Direct numerical simulation of gas transfer across the air–water interface driven by buoyant convection

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.