By applying the theory of random walk to a turbulent flow, the frequency distribution functions of wind speed and wind direction are derived. The turbulence in the flow is assumed to be homogeneous and isotropic in the horizontal, and further the phase angles of each component of the Fourier series of the finite variable wind speed are assumed to be at random and independent of each other.
Further by using the frequency distribution functions of wind speed, the diffusivity in the horizontal is obtained. Because there is no conclusive Lagrangian correlation function, we discussed the diffusivity using some correlation functions.
The theory is tested by using the records obtained in the Research Institute of Atomic Energy in Tokai Mura, Ibaraki Prefecture.