Compressibility effects on the first global instability mode of the vortex formed in a regularized lid-driven cavity flow

Abstract

Abstract The effect of compressibility on the stability of a two-dimensional (2D) lid-driven cavity flow was investigated using a global linear stability analysis in this study. In a previous study, Bergamo et al. (2015) [12] revealed that compressibility has a stabilizing effect on dominant instability modes of this flow. However, the detailed mechanism of this stabilization effect has not been elucidated. The present study focused on the mechanism of this stabilizing effect on the first instability mode which causes a periodic oscillation to a primary vortex formed in the cavity. Our results show that the compressibility has a stabilizing effect on this flow due to the baroclinic torque and vorticity-dilatation term which appear in the vorticity transport equation. The distribution of these terms show that the vorticity-dilatation effect suppresses the changes in the perturbed vorticity (i.e., stabilizes the flow), and the baroclinic torque deforms the perturbed vorticity distribution. Furthermore, the effect of baroclinic torque was quantitatively estimated by solving the forced compressible stability problem in which the corresponding linearized equations are artificially forced to cancel the baroclinic torque. The results clearly show that the baroclinic torque decreases the growth rate of the first instability mode. However, the quantitatively estimated variation in the critical Reynolds number caused by the baroclinic torque indicates this term is not the most dominant mechanism of the stabilization effect and dilatation effects would be more significant.