Direct numerical simulation of turbulent open channel flows at moderately high Reynolds numbers

Well-resolved direct numerical simulations of turbulent open channel flows (OCFs) are performed for friction Reynolds numbers up to Reτ = 2000. Various turbulent statistics are documented and compared with the closed channel flows (CCFs). As expected, the mean velocity profiles of the OCFs match well with the CCFs in the near-wall region but diverge notably in the outer region. Interestingly, a logarithmic layer with Kárman constant κ = 0.363 occurs for OCF at Reτ = 2000, distinctly different from CCF. Except for a very thin layer near the free surface, most of the velocity and vorticity variances match between OCFs and CCFs. The one-dimensional energy spectra reveal that the very-large-scale motions (VLSMs) with streamwise wavelength λx > 3h or spanwise wavelength λz > 0.5h contribute the most to turbulence intensity and Reynolds shear stress in the overlap and outer layers (where h is the water depth). Furthermore, the VLSMs in OCFs are stronger than those in CCFs, resulting in a slightly higher streamwise velocity variance in the former. Due to the footprint effect, these structures also have significant contributions to the mean wall shear stress, and the difference between OCF and CCF enlarges with increasing Reτ . In summary, the free surface in OCFs plays an essential role in various flow phenomena, including the formation of stronger VLSMs and turbulent kinetic energy redistribution.