Abstract
A series of direct numerical simulations of mass transfer across the air–water interface driven by buoyancy-induced convection have been carried out to elucidate the physical mechanisms that play a role in the transfer of heat and atmospheric gases. The buoyant instability is caused by the presence of a thin layer of cold water situated on top of a body of warm water. In time, heat and atmospheric gases diffuse into the uppermost part of the thermal boundary layer and are subsequently transported down into the bulk by falling sheets and plumes of cold water. Using a specifically designed numerical code for the discretization of scalar convection and diffusion, it was possible to accurately resolve this buoyant-instability-induced transport of atmospheric gases into the bulk at a realistic Prandtl number ($\mathit{Pr}=6$) and Schmidt numbers ranging from$\mathit{Sc}=20$to$\mathit{Sc}=500$. The simulations presented here provided a detailed insight into instantaneous gas transfer processes. The falling plumes with highly gas-saturated fluid in their core were found to penetrate deep inside the bulk. With an initial temperature difference between the water surface and the bulk of slightly above$2$ K, peaks in the instantaneous heat flux in excess of$1600~\text{W}~\text{m}^{-2}$were observed, proving the potential effectiveness of buoyant-convective heat and gas transfer. Furthermore, the validity of the scaling law for the ratio of gas and heat transfer velocities$K_{L}/H_{L}\propto (\mathit{Pr}/\mathit{Sc})^{0.5}$for the entire range of Schmidt numbers considered was confirmed. A good time-accurate approximation of$K_{L}$was found using surface information such as velocity fluctuations and convection cell size or surface divergence. A reasonable time accuracy for the$K_{L}$estimation was obtained using the horizontal integral length scale and the root mean square of the horizontal velocity fluctuations in the upper part of the bulk.
Highlights
During the past decade, gas transfer across the air–water interface has received increasing interest because of its importance to the global greenhouse gas budget
This paper reports on the results obtained in a series of Direct numerical simulations (DNS) calculations of interfacial gas transfer driven by buoyant convection
Large-scale DNS of mass transfer across a flat clean surface driven by buoyant convection have been carried out
Summary
Gas transfer across the air–water interface has received increasing interest because of its importance to the global greenhouse gas budget. Important gases typically have a low (O2, CO, NO) to moderate (CO2) solubility Because of this and their significantly lower diffusivities in water than in air ( kL kg), for such gases kL/K kg is small and their transfer process at the air–water interface is concentrated in an extremely thin boundary layer (10–1000 μm) on the liquid side (see Liss 1973; Jähne & Haussecker 1998). Direct numerical simulations (DNS) related to heat/mass transfer across the free surface of an open channel flow have been performed by various research groups (Nagaosa 1999; Yamamoto, Kunugi & Serizawa 2001) These simulations showed a correlation between the vortices ejected from the bottom region and the near-surface concentration field, and proved the usefulness of DNS in obtaining detailed statistics of the scalar fields. The problem under consideration is the gas transfer across the air–water interface driven by buoyant convection caused by temperature differences between the water surface and the bulk.
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