Convective and absolute instabilities of double-diffusive convection with shear

Abstract

In this study, we investigate the spatiotemporal instability of double-diffusive convection with and without a Couette flow, focusing mainly on the characters of transverse rolls. In the absence of shear, double-diffusive convection is always absolutely unstable even in the oscillatory instability regime, which is different from other flows that can also take the form of oscillatory convection. In the pure diffusive convection, before the transition from the oscillatory instability to steady instability, a saddle shift phenomenon is observed, which is related to the subcritical bifurcation of the steady branch. The presence of shear breaks the symmetry of oscillatory instability and along the neutral stability curve the spatiotemporal evolution of disturbance is determined by the competition between the shear intensity and the phase speed of oscillatory eigenmode traveling upstream. Therefore, as the shear intensity increases a transition from the absolute instability to the convective instability is expected, whereas as buoyancy strengthens the absolute instability eventually sets in again. On the other hand, the spatiotemporal instability of the sheared fingering convection is similar to the sheared Rayleigh–Bénard convection, in which the flow always undergoes a transition from the convective instability to absolute instability. In this case, increasing the Prandtl number or decreasing the diffusivity ratio between the two components, the region of convective instability expands due to the increasing viscous dissipation caused by the shear flow.