Nonlinear development of crossflow vortices

Nonlinear crossflow vortices in an incompressible three-dimensional boundary layer are computed by weakly nonlinear theory and direct numerical simulations. The parallel basic flow is defined by Falkner-Skan-Cooke similarity profiles. The temporal evolution of spanwise periodic, quasi-two-dimensional disturbances without variations along the vortex axis is considered. The nonlinear theory is based on the approach of Herbert (1980, 1983). The theory predicts the existence of the finite amplitude equilibrium states seen in earlier simulations. When the disturbance amplitudes are small, there is very good quantitative agreement in the fundamental disturbance velocity components between the theory and the simulations.