Thermohaline convective instability in an inclined porous layer with permeable boundaries

Abstract

This study aims at investigating the onset of thermohaline convective instability in an inclined porous layer of finite width confined between two permeable boundaries. The instability in the flow is driven by the combined effect of temperature and solute concentration gradients acting vertically across the layer, and it depends on the angle of inclination at which that layer is inclined to the horizontal. This work complements previous studies on the double-diffusive convective instability by extensively discussing the effect of the solute concentration gradient for the case when the thermal and solutal buoyancy forces have comparable magnitudes and they act in the same and opposite directions. The investigation is illustrated by the results associated with the cases when the diffusivity ratio is thermally dominant, when the diffusivity ratio is thermally suppressed, and when the two components diffuse with the same intensity. A wide spectrum of the neutral stability curves are presented at different inclinations, which depict the instability in the basic state prevailing in the form of stationary and oscillatory modes. The neutral stability curves are seen to exhibit some exceptional behavior in the case when the thermal buoyancy and the solutal buoyancy act in the opposite directions. It is observed that the instability is always initiated by the non-traveling modes, except in the case when the thermal diffusivity is reasonably higher than the solutal diffusivity and when the two buoyant forces are acting in the opposite directions. The ratio of the two buoyant forces has an exceptionally non-monotonic impact on the instability, if considered in the vertical porous layer.