Numerical analysis of the interface deformation and energy exchange in free-surface turbulence

Two-phase direct numerical simulations (DNS) are used to explore the dynamics of free-surface turbulence (FST), focusing on low to moderate Froude numbers (Fr), with significant interface deformation and bubble entrainment. Influence from Fr is seen on the free-surface stretching, 2D compressibility ratio, and turbulent kinetic energy (TKE) modulation. Vortical structures align strongly parallel to the interface, and at lower Fr, kinetic energy redistributes between components, aligning with rapid distortion theory (RDT), while higher Fr preserves isotropy. A dual energy cascade is revealed, with third-order structure functions indicating upscale flux at large scales and near-equilibrium fluxes in the inertial subrange. Discrete wavelet transforms show a -3 spectral slope in the inertial subrange resembling 2D turbulence, with less decay at the highest wavenumbers closest to the interface. A non-monotonic behavior of the turbulent dissipation is observed, with analysis of the flow topology showing mainly extensional strain within the viscous layer, and regions of pure rotation within the blockage layer. Using a filtering approach, we compute the scale local and non-local contributions of the inter-scale energy transfer. Non-local interactions increase near the interface, along with a simultaneous increase in both downscale and upscale fluxes. These findings elucidate scale- and proximity-dependent TKE transport in multiphase flows, with implications for sub-grid modeling.