Wall-transpiration feedback control of laminar streaks using an adjoint approach

This paper presents theoretical and numerical results on the penetration of small-amplitude free-stream vortical disturbances into an incompressible laminar boundary layer, and the wall-based adjoint feedback control of the resulting streamwise-elongated, low-frequency fluctuations within the boundary layer. The theoretical formulation of the low-frequency disturbances, also called laminar streaks or Klebanoff modes, follows the work of Leib, Wundrow & Goldstein [13] and is based on the incompressible linearised unsteady boundary region equations. The outer boundary conditions of this system synthesize the mutual interaction between the boundary layer and the free-stream vortical fluctuations, which generated the low-frequency streaks. Adjoint theory is applied to the equations of motion, and wall-transpiration is employed to attenuate the Klebanoff modes. Our results extend the findings of the adjoint-based work by Cathalifaud & Luchini [5], which utilised the steady boundary region equations without including the effect of free-stream disturbances in the formulation.