Comparison between Gaussian and advection diffusion equation of Eulerian and Lagrangian integral time scales in stable condition

The displacement mean-square parameters (X^2 ) ̅(t),(Y^2 ) ̅(t)and (Z^2 ) ̅(t)need to be increasing functions of time. In a stable and homogeneous field of turbulence, the variances of Lagrangian velocity fluctuations must be equal to the corresponding Eulerian velocity variances and independent of time. The mean-square particle displacement rises proportionately to the square of the diffusion time "t2" for small diffusion times. The mean-square diffusion finally becomes proportional to the diffusion time (t) and the Lagrangian integral time scale (TiL) for long diffusion times. The three-dimensional advection-diffusion equation and Gaussian model are computed using these dispersion values. The results of these concentrations are contrasted with Iodine-131 experimental data that was gathered at the Egyptian Atomic Energy Authority under steady conditions.