Stability of natural convection in a heated vertical corner

The spatial stability of three-dimensional non-parallel natural convection in a uniformly-heated vertical corner is examined for the first time. Two self-similar steady base flows are determined, which are distinguished by their behaviour far from the corner. The first solution (A) reduces to the flow induced by a heated semi-infinite vertical plate, with a crossflow component that is driven by the entrainment into the corner. The second solution (B) is new and in contrast has a crossflow that increases linearly with the spanwise coordinate. In both solutions, the crossflow is directed towards the corner, being driven by the so-called chimney effect’. By adopting a PSE approach, we show that the computed base flows become unstable to viscous modes at sufficiently large Grashof numbers. In the case of solution A, the eigenmodes that initially dominate are well approximated by the two-dimensional stability problem for the boundary layer over a heated vertical plate. However, further downstream these modes are later overcome by modes that are corner-specific (and cannot be captured by a simpler planar far-field stability problem).