An investigation of the flow modification in a turbulent channel with gain-based optimal forcing*

Direct numerical simulations of turbulent channel at Re$_{\mathrm{\tau \thinspace }}=$ 180 with two-dimensional traveling wave forcing are performed. The chosen forcing parameters, that is, the wall-parallel wavelength and wave-speed, are representative of the near-wall cycle. The wall-normal forcing shape is obtained using the resolvent analysis of McKeon {\&} Sharma (Journal of Fluid Mechanics, vol. 658, 2010). The results obtained from direct simulations are found to compare well with the resolvent analysis predictions for different forcing amplitudes. The turbulence statistics and visualizations of three-dimensional unsteady flow field shed light on the flow evolution in response to forcing.