Characteristics of turbulent diffusion in the atmospheric surface layer are theoretically treated, and the results are corroborated by experimental data in Parts I to V.
The results are as follows: D e tailed discussion on the universal function is given in Parts I to IV. The theoretical relations of the stability to the turbulent heat flux and eddy diffusion coefficient are compared with the experimental ones. It is to be emphasized that the experimental data show good agreement with the theory.
Relations between the standard deviation of smoke cloud and the down-wind distance are derived theoretically and are compared with the experimental data in wider range of stability. Detailed discussion is given in Part IV.
Data obtained in the Project Green Glow are analysed by the numerical experiment in Part V. Taking the experimental site into account, the concentration patterns in the vertical direction are in good agreement with the experimetal data especially in the stratified flow.
As discussed in Parts I to IV we have obtained good relations between the standard deviation of the smoke plume and the travel distance in the atmospheric surface layer. The conclusion, however, can't be decisive because it is not confirmed with respect to the turbulent-scale using observed facts. In Part VI and VII, the more detailed universal character of turbulence in the atmospheric surface layer is discussed using data obtained from two projects. One of them, nicknamed Futtu Project, was made in Japan by the Meteorological Research Institute. The other was the Great Plain Project in the U. S. A.
First, micro-meteorological data are again analysed to determine the flux-gradient relationships for the transfer of momentum, sensible heat, as well as water vapor in the atmospheric surface layer in Part VI.
The results obtained agree well with the universal relationships under the condition of
z/L varying from 0 to -1 for the unstable and from 0 to 0.25 for the stable.
In Part VII, a set of w ind, temperature and water vapor profile formulae is examined for the constant flux atmospheric surface layer. These formulae imply a relationship between eddy diffusivity and the stability parameter
z/L.
The derivation shows that the gradient Richardson number Ri is not equal to the
z/L. Empirical evidence for the validity is obtained.
A turbulent-scale, which is derived in this part, is related to the eddy diffusivities. The results show that the eddy diffusivities for momentum, sensible heat and water wapor can be expressed respectively by
KM=ε
1/3⋅
Lu4/3KH=ε
1/3⋅
Lu1/3⋅
LθKw=ε
1/3⋅
Lu1/3⋅
Lwhere,
Li indicates the turbulent-scale in the vertical direction for wind, temperature and water vapor respectively with a subscript of
u, θ, as well as
w. ε is the dissipation rate of turbulent energy.
Finally, the turbulent diffusion in the vertical direction is reexamined using the results obtained in Part VI, which can show the diffusion process by a simple rule; the ratio of vertical dispersion to the down-wind distance increases greatly with small wind shear and light mean wind speed, and decreases with large wind shear and strong mean wind speed in non-dimensional forms.
It must, however, be noticed that the sim p le rule mentioned above applies only to open level country and makes no allowance for the possible disturbing effects of buildings and topographical features.
View full abstract