Transition control of the Blasius boundary layer using passivity

The control problem for linearised three-dimensional perturbations about a nominal laminar boundary layer over a flat plate (the Blasius profile) is considered. With a view to preventing the laminar to turbulent transition, appropriate inputs, outputs, and feedback controllers are synthesised that can be used to stabilise the system. The linearised Navier–Stokes equations are reduced to the Orr–Sommerfeld and Squire equations with wall-normal velocity actuation entering through the boundary conditions on the wall. An analysis of the work-energy balance is used to identify an appropriate sensor output that leads to a passive system for certain values of the streamwise and spanwise wavenumbers. Even when the system is unstable, it is demonstrated that strictly positive real feedback can stabilise this system using the special output.