VORTEX INSTABILITIES IN 3-DIMENSIONAL BOUNDARY-LAYERS - THE RELATIONSHIP BETWEEN GORTLER AND CROSS-FLOW VORTICES

The inviscid and viscous stability problems are addressed for a boundary layer which can support both Gortler and crossflow vortices. The change in structure of Gortler vortices is found when the parameter representing the degree of three-dimensionality of the basic boundary-layer flow under consideration is increased. It is shown that crossflow vortices emerge naturally as this parameter is increased and ultimately become the only possible vortex instability of the flow. It is shown conclusively that at sufficiently large values of the crossflow there are no unstable Gortler vortices present in a boundary layer which, in the zero-crossflow case, is centrifugally unstable. The results suggest that in many practical applications Gortler vortices cannot be a cause of transition because they are destroyed by the three-dimensional nature of the basic state. In swept-wing flows the Gortler mechanism is probably not present for typical angles of sweep of about 20-degrees. Some discussion of the receptivity problem for vortex instabilities in weakly three-dimensional boundary layers is given; it is shown that inviscid modes have a coupling coefficient marginally smaller than those of the fastest growing viscous modes discussed recently by Denier, Hall & Seddougui (1991). However, the fact that the growth rates of the inviscid modes are the larger in most situations means that they are probably the more likely source of transition.