Nonlinear stability of boundary layers for disturbances of various sizes

The nonlinear stability of small disturbances to the Blasius boundary layer is considered within a rational, high Reynolds number ($Re$), framework for a complete range of disturbance sizes $(\delta)$. The nonlinear properties of the disturbance amplitude depend crucially on the size $\delta $ relative to the inverse powers of $Re$. Most attention is given to the largest size of disturbance that can be dealt with, near the lower branch of the neutral curve, namely $\delta =O(Re^{-\frac{1}{8}})$, for which nonlinear effects yield supercritical equilibrium amplitudes. The nonlinear properties of smaller disturbances are profoundly affected by (inter alia) non-parallel flow effects. Comparisons are made with previous numerical studies and the importance of nonparallel flow effects in fixing the neutral curve(s) around which the nonlinear theory holds is discussed.