# A modified first-order model for scalar diffusion in the convective boundary layer

## 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 transports 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 differentmore »

- Authors:

- (Univ. of Tokyo (Japan))

- Publication Date:

- OSTI Identifier:
- 5606350

- Resource Type:
- Journal Article

- Journal Name:
- Journal of the Atmospheric Sciences; (United States)

- Additional Journal Information:
- Journal Volume: 50:16; Journal ID: ISSN 0022-4928

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 54 ENVIRONMENTAL SCIENCES; DIFFUSION; MATHEMATICAL MODELS; EARTH ATMOSPHERE; ATMOSPHERIC CIRCULATION; BOUNDARY LAYERS; COMPUTERIZED SIMULATION; CONVECTION; METEOROLOGY; NUMERICAL DATA; TURBULENT FLOW; DATA; ENERGY TRANSFER; FLUID FLOW; HEAT TRANSFER; INFORMATION; LAYERS; MASS TRANSFER; SIMULATION; 540110*

### Citation Formats

```
Hamba, Fujihiro.
```*A modified first-order model for scalar diffusion in the convective boundary layer*. United States: N. p., 1993.
Web. doi:10.1175/1520-0469(1993)050<2800:AMFOMF>2.0.CO;2.

```
Hamba, Fujihiro.
```*A modified first-order model for scalar diffusion in the convective boundary layer*. United States. doi:10.1175/1520-0469(1993)050<2800:AMFOMF>2.0.CO;2.

```
Hamba, Fujihiro. Sun .
"A modified first-order model for scalar diffusion in the convective boundary layer". United States. doi:10.1175/1520-0469(1993)050<2800:AMFOMF>2.0.CO;2.
```

```
@article{osti_5606350,
```

title = {A modified first-order model for scalar diffusion in the convective boundary layer},

author = {Hamba, Fujihiro},

abstractNote = {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 transports 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. 24 refs., 10 figs.},

doi = {10.1175/1520-0469(1993)050<2800:AMFOMF>2.0.CO;2},

journal = {Journal of the Atmospheric Sciences; (United States)},

issn = {0022-4928},

number = ,

volume = 50:16,

place = {United States},

year = {1993},

month = {8}

}