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We examine the efficacy of streamwise traveling waves generated by azero-net-mass-flux surface blowing and suction for controlling the onset ofturbulence in a channel flow. For small amplitude actuation, we utilize weaklynonlinear analysis to determine base flow modifications and to assess theresulting net power balance. Receptivity analysis of the velocity fluctuationsaround this base flow is then employed to design the traveling waves. Oursimulation-free approach reveals that, relative to the flow with no control,the downstream traveling waves with properly designed speed and frequency cansignificantly reduce receptivity which makes them well-suited for controllingthe onset of turbulence. In contrast, the velocity fluctuations around theupstream traveling waves exhibit larger receptivity to disturbances. Ourtheoretical predictions, obtained by perturbation analysis (in the waveamplitude) of the linearized Navier-Stokes equations with spatially periodiccoefficients, are verified using full-scale simulations of the nonlinear flowdynamics in companion paper, Lieu, Moarref & Jovanovi\'c (2010).

Controlling the onset of turbulence by streamwise traveling waves. Part 1: Receptivity analysis