Stability of the double-diffusive convection generated through the interaction of horizontal temperature and concentration gradients in the vertical slot

Previously, the double-diffusive convection (or the DDC) generated through the interaction between horizontal temperature and concentration gradients had been investigated by both experimental and computational studies. In the present study, we employ a theoretical approach by performing linear stability analysis to examine the stability characteristics of the DDC under a wide range of physical parameters. Results show that, under the competition between the two gradients, the stability can be discerned into thermal, salt-finger, and diffusive types, where all are influenced by both the Prandtl number Pr and Lewis number Le. The onset of instability can be the stationary shear mode (or the SSM) or the oscillatory buoyant mode (or the OBM), depending on both Pr and Le. Specifically, for the solute Grashof number Gs < 10, the onset of instability changes from SSM to OBM at the transition boundary Pr = 12.5; for the thermal Grashof number Gt < 10, the transition boundary is governed by the relation Pr = 12.5Le−1.11 + 0.46. We compare the present results with those of previous studies to justify the linear stability analysis’s correctness and infer that the DDCs observed by previous experiments and nonlinear computations are nonlinear salt-finger convection.