Studies of the Shimmering Phenomena by Heating (“KAGERO”) in the Atmospheric Surface Layer

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  • INOUE E.
    Division of Meteorology, National Institute of Agricultural Sciences

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Other Title
  • 陽炎現象の研究
  • Part 2. Turbulent Diffusion Phenomena in the Shimmering Layer
  • (2) 陽炎の中の乱流拡散現象

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Characteristics of turbulence in the atmospheric surface layer under an extremely unstable condition, in which the shimmering is predominant, are dealt with theoretically. The shimmering velocity «w2»1/2 and the shimmering temperature «θ2»1/2 are given respectively by<br>«w2»1/2≈(qg/cpρΘ0)1/3Z1/3 and «θ2»1/2≈(q/cpρ)2/3(g/Θ0)-1/3Z-1/3.<br>The mass rate of energy supply εk by thermal stratification and the mass rate of energy dissipation εh due to mechanical turbulence are also given respectively by<br>εk=gq/Θ0cpρ and εh=V*3/kZ<br>Comparing εk and εh with each other the characteristic height L is obtained as<br>L=V*3/kg/Θ0q/cpρ<br>which corresponds to the stability length given by Monin and Obukhov (1954). Above the height L the energy supply εk predominates and, on the contrary, beneath L the energy dissipation εh does. The differences in the scale and the life time of eddies of both types, i. e. shimmering and mechanical type, are given, and the life ime of shimmering eddy is represented by<br>τz≈(gq/Θ0cpρ)-1/3Z2/3, <br>which means that the life time increases with height following the “2/3 power law”.<br>The “1/3 power law” of shimmering velocity gives rise to the “3/2 power law” of the diffusion height H of smoke with the downwind distance x from the continuous source making use of the Kazanskii-Monin method (1957) of calculating the diffusion height, in which the relations<br>dH/dx_??_«w2»1/2/U, «w2»1/2_??_Z1/3_??_H1/3 and U≈const.<br>are taken into account. The rapid increase of diffusion height with distance, i. e. H_??_x3/2, is proved by an experimental result.

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