Stochastic modeling of surface scalar-flux fluctuations in turbulent channel flow using one-dimensional turbulence

Accurate and economical modeling of near-surface transport processes is a standing challenge for various engineering and atmospheric boundary-layer flows. In this paper, we address this challenge by utilizing a stochastic one-dimensional turbulence (ODT) model. ODT aims to resolve all relevant scales of a turbulent flow for a one-dimensional domain. Here ODT is applied to turbulent channel flow as stand-alone tool. The ODT domain is a wall-normal line that is aligned with the mean shear. The free model parameters are calibrated once for the turbulent velocity boundary layer at a fixed Reynolds number. After that, we use ODT to investigate the Schmidt ($Sc$), Reynolds ($Re$), and Peclet ($Pe$) number dependence of the scalar boundary-layer structure, turbulent fluctuations, transient surface fluxes, mixing, and transfer to a wall. We demonstrate that the model is able to resolve relevant wall-normal transport processes across the turbulent boundary layer and that it captures state-space statistics of the surface scalar-flux fluctuations. In addition, we show that the predicted mean scalar transfer, which is quantified by the Sherwood ($Sh$) number, self-consistently reproduces established scaling regimes and asymptotic relations. For high asymptotic $Sc$ and $Re$, ODT results fall between the Dittus--Boelter, $Sh\sim Re^{4/5}\,Sc^{2/5}$, and Colburn, $Sh\sim Re^{4/5}\,Sc^{1/3}$, scalings but they are closer to the former. For finite $Sc$ and $Re$, the model prediction reproduces the relation proposed by Schwertfirm and Manhart (Int. J. Heat Fluid Flow, vol. 28, pp. 1204-1214, 2007) that yields locally steeper effective scalings than any of the established asymptotic relations. The model extrapolates the scalar transfer to small asymptotic $Sc\ll Re_\tau^{-1}$ (diffusive limit) with a functional form that has not been previously described.
Comment: Accepted manuscript. 30 pages, 13 figures. Version-of-record available online 11/30/2021 at URL: https://www.sciencedirect.com/science/article/pii/S0142727X21001193