Direct numerical simulation of turbulent scalar transport across a flat surface

Abstract

AbstractTo elucidate the physical mechanisms that play a role in the interfacial transfer of atmospheric gases into water, a series of direct numerical simulations of mass transfer across the air–water interface driven by isotropic turbulence diffusing from below has been carried out for various turbulent Reynolds numbers ($R_T=84,195,507$). To allow a direct (unbiased) comparison of the instantaneous effects of scalar diffusivity, in each of the DNS up to six scalar advection–diffusion equations with different Schmidt numbers were solved simultaneously. As far as the authors are aware this is the first simulation that is capable to accurately resolve the realistic Schmidt number, $\mathit{Sc}=500$, that is typical for the transport of atmospheric gases such as oxygen in water. For the range of turbulent Reynolds numbers and Schmidt numbers considered, the normalized transfer velocity $K_L$ was found to scale with $R_T^{-{1/2}}$ and $\mathit{Sc}^{-{1/2}}$, which indicates that the largest eddies present in the isotropic turbulent flow introduced at the bottom of the computational domain tend to determine the mass transfer. The $K_L$ results were also found to be in good agreement with the surface divergence model of McCready, Vassiliadou & Hanratty (AIChE J., vol. 32, 1986, pp. 1108–1115) when using a constant of proportionality of 0.525. Although close to the surface large eddies are responsible for the bulk of the gas transfer, it was also observed that for higher $R_T$ the influence of smaller eddies becomes more important.