Convective and absolute instabilities in inclined buoyancy layers

Abstract

The linear instability of the buoyancy-driven flow adjacent to an inclined heated wall immersed in a thermally stratified medium is studied theoretically and numerically. For the temporally unstable system, spatiotemporal stability analysis is carried out to delineate the parameter space (Grashof number, Prandtl number, and tile angle) for convective/absolute instability. We provide an example of an absolute instability of the buoyancy layer on an inclined buoyancy layer. It is shown that the tile angle and Prandtl number have a dramatic influence on the spatial-temporal properties of the flow. For fixed Pr = 6.7, increasing tile angle decreases the domain of absolute instability, and when tile angle is greater than 20°, the absolute instability disappears. The flow will change from convectively unstable to absolutely unstable with the increase of Pr. Results from the direct numerical simulation are in agreement with the predictions of the linear temporal and spatial-temporal instabilities. These encouraging results should be helpful for understanding such a buoyancy-driven flow system.