Abstract: In previous research, the main consideration for disturbance distribution in the transition and turbulence of a flat plate boundary layer is uniform along the spanwise direction, which is relatively easy to study. But in actual situation, the disturbance form is diverse. The boundary layer may be three-dimensional and the disturbance distribution may not be uniform along the spanwise direction. Compared with the disturbance form studied before, the non-uniform disturbance distribution along the spanwise direction in a three-dimensional flat plate boundary layer is a more complex disturbance form and it is closer to natural transition. Therefore, it is of important significance to study the transition and turbulence caused by this disturbance form. For the flat plate boundary layers, the governing equations are the non-dimensional Navier-Stokes perturbation equations. The difference scheme of three order precision is used for time discrete. For the space discrete, the pseudo-spectrum is used in spanwise direction and the high precision difference schemes are employed in streamwise and normal directions. Numerical simulation is performed to study two cases of small amplitude spanwise wave packet disturbance and finite amplitude spanwise wave packet disturbance. The evolution of small amplitude wave packets disturbance is calculated by the numerical simulation and the linear stability theory (LST). The evolution results are in close agreement with the linear stability theory results. The transition and turbulence processes caused by finite amplitude spanwise wave packets disturbance are analyzed. The evolution characteristics in physics and spectrum space are detailed described. The different positions are compared and the results are that for the different positions, the transition positions are different, but the transition processes and characteristics are similar.

Key words: boundary layer, wave packet, transition, turbulence, numerical simulation