Direct numerical simulation of buoyant-convectively driven gas transfer across gas-liquid interfaces

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The proposed project deals with the transfer of gaseous substances across a gas-liquid interface driven by buoyant-convective instability. The physical mechanisms that play a role in buoyancy-driven convective gas transfer are not well understood, despite of their significant contributions to the global heat budget and environmentally important gas cycles (including green-house gas cycles). Though numerous empirical relations to predict the gas transfer velocity have been reported in the literature, the dynamics of the interaction between the near-surface turbulent field and the interfacial gas flux in buoyancy driven flow are yet to be fully described. As the interfacial mass transfer of such low-diffusive (high Schmidt number) substances is characterized by very thin diffusive layers near the interface and the instantaneous occurrence of steep concentration gradients in other regions, performing detailed laboratory measurements is extremely difficult. At the same time existing direct numerical simulations (DNS) - constrained by the high demand on computational resources needed to resolve all scales of motion - are mostly limited to low Schmidt numbers (typically less than 10) and/or low Reynolds numbers. We propose to perform direct numerical simulations of buoyancy-driven gas transfer using a specifically-designed numerical code for the discretization of scalar convection and diffusion. To our knowledge, the present study will be the first to perform direct numerical simulation of mass transfer driven by a buoyant-convective instability at realistically high Schmidt numbers up to 500. The detailed data will allow us to determine first and foremost the correlation between the fluctuating concentration and velocity fields -- a quantity which today is extremely difficult to measure with high fidelity in laboratory experiments. In those few experiments which are able to measure this quantity, the trustworthy measurement is typically restricted to a region not too close to the interface and not too deep into the bulk of the fluid. Furthermore, three-dimensional time- and space-resolved measurements of the aforementioned fields do not exist for this flow. The main impact of the proposed project will be a more reliable prediction of the gas transfer rates in the framework of e.g. the global CO2 budget or the oxygen re-aeration in water bodies. More specifically, we will determine the scaling law of the interfacial mass transfer as a function of the Schmidt and Rayleigh numbers. In an application (such as remote sensing) this result will allow to reconstruct the mass transfer rate of a given gas from rescaling of the information on the thermal field alone.