 0 F 5R 0 q s r [e.g., Sommer et al, 2013], where R 0 q is defined by equation (6) using the differences across the step.…”

“…The destabilizing temperature increase toward the sediment is caused by geothermal heating and various warm subaquatic springs. Lake Kivu is an ideal system for studying double diffusion with approximately 300 well-mixed layers distributed almost throughout the entire water column [Newman, 1976;Schmid et al, 2010;Sommer et al, 2013].…”

“…The initial temperature profile has been chosen arbitrarily with an ''erf'' shape, and the boundary conditions have been applied in this case by fixing the heat flux. The imposed value is the same (/ H 5100 mW m 22 ) at the upper and lower boundary of the domain [Sommer et al, 2013]. …”

“…The first case is Powell Lake, with a clearly visible staircase structure in the deep water [Osborn, 1973;Scheifele et al, 2014]. The staircase structure of the second case, Lake Kivu, has been intensively studied through the collection of a large number of microstructure (conductivity, temperature, and depth) profiles [Sommer et al, 2013]. The last examined case, Lake Nyos, is particularly interesting because the formation dynamics of the typical double-diffusive structure has been observed and temperature and salinity profiles have been measured over some years [Schmid et al, 2003[Schmid et al, , 2004.…”