Numerical Study of Salt Fingers Dynamics: Effects of the Density Inversion

In the present study, numerical simulations have been employed to understand the effect of the density inversion on the finger structures dynamics and mixing process. A numerical methodology based on the finite volume method with high accuracy schemes were employed to solve the two-dimensional Navier-Stokes equations for high buoyancy ratio (R rho = 6) and moderate thermal Rayleigh number (RaT = 7 x 106). The density is assumed to depend quadratically on the temperature and linearly on the salinity. Three cases of nonlinear parameters were considered: linear case epsilon = 0, weak nonlinear case epsilon = 1 and highly nonlinear case epsilon = 3. A qualitative and quantitative description of the fingers dynamics emphasizing the mixing properties has been performed. It was found that the density inversion affect significantly the flow pattern, and its motions become asymmetric with respect to the mid-height of the computational domain as nonlinear parameter increase. In the nonlinear cases, the sinking fingers evolve quickly and dramatically increasing, owing to the enhancement of the buoyancy force acting them. The mixing properties were inspected by using the probability density function of the salinity PDF(S*). The results illustrate that the density inversion acts a significant role in the mixing process. It was shown that the increase in the nonlinear parameter enhances the dynamic of mixing in the lower layer of the system.