Scaling Gas Transfer with Turbulent Dissipation for a Range of Environmental Processes

For sparingly soluble gases, theory predicts that the gas transfer velocity, k, is controlled by turbulence in the surface aqueous boundary layer, which dictates the rate at which gases can be brought into contact with the surface to exchange with the atmosphere. Since gas transfer has been shown to scale with wind-generated turbulence in many field and laboratory wind-wave experiments, wind-based relationships to model k are typically used for gas exchange estimates from the open oceans to estuaries and rivers despite the acknowledged role of physical processes not related to wind (e.g., tidal currents, rain, stratification, surfactants, and water depth). In an effort to explicitly relate turbulence near the surface aqueous boundary layer to gas exchange, models have been developed for k based on the turbulent kinetic energy dissipation rate, ε. A fundamental relationship shows k scales with ( ) nSc−41εν, where the Schmidt number, Sc, is defined as the ratio of the kinematic viscosity of water, ν, to mass diffusivity. The Schmidt number exponent n is believed to vary between and depending on the surface boundary conditions. This expression for k based on ε is consistent with mass diffusion across a layer of the thickness of the Batchelor [1959] scale [Melville, 1996], and has been derived by Lamont and Scott [1970] using surface-renewal theory [Danckwerts, 1951] and also has been derived by Kitaigorodskii [1984] in the context o