The stability of electrohydrodynamic flow between two horizontal plates with a vertical electrical conductivity gradient has been investigated in the presence of an imposed weak shear flow. The weak shear flow is driven by the horizontal pressure gradient, and the electrical conductivity gradient is generated by the concentration variation of the charge-carrying solute. An external electric field is applied across the fluid layer, and then the interaction between the unstable stratification of electrohydrodynamic flow and the shear arising from the plane Poiseuille flow is studied. A linear stability analysis has been implemented by considering both the longitudinal and transverse modes. Unlike the thermally stratified plane Poiseuille flow in which the longitudinal mode always dominates the onset of instability and is virtually unaffected by the superimposed shear flow, the instability of this mixed electrohydrodynamic–Poiseuille flow system is found to depend heavily on the shear flow, and the transverse mode may prevail over the longitudinal mode when the momentum of shear flow is sufficiently small. Particularly, an oscillatory longitudinal mode is found to exist, and it may become the critical mode when the conductivity gradient is small enough. The present results verify that an imposed weak shear flow may enhance the electrohydrodynamic instability in a fluid layer with electrical conductivity gradient.

Thermal convection in a two-layer system comprised by a fluid layer overlying a layer of porous media saturated with the same fluid has been investigated. The system is heated from below and subjected to a horizontally plane Poiseuille flow. The interaction between both instability mechanisms, the unstably stratification and the shear arising from the plane Poiseuille flow, is studied and a completely linear stability analysis has been carried out by considering both longitudinal rolls ͑LRs͒ and transverse rolls ͑TRs͒. It is found that the neutral curves of both modes may be bimodal, which is dependent on the depth ratio, the ratio of the depth of fluid layer to that of the porous layer. The stability characteristics of LRs are found to be invariant with the Reynolds number based on the horizontal Poiseuille velocity and the Prandtl number of the fluid, and the instability is always dominated by this mode if the Reynolds number is within low or moderate strength. The superimposed Poiseuille flow seems to exert a stabilizing effect on the traveling TRs and the critical transverse mode tends to be within the porous layer with low propagating speed. However, if the Reynolds number is sufficiently large, a shear instability mode appears abruptly with higher propagating speed and then dominates the system instability.

No abstract

No abstract

No abstract