Quantifying the surface layer generated by strong free-surface turbulence

We consider free-surface flows driven by turbulence beneath the surface, particularly the strong free-surface turbulence (FST) regime, characterised by large Froude number Fr²T=ε /uᵣₘₛ g\, 0.1 . We study the surface layer, where air and water are highly mixed and turbulence modelling is challenging. We develop a definition of the surface-layer thickness δ ₛ based on the vertical derivative of intermittency γ at the mean free surface η ̄ , which, unlike previous definitions, is independent of the tail behaviour of γ . From direct numerical simulation (DNS) of statistically stationary, horizontally homogeneous strong FST, we show that scaling by z^* = (z-η ̄)/δ ₛ collapses γ across a wide range of Fr²T∈ [0.03,0.3] . The distribution more closely follows logistic rather than Gaussian behaviour. From the near-surface turbulence obtained from DNS, we make two general observations. First, we show that for strong FST there is minimal direct effect of the free surface on the isotropy, turbulence kinetic energy k̃ or dissipation rate ε beneath the surface layer ( z^*< -0.5 ). Instead, turbulence is only indirectly affected through the flux of kinetic energy into the surface layer. Second, we show that many relevant metrics within the surface layer ( z^*∈ [-0.5, 0.5] ) collapse when appropriately scaled by uᵣₘₛ²=2k̃/3 and ε measured at z^*=-0.5 . These observations suggest the possibility of a turbulence closure model which avoids direct modelling of k̃ and ε in the surface layer. Towards this, we show that, across a wide range of FrT² , surface-layer thickness can be predicted by δ ₛ ≈ 11.1 \,uᵣₘₛ² g⁻¹ and energy flux into the surface layer by W ≈ 0.41 \,ε δ ₛ .