Application of an analytical solution for unsteady, advective-diffusion to dispersion in the atmosphere

Application of an analytical solution for unsteady, advective-diffusion to dispersion in the atmosphere—II

II—results

Nunge, Richard J.

Abstract In Part I of this work (hereafter referred to as I), an analytical technique was described for solving time-dependent, advective-diffusion problems and particular solutions were described for a wind which is linear in the vertical coordinate and either steady or periodic in time. In Part II, results in the form of first and second order dispersion coefficients, isopleths of dimensionless concentrations of 1 per cent of the initial concentration and ground level concentrations are presented for the linear time-independent wind in two-dimensions, ignoring downwind turbulent diffusion and assuming a constant vertical eddy mixing coefficient. The effects of initial cloud elevation and different ratios of horizontal advection to vertical diffusion are considered by changing the values of the mean wind and the vertical diffusion coefficient. The interactions of these two mechanisms as they affect the cloud dispersion over a time period equal to the time required for the maximum point concentration to fall to I per cent of its initial value are discussed. Although the model imposes an impenetrable upper boundary for vertical diffusion, it is found that this does not influence the results until times on the order of the decay time above. Thus the system models closely an unbounded atmosphere. Further results are obtained for a wind distribution which is linear in the vertical coordinate and has periodic reversals of direction in time. Isopleths of constant concentration, ground level concentration and the first and second order dispersion coefficients are discussed with regard to the mechanisms involved. A particularly startling result is a sign reversal of the second order dispersion coefficient, which serves as the effective horizontal diffusion coefficient. Physically, this means that during certain periods of time the wind reversal forces a horizontal reconsolidation of the pollutant cloud in the average over the vertical extent of the model.