On using the streamwise traveling waves for variance suppression in channel flows

We assess the efficacy of using a zero-net-mass- flux blowing and suction in the form of an upstream traveling wave for transition control in channel flows. Our study is motivated by a recent paper by Min et at. (J. Fluid Mech., vol. 558) where it was shown that this type of surface actuation yields a sustained sub-laminar drag in a fully developed channel flow. We develop models that govern the dynamics of velocity fluctuations in the presence of stochastic outside disturbances (such as free-stream turbulence and acoustic waves) and show how changes in control parameters affect the fluctuations´ kinetic energy density. Effectively, we establish that properly designed streamwise traveling waves can be used to suppress variance of both the streamwise streaks and the Tollmien- Schlichting waves in transitional channel flows.