Optimal perturbations for boundary layers subject to stream-wise pressure gradient

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Abstract
Configurations of perturbation velocity which optimally excite an algebraic growth mechanism in the Falkner–Skan boundary layer are studied using a direct–adjoint technique. The largest transient amplification is obtained by stream-wise oriented vortices, in agreement with previous results for the Blasius boundary layer. Adverse pressure gradient is found to increase the resulting growth, the reverse is true for accelerated flows. It is shown that optimally excited algebraic mechanisms are capable of competition with optimally excited Tollmien–Schlichting waves in super-critical flows before succumbing to viscous damping. Disturbances optimized for maximal amplification over shorter periods are generally oblique and can experience significant transient growth; it is argued that they should not be dismissed when searching for rapidly growing perturbations which may preferentially induce early transition. Optimal disturbances transform into streaks downstream of their inception, attesting to the ubiquity of these flow structures.