Effects of horizontal gradients on thermohaline instabilities in infinite porous media

Abstract

Thermohaline instabilities produced by horizontal gradients of temperature and salinity in a saturated homogeneous isotropic infinite porous medium are studied using linear stability analysis. In the basic state horizontal gradients of temperature and salinity are taken to be mutually compensating, so that the basic-state fluid density does not vary horizontally. It is found that under these conditions the fluid is always unstable. In a porous medium, assuming the solid matrix to be impervious to dissolved salts, the effective advection rates of heat and dissolved salts are different. Because of this difference any disturbance involving a horizontal component of displacement creates net horizontal density gradients, and thus destabilizes the predominantly hydrostatic force balance. When the vertical Rayleigh number is positive, the typical velocity field consists of almost vertical layers of fluid sliding past each other in opposite directions (salt fingers). When the vertical Rayleigh number is negative the fluid layers are almost horizontal, similar to the interleaving observed in Newtonian fluids. Resulting perturbation fluxes of heat and salt always tend to reduce the basic-state concentration gradients, and typically also the gravitational potential energy of the fluid. We also make some tentative estimates regarding properties of these instabilities at the fully developed state. It seems that thermohaline fine structures, similar to oceanic observations, are also possible in porous media.