The effect of buoyancy on upper-branch Tollmien-Schlichting waves

We investigate the effect of buoyancy on the upper-branch linear stability characteristics of an accelerating boundary-layer flow. The presence of a large thermal buoyancy force significantly alters the stability structure. As the factor G (which is related to the Grashof number of the flow, and defined in Section 2) becomes large and positive, the flow structure becomes two layered and disturbances are governed by the Taylor-Goldstein equation. The resulting inviscid modes are unstable for a large component of the wavenumber spectrum, with the result that buoyancy is strongly destabilizing. Restabilization is encountered at sufficiently large wavenumbers. For G large and negative the flow structure is again two layered. Disturbances to the basic flow are now governed by the steady Taylor-Goldstein equation in the majority of the boundary layer, coupled with a viscous wall layer. The resulting eigenvalue problem is identical to that found for the corresponding case of lower-branch Tollmien-Schlichting waves, thus suggesting that the neutral curve eventually becomes closed in this limit.