Downstream traveling waves: an effective means for preventing transition to turbulence

Dr. Mihailo Jovanovic, University of Minnesota

n this talk we assess the efficacy of a zero-net-mass-flux blowing and suction in the form of streamwise traveling waves for transition control in a channel flow. It was recently shown that the net power balance for this type of actuation is always negative if the uncontrolled flow stays laminar. However, we show that a positive  net power balance can be achieved when the uncontrolled flow becomes turbulent but the controlled flow stays laminar. Starting from this observation, we develop a framework for selection of traveling wave parameters for control of transition with a positive net power balance. Our model-based approach shows that, relative to the uncontrolled flow, the velocity fluctuations around the upstream traveling waves at best exhibit similar sensitivity to background disturbances. In contrast, the properly designed downstream traveling waves can significantly reduce sensitivity  which makes them well-suited for preventing transition. Our theoretical findings   are confirmed by direct numerical simulations of the Navier-Stokes (NS) equations  which show that a positive net efficiency as large as 25% relative to the uncontrolled turbulent flow can be achieved. This (i) elucidates the predictive power of the developed theoretical framework for model-based vibrational flow control, and (ii) suggests that the linearized NS equations with uncertainty represent an effective control-oriented model for preventing transition.