Transient growth in diffusive convection with and without shear

A linear nonmodal analysis is performed to investigate the transient growth of diffusive convection in the absence/presence of a bounded Couette flow. The results first examine the properties of transient growth of the pure diffusive convection and interpret the mechanism to cause this growth. Then, the transient growth of diffusive convection with a Couette flow is investigated. Three nonmodal instability regimes regarding the transient growth of the mixed convection are identified, and two mechanisms of the double diffusion to enhance the lift-up mechanism are revealed.