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 al. (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.