Effects of horizontal gradients on thermohaline instabilities in a thick porous layer

Linear stability analysis is used to examine the effects of horizontal gradients of temperature and salinity on characteristics of thermohaline instabilities in a saturated, homogeneous, isotropic, horizontal porous layer. The emphasis is on obtaining analytical results valid in the limit of large Rayleigh numbers. The present results are compared with an earlier infinite medium study (Sarkar and Phillips, to appear in J. Fluid Mech.) to understand how horizontal impervious boundaries affect the dynamics. It appears that the geometric constraints imposed by the boundaries tend to eliminate the most effective of unstable modes. Thus the boundaries have a stabilizing effect. Necessary conditions for the boundaries to not have an appreciable effect on the overall dynamics of instabilities are also obtained. The properties of both neutrally stable and supercritical disturbances are described. The supercritical convection cells are similar to salt fingers or horizontal interleaving depending on whether the vertical Rayleigh number is positive or negative, respectively. This is in contrast to the critical modes (i.e., neutrally stable disturbances corresponding to the minimum vertical Rayleigh number) where the convection cells are almost horizontal and are about as thick as the porous layer.