Linear optimal control of transient growth in turbulent channel flows

This work investigates the suppression of linear transient growth in turbulent channel flows via linear optimal control. Two control algorithms are employed, i.e. the linear quadratic regulator (LQR) control based on full information of flow fields, and the linear quadratic Gaussian (LQG) control based on the information measured at walls. The influence of these controls on the development of both small-scale and large-scale perturbations is considered. The results show that the energy amplification of large-scale perturbations is significantly suppressed by both LQR and LQG controls, while small-scale perturbations are affected only by LQR control. The effects of the weighting parameters and control price on control performance are also analyzed for both controls, which reveals that different weighting parameters in the cost function do not qualitatively change the evaluation of control performance. As the control price increases, the effectiveness of both controls decreases markedly. For small-scale perturbations, the upper limit of the effective range of control price is lower than that for large-scale perturbations. When the Reynolds number is increased, it indicates that both LQR and LQG control become more effective in suppressing the energy amplification of large-scale perturbations.