Stability of Nonlinear Viscous Vortices in Three-Dimensional Boundary Layers

摘要

Recently it has been demonstrated that three-dimensionality can play an importantrole in dictating the stability properties of any Gortler vortices which a particular boundary layer may support. According to a linearised theory vortices within a high Gortler number flow can take one of two possible forms within a two-dimensional flow supplemented by a small crossflow of size O(Re-1/2G3/5) where Re is the Reynolds n ber of the flow and G the Gortler number. Bassom and Hall (1991) showed that these forms are characterised by 0(1) wavenumber inviscid disturbances and larger, O(Gl/5, wavenumber modes which are trapped within a thin layer adjacent to the bounding surface. Here we concentrate on the latter, essentially viscous vortices and describe their weakly nonlinear stability properties in the presence of crossflow. It is shown conclusively that the effect of crossflow is to stabilise the nonlinear disturbances and the calculations herein allow stable, finite amplitude perturbations t be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a practical setting and asymptotic work permits discussion of the stability, properties of modes with wavenumbers which are small relative to the implied 0 Gl/5 scaling. crossflow, nonlinear, 'viscous vortices'.