Instability of Boundary Layers on Heated Flat Plates

摘要

The stability of a boundary layer on a heated flat plate is investigated in thelinear regime. The flow is shown to be unstable to longitudinal vortex structures which in general develop in a nonparallel manner in the streamwise direction. Solutions of the nonparallel equations are obtained numerically at 0(1) values of the appropriate stability parameter, ie the Grashof number. The particular cases investigated relate to the situations when the instability is induced by localized or distributed wall roughness or nonuniform wall heating. The case when the vortices are induced by freestream disturbances is also considered. The fastest growing mode is found to be governed by a quasi-parallel theory at high wavenumbers. The wavenumber and growth rate of the fastest growing mode are found in closed form. At low wavenumbers the vortex instability is shown to be closely related to Tollmein-Schlichting waves, the effect of wall heating or cooling on the latter type of instability is discussed.