The effects of nonlinearity on crossflow receptivity

Using a vorticity form of the Navier-Stokes equations the effects of nonlinearity on the development and receptivity of crossflow disturbances in the Swept Hiemenz boundary-layer are investigated. Steady perturbations are generated using wall suction and blowing that are distributed periodically as either a strip or point holes. The method, size and the location of the forcing are shown to significantly influence the receptivity of the crossflow within the boundary-layer. Perturbations excited by periodic blowing holes have considerably larger amplitudes than those generated by suction holes or strips. A linear log relationship is derived that relates the receptivity amplitude of the linear only disturbances with the chord position that the nonlinear primary Fourier perturbation attains a state of equilibrium: location that the maximum absolute amplitude of the primary disturbance shows distinct differences to the linear only solution. Further the size of the chordwise velocity perturbation at the location corresponding to equilibrium can be predicted directly from the linear only solutions. Thus, if the receptivity amplitude of the linear perturbation is smaller than some given threshold magnitude, nonlinear flow characteristics can be predicted directly from the computationally less expensive linear analysis.