Fluxes through double-diffusive staircases at low Prandtl number.

Oscillatory double-diffusive convection (ODDC) occurs in regions of fluid characterized by a stabilizing composition gradient and a destabilizing temperature gradient. As demonstrated by previous studies, ODDC often evolves into a ‘staircase’ structure, consisting of stacks of fully convective regions separated by stable interfaces. In this regime of layered convection, the governing parameters are the Prandtl number, the diffusivity ratio, the density ratio R, and the height of the steps. In this work, we systematically study the dynamics of layered convection for a uniform staircase (using DNS in a triply-periodic domain) and propose a new model for the temperature, composition and density flux through the staircase as functions of the input parameters. We also demonstrate that these flux laws remain valid in slowly evolving staircases observed in DNS with fixed flux boundary conditions.