Drag reduction in turbulent channel flow by phase randomization

Abstract

Results of numerical simulations of plane turbulent channel flow are presented in which a forcing is introduced which derives from the randomization of selected Fourier modes. In all cases, the randomization is introduced uniformly throughout the channel. The properties of the resulting turbulence are strongly dependent on both the wave numbers whose phases are randomized and the forcing frequency. Two principal wave-number bands have been selected. The first includes a selected subset of the largest length scales of the turbulence. Forcing in this band results in a fully sustained maximum mass flux increase above that of normal turbulence of 30%, which translates into a drag reduction of 58%. Many of the statistical properties of the simulated drag-reduced turbulence generated in this manner are in good qualitative agreement with the statistical properties of turbulence observed in experiments in which drag reduction is achieved through the introduction of small concentrations of long-chained polymers into the flow. In a second set of simulations, the phases of the intermediate and smallest wavelengths were randomized. Forcing at these scales of motion results in a drag increase. Speculations on the mechanism of the drag reduction by phase randomization are offered.