Dispersion in sheared Gaussian homogeneous turbulence

By integrating the Fokker-Planck equation corresponding to a Lagrangian stochastic trajectory model, which is consitent with the selection criterion of Thomson (1987), an analytical solution is given for the joint probability density functionp(xi, ui, t) for the position (xi) and velocity (ui) at timet of a neutral particle released into linearly-sheared, homogeneous turbulence. The solution is compared with dispersion experiments conforming to the restrictions of the model and with a shortrange experiment performed in highly inhomogeneous turbulence within and above a model crop canopy. When the turbulence intensity, wind shear and covariance are strong, the present solution is better than simpler solutions (Taylor, 1921; Durbin, 1983) and as good as any numerical Lagrangian stochastic model yet reported.

[1]  Geoffrey Ingram Taylor,et al.  Diffusion by Continuous Movements , 1922 .

[2]  S. Corrsin,et al.  Heat Transfer in Isotropic Turbulence , 1952 .

[3]  P. Saffman.  The effect of wind shear on horizontal spread from an instantaneous ground source , 1962 .

[4]  F. B. Smith.  The role of wind shear in horizontal diffusion of ambient particles , 1965 .

[5]  Akira Okubo,et al.  DIFFUSION FROM A CONTINUOUS SOURCE IN A UNIFORM SHEAR FLOW1 , 1969 .

[6]  Stavros Tavoularis,et al.  Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. Part 1 , 1981, Journal of Fluid Mechanics.

[7]  Stavros Tavoularis,et al.  Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 2. The fine structure , 1981, Journal of Fluid Mechanics.

[8]  P. A. Durbin,et al.  Stochastic differential equations and turbulent dispersion , 1983 .

[9]  M. Raupach,et al.  Experiments on scalar dispersion within a model plant canopy part I: The turbulence structure , 1986 .

[10]  Peter A. Coppin,et al.  Experiments on scalar dispersion within a model plant canopy part II: An elevated plane source , 1986 .

[11]  Stephen B. Pope,et al.  A generalized Langevin model for turbulent flows , 1986 .

[12]  D. Thomson.  Criteria for the selection of stochastic models of particle trajectories in turbulent flows , 1987, Journal of Fluid Mechanics.

[13]  M. Chung,et al.  Measurement of turbulent dispersion behind a fine cylindrical heat source in a weakly sheared flow , 1989, Journal of Fluid Mechanics.

[14]  Turbulent Diffusion Behind a Heated Line Source in a Nearly Homogeneous Turbulent Shear Flow , 1989 .

[15]  S. Tavoularis,et al.  Measurements of heat diffusion from a continuous line source in a uniformly sheared turbulent flow , 1989, Journal of Fluid Mechanics.

[16]  Michael R. Raupach,et al.  A practical Lagrangian method for relating scalar concentrations to source distributions in vegetation canopies , 1989 .