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

Abstract

Three-dimensional direct numerical simulations are performed that give us an in-depth account of the evolution and structure of the double-diffusive interface. We examine the diffusive convection regime, which, in the oceanographically relevant case, consists of relatively cold fresh water above warm salty water. A 'double-boundary-layer' structure is found in all of the simulations, in which the temperature (T) interface has a greater thickness than the salinity (S) interface. Therefore, thin gravitationally unstable boundary layers are maintained at the edges of the diffusive interface. The TS-interface thickness ratio is found to scale with the diffusivity ratio in a consistent manner once the shear across the boundary layers is accounted for. The turbulence present in the mixed layers is not able to penetrate the stable stratification of the interface core, and the TS-fluxes through the core are given by their molecular diffusion values. Interface growth in time is found to be determined by molecular diffusion of the S-interface, in agreement with a previous theory. The stability of the boundary layers is also considered, where we find boundary layer Rayleigh numbers that are an order of magnitude lower than previously assumed.

An axisymmetric non-hydrostatic model for double-diffusive water systems

“…Hilgersom et al: An axisymmetric non-hydrostatic model for double diffusion Yoshida and Nagashima (2003) have shown that 2-D numerical models are already well able to simulate small-scale processes in laboratory set-ups. On a larger scale, Sommer et al (2014) confirm the findings of Carpenter et al (2012) with 2-D DNS and high-resolution measurements of a double-diffusive staircase in Lake Kivu for density ratios larger than 3, noting that in these systems external turbulence by shear or internal waves should be absent to maintain diffusion as the main driver for salt and heat transport. Noguchi and Niino (2010a, b) used 2-D DNS to study the spontaneous layer formation in the double-diffusive convection regime and explore the layer formation from the nonlinear evolution of disturbances.…”

“…The vertical saline and thermal density fluxes across the interface, F c , are calculated on each grid location by time differentiating the salt and heat volumes above the interface according to Carpenter et al (2012):…”

“…The simulated salt and heat fluxes are compared with theoretical fluxes based on molecular diffusivities and doublediffusion-specific eddy diffusivities according to the equation (Carpenter et al, 2012) …”

“…For systems of double-diffusive convection, we calculate the evolution of the boundary layer thicknesses h c according to Carpenter et al (2012):…”

“…Their 3-D simulations of large-scale instability in salt-fingering systems are the first known successful direct numerical simulations (DNSs). Carpenter et al (2012) were among the first to model systems in the double-diffusive convection regime with 3-D DNS. Their detailed simulations showed that, in this regime, the salt and heat fluxes across the interface are largely governed by molecular diffusion and that these salt and heat diffusion rates control the thickness of the salt and heat interface, respectively.…”