Three-dimensional inviscid waves in buoyant boundary layer flows

The stability of weakly three-dimensional buoyancy-driven boundary layers to travelling waves is considered. It is shown that in the absence of crossflow inviscid modes are unstable and, as the degree of crossflow is increased, the short waves are the first to be stabilised – longer waves require an enhanced level of three-dimensionality of the basic flow for stabilisation. A combination of asymptotic and numerical techniques are used to provide a complete description of the inviscid modes over the whole wavenumber spectrum. The study is also extended to consider pure vortex “roll-cell” modes which can exist within unstably stratified (buoyancy driven) flows and these are found to stabilise in the presence of crossflow.