Algebraic growth of disturbances in a laminar boundary layer

The temporal evolution of small three‐dimensional disturbances with a large streamwise scale in viscous, parallel, semi‐bounded flows is studied. In the limit of the initial disturbance being independent of the streamwise coordinate, the vertical velocity component consists solely of a continuous spectrum part. Tollmien–Schlichting waves do not appear in this special case. The streamwise perturbation velocity is obtained by solving a forced initial value problem. While the vertical velocity remains constant for small times, the streamwise perturbation velocity exhibits a linear growth due to the forcing. Eventually, viscous dissipation becomes dominant and the disturbance decays. Asymptotic solutions valid for small and large times are presented. The relation of these results to the longitudinal streaky structure found in many shear flows is discussed.