A quantitative study on the turbulent kinetic energy redistribution in the near free-water-surface region of open channel flows

Open channel flows (OCFs) exhibit unique characteristics compared with other wall-bounded flows due to the presence of a free water surface. One of the well-known features is the turbulence kinetic energy (TKE) redistribution phenomenon in the near free-water-surface region. Unlike previous qualitative demonstrations, the present study aims providing a quantitative investigation of this phenomenon. Specifically designed super long domain direct numerical simulations (DNSs) of OCFs and closed channel flows (CCFs) are performed at three low-to-moderate friction Reynolds numbers (Reτ = 180–1000). The numerical configurations of the two flows (i.e., temporal and spatial resolution, domain size, Reynolds number, etc.) at identical Reτ are set to be the same, with the upper boundary being the only difference between them, to allow meaningful comparisons while super long domain sizes are adopted to facilitate fully spectral comparisons of the TKE features between the two flows. With such specifically designed DNS datasets, quantitative investigations of the TKE redistribution phenomenon in OCFs have been made. It is revealed that, as Reτ increases from 180 to 1000, the streamwise and spanwise TKE components of OCFs are higher than those of CCFs by 12%–23% and 28%–17%, respectively, while in the vertical direction OCFs are lower in TKE by 44%–31%. Overall, the TKE of OCFs is higher than that of CCFs by 3%–9% as Reτ increases from 180 to 1000. The comparison of OCFs and CCFs in pre-multiplied energy spectra reveals that VLSMs play a dominant role in the TKE redistribution phenomenon in OCFs.