Vertical, lateral and longitudinal eddy diffusivities for a decaying turbulence in the convective boundary layer

A general method to derive eddy diffusivities in a convective decaying turbulence in the convective boundary layer (CBL) is proposed in this paper. The method is based in a model for the budget equation describing the 3D energy density spectrum and the Taylor statistical diffusion theory. Firstly, on the basis of a dimensional analysis, the unknown inertial transport term present in dynamical equation for the 3D spectrum is parameterized. The 3D energy density spectrum equation is resolved. To calculate the longitudinal and lateral components of the eddy diffusivity the turbulent field is considered isotropic in the horizontal direction. The 1D vertical spectrum is derived from the 3D spectrum decaying, employing a weight function that allows to select the magnitude of the vertical spectral component for the construction of the decaying 3D energy density spectrum. Finally, it is reported that an numerical comparison of the proposed 1D eddy diffusivities decaying with the results for convective boundary layer decaying by LES calculations. This eddy diffusivity can be used in the diffusion-advection equation to calculate the field of concentration of pollutants in the low atmosphere.