Controlling the onset of turbulence by streamwise traveling waves. Part 2. Direct numerical simulations

Abstract: This work builds on and confirms the theoretical findings of Part 1 of this paper, Moarref & Jovanovi\'c (2010). We use direct numerical simulations of the Navier-Stokes equations to assess the efficacy of blowing and suction in the form of streamwise traveling waves for controlling the onset of turbulence in a channel flow. We highlight the effects of the modified base flow on the dynamics of velocity fluctuations and net power balance. Our simulations verify the theoretical predictions of Part 1 that the upstream traveling waves promote turbulence even when the uncontrolled flow stays laminar. On the other hand, the downstream traveling waves with parameters selected in Part 1 are capable of reducing the fluctuations' kinetic energy, thereby maintaining the laminar flow. In flows driven by a fixed pressure gradient, a positive net efficiency as large as 25 % relative to the uncontrolled turbulent flow can be achieved with downstream waves. Furthermore, we show that these waves can also relaminarize fully developed turbulent flows at low Reynolds numbers. We conclude that the theory developed in Part 1 for the linearized flow equations with uncertainty has considerable ability to predict full-scale phenomena.