Absolute and convective instabilities of natural convection flow in boundary-layer regime

The spatiotemporal instability of the buoyancy-driven flow adjacent to a vertically heated wall, which is immersed in thermally stratified medium, is studied theoretically and numerically. The temperature gradients ratio between the wall and the ambient fluid is shown to lead to rich scenario of absolute-convective instability transitions. The direct numerical simulations consistent with the theoretical prediction are presented. The supercritical steady state, found in previous simulations of the natural convection in vertically heated square cavity, is explained in terms of the convective instability, and the nonlinear effect on the convectively unstable waves is discussed as well.