Drag reduction effects by a spanwise traveling wave of wall deformation in a turbulent channel flow are investigated by means of direct numerical simulation. The flow rate is kept constant at the bulk Reynolds number of Reb = 5600. A parametric study is performed by varying three parameters of the wave (i.e., the amplitude, the wavenumber, and the phase speed). Within the range of parameters investigated, the maximum drag reduction rate and the maximum net energy saving rate are found to be 13.4% and 12.2%, respectively. The drag reduction rate is found to be reasonably scaled by a product of the magnitude of the induced velocity and the thickness of the Stokes layer. An analysis using the FIK identity [K. Fukagata, K. Iwamoto, and N. Kasagi, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14, L73 (2002)] with a three-component decomposition reveals that the drag reduction is mainly attributed to a decrease in the random component of the Reynolds shear stress. The turbulence statistics are investigated in detail and the drag reduction mechanism is explained by the induced spanwise flow due to the traveling wave rather than the riblet-like geometric structure. Although the amount of drag reduction rate is comparable to that of the conventional riblets, the quasi-streamwise vortices are found to be suppressed even when the spanwise wavelength is larger than the typical diameter of quasi-streamwise vortices.
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