Aerosol size distribution in a coagulating plume: analytical behavior and modeling applications

A new analytical expression that describes the particle size distribution in an expanding plume in terms of N_T is derived. This solution can be extended to include the effects of soot particles on the evolving volatile sulfuric acid aerosols in an aircraft wake. The analytical solution is applied to evaluate errors associated with numerical diffusion in a detailed microphysical code. The analytical expressions derived here can also be employed to initialize models that do not resolve individual aircraft plumes, by providing a simple means for parameterizing the initial aerosol properties after an approximate mixing time.