Direct numerical simulation on relevance of fluctuating velocities and drag reduction in turbulent channel flow with spanwise space-dependent electromagnetic force

Based on the Fourier-Chebyshev spectral method, the control of turbulent channel flow by space-dependent electromagnetic force and the mechanism of drag reduction are investigated with direct numerical simulation (DNS) methods for different Reynolds numbers. A formula is derived to express the relation between fluctuating velocities and the friction drag coefficient. With the application of electromagnetic force, the in-depth relations among the fluctuating velocities near the wall, Reynolds stress, and the effect of drag reduction for different Reynolds numbers are discussed. The results indicate that the maximum drag reductions can be obtained with an optimal combination of parameters for each case of different Reynolds numbers. The fluctuating velocities along the streamwise and normal directions are suppressed significantly, while the fluctuating velocity along the spanwise direction is enhanced dramatically due to the spanwise electromagnetic force. However, the values of Reynolds stress depend on the fluctuating velocities along the streamwise and normal directions rather than that along the spanwise direction. Therefore, the significant effect of drag reduction is obtained. Moreover, the maximum drag reduction is weakened due to the decay of control effect for fluctuating velocities as the Reynolds number increases.