A model for turbulent diffusion in a vertically inhomogeneous atmospheric boundary layer

Abstract

An analytical solution of the one-dimensional turbulent diffusion equation considering non-Fickian closure in a vertically inhomogeneous atmospheric boundary layer (ABL) is presented. The presented solution is improved and more physically consistent in the description of dispersion because it includes (for the first time) the explicit gravitational settling (ws) of large particles. Moreover, deposition velocity (vd) as a boundary condition, vertical turbulent velocity (σw), skewness (Sk), vertical Lagrangian time (TLw) scale and relaxation time (τ) ("finite-velocity" diffusion) are included. Via numerical simulations, we analyzed the influence of the countergradient term, dry deposition to the ground and gravitational settling on the concentration field. Our results demonstrate an example of the usefulness of analytical solutions to the advection-diffusion equation.