The nonlinear evolution of a wavetrain emanating from a point source in a boundary layer

Abstract

The paper reports on an investigation into the nonlinear evolution of a wavetrain emanating from a point source in a flat-plate boundary layer. The work was mainly experimental, but calculations using linear and nonlinear stability theory and parabolized stability equations were also performed to support the conclusions. The amplitudes of the disturbances used were very small and, as a consequence, turbulence was not reached within the experimental domain. Nevertheless, interesting nonlinear behaviour was observed. The nonlinear regime was characterized by the appearance of a three-dimensional mean flow distortion in the form of longitudinal streaks. It was possible to distinguish two different stages of the nonlinear regime. In the first stage, the streak pattern displayed relatively low spanwise wavenumbers. The pattern appeared to have grown algebraically from a pair of counter-rotating streamwise vortices. Weakly nonlinear calculations suggested that the vortices arise from the interaction of the spanwise and the wall-normal velocity components. The second stage exhibited more streaks and higher spanwise wavenumbers. This stage was found to be associated with a peak-and-valley structure of the wave amplitude. A remarkable feature was that the streamwise position of the onset of the second stage of the nonlinear regime was not affected by the amplitude of the disturbance. Parabolized stability calculations suggested that the peak-and-valley structure was the outcome of a secondary instability of the fundamental type. An interaction similar to that of the first nonlinear stage involving the waves composing the peak-and-valley structure yielded other streamwise vortices and hence a different streak pattern. The results also suggested that, because the wave amplitudes were very small, the linear stability influenced the nonlinear evolution. Indeed, the onset of the second stage of the nonlinear regime appeared to be associated with the proximity of the second branch of the linear stability diagram.