Instabilities of buoyancy-induced flow along vertical cylinder in thermally stratified medium

Abstract

In this paper, the instability of the buoyancy-driven boundary layer on a vertical cylinder is considered. We provide a mathematical description of a vertical cylinder immersed in a stably stratified fluid, and the analytical solutions of the basic flow are derived. Based on linear stability analysis, the effects of Prandtl number and transversal curvature have been investigated. It is found that the most unstable mode for Pr = 0.7 is three-dimensional for the cylindrical radii between 0.03 and 46, while the critical modes are axisymmetric for Pr = 7 and 100. All the results for different Pr are consistent with those of the vertical plate when the radius is large enough. Additionally, for absolute instability analysis, there exists absolute instability in the present model when the dimensionless radius is less than 0.31, which is quite different from the results obtained in the vertical plate. These encouraging results revealed in this paper should be helpful for understanding such a buoyancy-driven flow system.