WEAKLY NONLINEAR STABILITY OF VISCOUS VORTICES IN 3-DIMENSIONAL BOUNDARY-LAYERS

Recently it has been demonstrated that three-dimensionality can play a n important role in dictating the stability of any Gortler vortices wh ich a particular boundary layer may support. According to a linearized theory, vortices within a high Gortler number flow can take one of tw o possible forms within a two-dimensional flow supplemented by a small crossflow of size O(Re-1/2G3/5), where Re is the Reynolds number of t he flow and G the Gortler number. Bassom & Hall (1991) showed that the se forms are characterized by O(1)-wavenumber inviscid disturbances an d larger O(G1/5)-wave-number modes which are trapped within a thin lay er adjacent to the bounding surface. Here we concentrate on the latter , essentially viscous, vortices. These modes are unstable in the absen ce of crossflow but the imposition of small crossflow has a stabilizin g effect. Bassom & Hall (1991) demonstrated the existence of neutrally stable vortices for certain crossflow/wavenumber combinations and her e we describe the weakly nonlinear stability properties of these distu rbances. It is shown conclusively that the effect of crossflow is to s tabilize the nonlinear modes and the calculations herein allow stable finite-amplitude vortices to be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a prac tical setting and asymptotic work permits discussion of the stability properties of modes with wavenumbers that are small relative to the im plied O(G1/5) scaling.