High thermal Rayleigh number with double-diffusive finger convection: Effect of nonlinear equation of state

In this study, we numerically investigate the effects of the nonlinearity in the equation of state on the structure of fingers and the transport mechanisms of salt and heat in double-diffusive finger convection, utilizing the finite volume approach with high-accuracy schemes to solve the two-dimensional Navier-Stokes equations. Our system is characterized by a low buoyancy ratio and a high thermal Rayleigh number, with density variation modeled as quadratic in temperature and linear in salinity. Three cases of nonlinear parameters were examined: the linear case (epsilon = 0), weak nonlinear case (epsilon = 1), and highly nonlinear case (epsilon = 3). It is shown that increasing the nonlinear parameter enhances the buoyancy force acting on descending fingers more than on ascending ones, resulting in narrower and faster-growing descending fingers. Conversely, ascending fingers are appreciably damped, growing more slowly but with greater width. This asymmetry in finger development gives rise to distinct convective patterns between the upper and lower layers, significantly influencing the formation of mixed layers. The mixing process was also examined by analyzing the probability density function of salinity PDF(S*). Our findings reveal that as the nonlinear parameter increases, the amount of salt transported by descending fingers from the upper to the lower layer decreases. This reduction in salt transport indicates a corresponding decline in mixing efficiency with higher values of the nonlinear parameter.