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Fujihiro Hamba

Abstract

The Green's function for scalar fluctuations is introduced into a large eddy simulation of the convective boundary layer to investigate nonlocal scalar transport. This Green's function is used to derive a nonlocal expression for the scalar flux and to evaluate a coefficient called the turbulent diffusivity function. Such an expression.shows that scalar transport is nonlocal in both spce and time. It is shown that the scalar flux in the middle of the boundary layer is influenced by the scalar gradient in the whole boundary layer. The top-down and bottom-up diffusion as well as the countegradient transport is explained by the turbulent diffusivity function. Moreover, a nonlocal expression for the pressure scalar correlation term in the second-order model is proposed using the same Green's function. It is shown that the nonlocal property of the pressure term accounts for the difference in the return-to-isotropy timescales between the top-down and bottom-up diffusion.

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Fujihiro Hamba

Abstract

A modified first-order model is proposed for scalar diffusion in the convective boundary layer. In addition to the eddy diffusivity term, the model includes a term proportional to the second derivative of the mean scalar. The coefficient of the new term is closely related to the skewness of the vertical velocity component and to the inhomogeneity of the turbulent field. The model is used to explain the difference in eddy diffusivity between the top-down and bottom-up diffusion as well as the countergradient transport of the bottom-up scalar. The model is different from the approach of top-down and bottom-up decomposition in the respect that the former does not assume a linear profile of scalar flux or does not depend on the ratio of the entrainment flux to the surface flux. Unlike a previous countergradient term, the proposed term does not need to be combined with the top-down and bottom-up decomposition. The model equation is numerically solved to obtain the scalar gradient profile for three types of scalar fluxes including a quadratic profile with respect to height. It is shown that results of the modified first-order model agree well with large-eddy simulation data. Results of the usual K model are very different from those of the modified first-order model in the upper half of the boundary layer. Numerical data or observations are required to determine profiles of two coefficients in the modified model. The profiles may vary from one turbulent flow to another. Further modeling of the coefficients is necessary to obtain a more general model.

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