Upstream travelling waves in the boundary layer of a horizontal mixed convection flow

The propagation of small disturbances in a mixed convection boundary layer pow over a horizontal plate is considered. Employing an asymptotic analysis with respect to a small buoyancy parameter K = Gr/Re-2 a triple deck struc ture of the perturbed pow field is found. Two effects contribute to the pre ssure perturbation in the lower deck: The displacement of the outer field a nd the buoyancy in the main deck. Linearizing the perturbation equations an d taking the Fourier transform with respect to time and the coordinate para llel to the wall the dispertion relation is derived. Considering the case t hat the buoyancy induced pressure dominates the displacement induced pressu re upstream travelling waves are found. These waves are confined to the bou ndary-layer and exist only in the case of the flow over a cooled plate. Fur thermore a stationary downstream growing mode exists which indicates that t he solution of the boundary layer equations is not unique.