The Existence of Görtler Vortices in Separated Boundary Layers

Abstract

The linear stability properties of Gortler vortices within a general separated boundary layer flow are addressed. There has been little previous theoretical work directed toward this problem and here we are able to characterize the important features of vortices over the complete wavenumber spectrum. This investigation complements earlier studies of vortices within an attached flow which demonstrated that there are three distinctive wavenumber regimes which together describe the most relevant possibilities for vortex behavior. In the first of these, at relatively small wavenumbers, the mode is inviscid in character; as the vortex wavenumber increases so the spatial amplification rate of the vortices increases until viscous effects become significant and the growth rate begins to diminish. As the wavenumber increases yet further so the vortex is completely stabilized. Here we discuss the corresponding structures which may exist within a separated flow and the most significant result we find is that the maximum growth rate of a mode in this type of flow is actually greater than that which occurs when the flow has not separated. In addition, the inviscid modes are shown to have a far more complicated configuration than within an attached boundary layer and, indeed, their structure can only be completely determined by implementation of numerical procedures.