Modal stability analysis of the density-stratified plane Couette–Poiseuille flow

Abstract

Shear and density stratification strongly affect the flow mechanism of the different atmospheric and ocean flows. In this paper, we investigate the stability characteristics of plane Couette–Poiseuille (CP) flow with stable density stratification in the vertical direction. A modal stability analysis is carried out to examine the exponentially growing instability of stratified plane CP flow under different controlling parameters. The domain of the flow is periodic in streamwise and vertical directions. The stability problem is solved numerically using the spectral collocation method. The present analysis is carried out for Reynolds number Re=104 with different speeds of moving wall and different strengths of stratification. The results show that the mass diffusivity impact on the flow instability mechanism is almost negligible beyond the Schmidt number Sc≥20. The three-dimensional mode is generally the most unstable mode for density-stratified CP flow. However, the most unstable mode in unstratified CP flow is always two-dimensional. In contrast to unstratified CP flow, the density-stratified CP flow is unstable even moving wall velocity exceeds 70% of the center velocity of the plane Poiseuille flow component. It is also observed that the moving wall velocity and density stratification simultaneously affect the stability of the flow, which shows the importance of the shear and stratification in the flow.