LAUSR

This paper investigates the impact of hydrodynamic dispersion on the stability of free convection in a saturated horizontal porous layer subject to a transient vertical concentration gradient and a steady horizontal background flow. A linear stability analysis (LSA) was conducted using the quasi-steady-state approximation to obtain neutral stability curves, critical times, and the corresponding wavenumbers as a function of dispersivity ratio (α) and longitudinal dispersion strength (β). The LSA results showed that the dispersive boundary layer becomes less unstable as longitudinal and transverse dispersivity increase. In addition, for the isotropic dispersive system with α = 1, the critical time and its corresponding wavenumber follow τc = 167.6/(1 − β) and κc = 0.0696 (1 − β), respectively. The nonlinear dynamics of the system were studied by examining the interaction of convective fingers, dissolution flux, and the time-dependent Sherwood number. Finally, the results were applied to 24 deep saline aquif...