The evolution of the double-diffusive instability: Salt fingers

Abstract

The finite-amplitude growth of finger convection at an interface of two uniform solutions is studied to determine the processes that govern the scale and amplitude of the convection, the growth of the fingering interface, and the transition of the convection to turbulence. A conceptual model of fingering processes is provided and details are studied by means of direct numerical simulation. The simulations obtain full finger convection and turbulence for ratios of viscosity to diffusivities in the range between 1 and 10. The study shows that the evolution of finger convection in its entirety is characterized by the scale and amplitude of the fastest growing finger mode. In the parameter range studied, the growth of the fingering interface is found to be controlled mostly by molecular diffusion. Convective flux divergence only plays a secondary role. The growth of the interface is shown to have the effect of increasing the horizontal scale of the convection while decreasing the buoyancy flux. However, the kinetic and potential energies remain statistically stationary for fully developed finger convection. Density inversion developed within finger convection is shown to play an important role in the breakup of finger structures into turbulence. The significance of ‘‘collective’’ instability in determining this transition is not substantiated by the simulation for the parameter values studied here.