THE EFFECT OF BUOYANCY ON UPPER-BRANCH TOLLMIEN-SCHLICHTING WAVES

We investigate the effect of buoyancy on the upper-branch linear stabi lity characteristics of an accelerating boundary-layer how. The presen ce of a large thermal buoyancy force significantly alters the stabilit y structure. As the factor G (which is related to the Grashof number o f the flow, and defined in Section 2) becomes large and positive, the flow structure becomes two layered and disturbances are governed by th e Taylor-Goldstein equation. The resulting inviscid modes are unstable for a large component of the wavenumber spectrum, with the result tha t buoyancy is strongly destabilizing. Restabilization is encountered a t sufficiently large wavenumbers. For G large and negative the flow st ructure is again two layered. Disturbances to the basic flow are now g overned by the steady Taylor-Goldstein equation in the majority of the boundary layer, coupled with a viscous wall layer. The resulting eige nvalue problem is identical to that found for the corresponding case o f lower-branch Tollmien-Schlichting waves, thus suggesting that the ne utral curve eventually becomes closed in this limit.