Use of Instabilities for Optimal Laminar Separation Delay

The velocity disturbances at a given upstream position, which counteract laminar separation downstream, are sought by means of nonlinear optimization. For steady disturbances, an informed guess based on linear analysis of transient perturbation growth leads to significant delay of separation and serves as a starting point for the nonlinear optimization algorithm. Nonlinear optimal perturbations enable further delay of the separation location, with moderate improvements relative to the linear analysis. The mechanism of separation delay is the generation of a mean flow distortion by nonlinear interactions during perturbation growth. The mean flow distortion enhances the momentum close to the wall, and thus counteracts the deceleration of the flow in that region. For unsteady disturbances, it is found that Tollmien-Schlichting waves obtained by local stability theory provide very good estimates of the nonlinearly optimal disturbances. The mechanism that counteracts separation is the enhancement of the wall-normal momentum transfer in the separated shear layer. Comparison of optimal steady and unsteady perturbations reveals that the latter are able to obtain a higher time-averaged peak wall pressure.