Spatial theory of optimal disturbances in boundary layers

A spatial theory is proposed for the linear transient growth of disturbances in a parallel boundary layer. Following from the consideration of a signaling problem, the spatial development of disturbances downstream of a source may be presented as a sum of decaying eigenmodes and Tollmien-Schlichting (TS) like instability modes. Therefore, the problem of optimal disturbances may be considered as an initial value problem on the subset of the decaying eigenmodes and a TS wave, and a standard optimization procedure may be applied for evaluation of the optimal transient growth. The results indicate that the most significant transient growth is associated with stationary streamwise vortices. Numerical examples illustrate that favorable pressure gradient decreases the overall amplification. Effects of compressibility and the wall cooling are investigated as well.