Double-Diffusive Interleaving: Properties of the Steady-State Solution

Double-diffusive interleaving is examined as it progresses from a linear instability toward finite amplitude. When the basic stratification is in the “finger” sense, the initial series of finger interfaces is unstable and one grows in strength at the expense of the others. At an intermediate stage of its development, the interleaving motions pass through a stage when every second interface in the vertical is stable to double diffusion. At a later time this interface turns into a “diffusive” double-diffusive interface. This study takes the fluxes of heat and salt across both the finger and diffusive interfaces to be given by the laboratory flux laws, and the authors ask whether a steady state is possible. It is found that the fluxes across the diffusive interfaces must be many times stronger relative to the corresponding fluxes across the finger interfaces than is indicated from existing flux expressions derived from laboratory experiments. The total effect of the interleaving motion on the vertical fluxes of heat and of salt are calculated for the steady-state solutions. It is found that both the fluxes of heat and salt are upgradient, corresponding to a negative vertical diffusion coefficient for all heat, salt, and density. For moderate to large Prandtl numbers, these negative effective diapycnal diffusivities of heat and salt are approximately equal so that the interleaving process acts to counteract some of the usual turbulent diapycnal diffusivity due to breaking internal waves.