This paper discusses the turbulent diffusivities of settling particles in a stationary turbulent field. A solution to the particle diffusivities is derived by the use of the equations of particle motion, the Eulerian spatial correlations approximated by exponential function and Taylor's diffusion theory. The present theory is applied to the analysis of experimental results or Snyder & Lumley (1971) for a grid-generated turbulence and of Calabrese & Middleman (1979) for the turbulent core region of a fully developed vertical pipe flow. The following results are obtained: (1) When the Eulerian spatial correlations, turbulent intensity and particle parameters are given, it is possible to evaluate the particle diffusivities through the present theory. (2) The theoretical results are in good agreements with the experimental results. (3) In isotropic turbulence, the particle diffusivities in the vertical direction are larger than those in the horizontal directions.
定常乱流場において,流体の乱れ強度が粒子の沈降速度より小さい場合に対し沈降性粒子の拡散係数に関する解析を行った.得られた結果を要約すると,(1)定常乱流場における沈降性粒子の変動速度のスペクトル,拡がり幅の自乗および拡散係数の理論解を提示した.(2)沈降性粒子の拡がり幅の自乗の理論解とSnyder and Lumley(1971)およびCalabrese and Middleman(1979)の実験結果との比較を行い,ほぼよい一致を得た.(3)等方性の乱れの場において,粒子の鉛直方向の拡散係数は水平方向より大きくなる.