Analysis of the subharmonic route to transition in boundary layers

Primary instabilty of the Blasius boundary-layer flow leads to growth of T-S waves and to a streamwise almost periodic modulation of the flow. The linear secondary instabilty of this modulated flow with respect to spanwise periodic, three-dimensional disturbances is studied. Of the various possible types of resonance in the Hill-type stablity equations, the case of principal parametric resonance is considered that may result in the growth of subharmonic disturbances. The conditions for subharmonic resonance and the role of Reynolds number and T-S amplitude are discussed. Growth rates of subharmonic disturbances and the spatial disturbance field are compared with experimental data. The results emphasize the important role of the subharmonic route to transition in low-disturbance environments.