1. Gas Transfer Across Air‐Water Interfaces in Inland Waters: From Micro‐Eddies to Super‐Statistics.
- Author
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Katul, Gabriel, Bragg, Andrew, Mammarella, Ivan, Liu, Heping, Li, Qi, and Bou‐Zeid, Elie
- Subjects
BODIES of water ,PROBABILITY density function ,KINEMATIC viscosity ,KINETIC energy ,AQUATIC ecology - Abstract
In inland water covering lakes, reservoirs, and ponds, the gas exchange of slightly soluble gases such as carbon dioxide, dimethyl sulfide, methane, or oxygen across a clean and nearly flat air‐water interface is routinely described using a water‐side mean gas transfer velocity kL‾ $\overline{{k}_{L}}$, where overline indicates time or ensemble averaging. The micro‐eddy surface renewal model predicts kL‾=αoSc−1/2νϵ‾1/4 $\overline{{k}_{L}}={\alpha }_{o}S{c}^{-1/2}{\left(\nu \overline{{\epsilon}}\right)}^{1/4}$, where Sc $Sc$ is the molecular Schmidt number, ν $\nu $ is the water kinematic viscosity, and ϵ‾ $\overline{{\epsilon}}$ is the waterside mean turbulent kinetic energy dissipation rate at or near the interface. While αo=0.39−0.46 ${\alpha }_{o}=0.39-0.46$ has been reported across a number of data sets, others report large scatter or variability around this value range. It is shown here that this scatter can be partly explained by high temporal variability in instantaneous ϵ ${\epsilon}$ around ϵ‾ $\overline{{\epsilon}}$, a mechanism that was not previously considered. As the coefficient of variation CVe $\left(C{V}_{e}\right)$ in ϵ ${\epsilon}$ increases, αo ${\alpha }_{o}$ must be adjusted by a multiplier 1+CVe2−3/32 ${\left(1+C{V}_{e}^{2}\right)}^{-3/32}$ that was derived from a log‐normal model for the probability density function of ϵ ${\epsilon}$. Reported variations in αo ${\alpha }_{o}$ with a macro‐scale Reynolds number can also be partly attributed to intermittency effects in ϵ ${\epsilon}$. Such intermittency is characterized by the long‐range (i.e., power‐law decay) spatial auto‐correlation function of ϵ ${\epsilon}$. That αo ${\alpha }_{o}$ varies with a macro‐scale Reynolds number does not necessarily violate the micro‐eddy model. Instead, it points to a coordination between the macro‐ and micro‐scales arising from the transfer of energy across scales in the energy cascade. Plain Language Summary: In inland water, the movement of slightly soluble gas molecules such as carbon dioxide, methane or oxygen across an air‐water interface is of significance to a plethora of applications in aquatic ecology, climate sciences, and limnology. The standard model, known as the micro‐eddy model, considers water packets ejected from deeper levels within an inland water body, making contact with a clean and nearly flat air‐water surface, exchanging molecules with the atmosphere, and subsequently sweeping back down. Under a set of restrictive assumptions about the statistics of contact duration and their inference from water‐side velocity statistics near the surface, prediction of the efficiency of the exchange process can be made and encoded in a so‐called gas transfer velocity. The work here demonstrates that this gas transfer velocity can be derived by assuming a turnover velocity of these water packets that follows a universal form based on a widely accepted theory of energy transfer across scales and contemporary refinements to it. Key Points: The micro‐eddy model (MEM) operationally describes the air‐water gas transfer velocity kL $\left({k}_{L}\right)$ for slightly soluble gasesThe MEM leads to kL ${k}_{L}$ being proportional to the Kolmogorov micro‐scale velocity vk $\left({v}_{k}\right)$Increased variability and intermittency in the turbulent kinetic energy dissipation rate act to reduce kL ${k}_{L}$ for the same vk ${v}_{k}$ [ABSTRACT FROM AUTHOR]
- Published
- 2024
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