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

We investigate the effect of buoyancy on the upper-branch linearstability characteristics of an accelerating boundary-layerflow. The presence of a large thermal buoyancy force significantlyalters the stability structure. As the factor G (which is relatedto the Grashof number of the flow, and defined in Section 2)becomes large and positive, the flow structure becomes two layeredand disturbances are governed by the Taylor-Goldstein equation.The resulting inviscid modes are unstable for a large componentof the wavenumber spectrum, with the result that buoyancy isstrongly destabilizing. Restabilization is encountered at sufficientlylarge wavenumbers. For G large and negative the flow structureis again two layered Disturbances to the basic flow are nowgoverned by the steady Taylor—Goldstein equation in themajority of the boundary layer, coupled with a viscous walllayer. The resulting eigenvalue problem is identical to thatfound for the corresponding case of lower-branch Tollmien—Schlichtingwaves, thus suggesting that the neutral curve eventually becomesclosed in this limit.