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C. C. Shir

Abstract

This paper deals with a numerical study of the influence of changes in surface roughness on the turbulent boundary layer in the lower layer of the atmosphere under neutral conditions. The whole set of equations governing the flow is solved by a finite-difference method. The turbulent energy equation is included to provide a better understanding of turbulent mechanisms. The pressure gradient is treated implicitly. Computational results agree well with Bradley's observations. A local minimum of surface stress is found at a short distance from the edge (dividing line) in the case of smooth-to-rough transition. Two boundary layers, a velocity layer and a stress layer, are found. The height of the velocity layer is about one-half that of the stress layer. Both layers follow the 4/5 power law. The height-to-fetch ratio for the internal boundary layer is found to be about 1/10 for the stress and 1/20 for the velocity. The height-to-fetch ratio for a new nearly equilibrium layer is about 1/100 for the smooth-to-rough case and 1/200 for the rough-to-smooth case far downwind. The stress is close to the upstream value for the upper portion of the transition layer. An inflection point of the velocity profile occurs in the transition region. The non-dimensional wind shear is significantly different from the value of unity which exists in an equilibrium flow.

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C. C. Shir

Abstract

A turbulent transport model is developed to study atmospheric turbulence in the planetary boundary layer. A total of nine equations governing the mean motion, mean turbulent stresses, and turbulence length scale are integrated numerically. In this preliminary study, only the ideal case of neutral lapse rate, barotropic, statistically stationary, and horizontally homogeneous conditions is treated.

The height of the boundary layer is investigated and found to be about 0.5 u */f, where u * and f are the friction velocity and Coriolis force parameter, respectively. The computed friction coefficient, the crossisobaric angle, the vertical profiles of mean wind, mean turbulent stresses, the turbulent length scale, and eddy coefficients agree well with observations and with Deardorff's results. Various terms in the turbulent stress equations, which are difficult to measure, are discussed. The direction of the stresses seems to align with the direction of the wind shear. The profiles of the turbulent diffusivity (a ratio of the turbulent to turbulent quantities) are similar to those of the eddy coefficient (a ratio of the turbulent to mean quantities). The profiles of the nondimensional eddy coefficient can he described by the simple form as KN=kze−4z. The profiles of the turbulent energy and the magnitude of the horizontal shear stresses can be approximately described by (1−z)α. The Coriolis force is found not to affect the turbulence significantly.

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C. C. Shir and L. J. Shieh

Abstract

A generalized urban air pollution model, based on numerical integration of the concentration equation, is developed for the study of air pollutant distributions over an urban area. The model computes the temporal and three-dimensional spatial concentration distributions resulting from specified multiple point and area sources by using currently available meteorological and source inventory data. A new method based on experiments and a turbulence transport model is used to estimate the turbulent diffusivity and atmospheric stability. Special treatments of the finite-difference scheme to accommodate the large variations of concentrations are discussed. An effort has been made to avoid any subjective analysis scheme for the preparation of the input data.

The model was used to study SO2 distributions in the St. Louis metropolitan area during 25 consecutive days in February 1965. The computed results were evaluated with respect to observed data by using various statistic methods. The computed results agree favorably with experimental measurements for both long-term and short-term average concentrations. Computations also indicate the model's capabilities and flexibilities for dealing with the rapid variations of atmospheric conditions. The advantages and limitations of the model are also discussed.

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