OPTIMAL CONTROL OF TRANSITION INITIATED BY OBLIQUE WAVES IN CHANNEL FLOW

Abstract

Using two diierent approaches to optimal control in channel ow an eeort is made to try to identify diierences and similarities. One approach is to use the Navier{Stokes equations and apply a gradient based optimization technique to nd the optimal control. The other approach is to make use of the linearized equations known as the Orr{Sommerfeld{Squire equations to compute the optimal control. Limiting ourselves to look only at oblique wave perturbations we compare the resulting energy evolution from application of the respective control strategies. Qualitatively the performance of the two approaches are similar, at least when they work under comparable conditions. The non-linear control can be more aggressive initially since there is no direct limitation on the time derivative of the control even though the discretization implicitly enforces some degree of penalty. Adjusting the parameters properly we can show that the control from the two approaches are very similar. Also we try to quantify the performance of the estimator based control, or compensation, using only measurements on the wall, compared to the full-state information control. The performance of the compensator is found to be good for small perturbations, especially if a good initial guess can be provided.