How Far Does the Influence of the Free Surface Extend in Turbulent Open Channel Flow?

Turbulent open channel flow is known to feature a multi-layer structure near the free surface. In the present work we employ direct numerical simulations considering Reynolds numbers up to Re$_τ$ = 900 and domain sizes large enough (L$_x$ = 12πh, L$_z$ = 4πh) to faithfully capture the effect of very-large-scale motions in order to test the proposed scaling laws and ultimately answer the question: How far does the influence of the free surface extend? In the region near the free surface, where fluctuation intensities of velocity and vorticity become highly anisotropic, we observe the previously documented triplelayer structure, consisting of a wall-normal velocity damping layer that scales with the channel height h, and two sublayers that scale with the near-surface viscous length scale ℓ$_V$ = Re$_b$$^{−1/2}$ h and with the Kolmogorov length scale ℓ$_K$ = Re$_b$$^{−3/4}$ h, respectively. The scaling laws previously proposed by Calmet and Magnaudet [J. Fluid. Mech. 474, 355–378 (2003)] are found to hold with the following exceptions. The thin layer, where the intensity of surface-parallel components of the vorticity rapidly decreases to zero, is here found to scale with the Kolmogorov length scale ℓ$_K$ rather than with the near-surface viscous scale ℓ$_V$ . ... mehrIn addition, we argue that the Kolmogorov length scale is the relevant scale for the mean velocity gradient near the free surface. Both the mean velocity gradient and the fluctuation intensity of the surface-parallel component of vorticity decay to zero in the Kolmogorov sublayer δ$_K$ ≈ 20 ℓ$_K$ . On the other hand, the layer, where the wall-normal turbulence intensity decreases linearly to zero near the free surface, scales with ℓ$_V$ rather than ℓ$_K$ as suggested by Calmet and Magnaudet. The corresponding near-surface viscous sublayer measures δ$_V$ ≈ ℓ$_V$ .