How is the free surface influence transported in turbulent open channel flows?

Abstract

We investigate how the influence of a free surface is transported in turbulent open channel flow by analysing matched open- and closed-channel direct numerical simulations up to $Re_\mathrm{\tau} \approx 900$ in a domain large enough to accommodate very-large-scale motions (VLSMs). The turbulent kinetic energy (TKE) budget shows that the surface influence is communicated primarily through transport terms. Near the free surface, pressure transport supplies energy towards the interface, whereas turbulent transport and dissipation are reduced; the resulting energy surplus is exported away from the surface predominantly by viscous diffusion. The near-surface budget terms do not exhibit a single universal similarity scaling: viscous diffusion is organised over the near-surface viscous scale $\ell_\mathrm{V}$, dissipation over the Kolmogorov sublayer scale $\ell_\mathrm{K}$, and pressure-related terms require the mixed velocity scale $u_\mathrm{b} u_\mathrm{\tau}^2 /h$. The pressure-strain redistribution further reveals outer-inner coupling: although intense pressure-strain events remain small-scale, their magnitude and directional bias are organised by low-velocity VLSM streaks. The free-surface influence is therefore best understood as a coupled multi-scale process involving local kinematic constraints, Reynolds-number-dependent surface layers, and outer-layer coherent motions.