Gas Transfer in Turbulent Free-Surface Flows with Air Entrainment: a simple framework for turbulence analysis
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Gas transfer across the air-sea interface is a critical process governing global biogeochemical cycles and climate dynamics. Given the complexity of the phenomena involved, gas transfer is often parameterized using a bulk formula of the form F = k_L ΔC, where F is the gas flux, ΔC is the concentration difference across the interface, and kL is the mass transfer coefficient. The mass transfer coefficient k_L is influenced by multiple factors including wind stress, wave breaking, turbulence, and air entrainment. While empirical models derived from laboratory and field experiments have been proposed to estimate k_L, the individual contribution of air entrainment to gas transfer remains poorly quantified, particularly in turbulent free-surface flows. Wave breaking and associated air entrainment have been shown to significantly enhance gas transfer rates [1]. However, isolating and quantifying the specific mechanisms through which entrained bubbles and turbulence contribute to mass transfer is challenging in realistic ocean conditions due to the complex interplay of multiple scales and processes. This work employs a simplified numerical framework, originally introduced by [2] and recently applied by [3, 4, 5], to investigate turbulence statistics, energy exchange, interface deformation and air entrainment in a controlled computational environment. Direct numerical simulation (DNS) of a computational domain where statistically stationary homogeneous isotropic turbulence (HIT) is sustained behind a deformable free surface is performed. We propose to introduce a dispersed gas phase to mimic air entrainment and systematically study its effect on interfacial mass transfer. The framework allows for precise control of turbulence intensity, bubble size distribution, and void fraction, enabling detailed analysis of individual contributions to the overall gas transfer coefficient. Results provide insights into the physical mechanisms governing gas exchange in air-entrained turbulent flows and offer improved parametrizations for large-scale ocean-atmosphere models. [1] Di Giorgio S., Pirozzoli S., Iafrati A., Geophys. Res. Lett., Vol. 52(15), 2025 [2] Guo X., Shen L., J. Comput. Phys., 228 (19), 2009. [3] Guo X., Shen L., J. Fluid Mech., 658, 2010 [4] Calado A., Balaras E., J. Fluid Mech., 1025, A52, 2025. [5] Gaylo D. B., Yue D. K. P., J. Fluid Mech., 1020, A40, 2025.
