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Dispersion from an area source in the unstable surface layer: an approximate analytical solution
Author(s) -
Wilson John D.
Publication year - 2015
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2609
Subject(s) - mechanics , eddy diffusion , dispersion (optics) , advection , plume , turbulence modeling , atmospheric dispersion modeling , meteorology , boundary layer , fetch , constant (computer programming) , thermal diffusivity , physics , mathematical analysis , mathematics , turbulence , geology , thermodynamics , chemistry , air pollution , computer science , optics , oceanography , organic chemistry , programming language
An approximate solution to the advection‐diffusion equation is given, applying to a plume in the unstably stratified surface layer emanating from a finite ground‐level area source of trace gas. The approximation consists firstly of representing the mean wind profile by a power law, and secondly, in ‘splitting’ the governing equation so as to determine two components of the mean concentration that, in sum, satisfy the boundary conditions. The solution, which is easy to evaluate, is compared with numerical simulations using a standard Lagrangian stochastic trajectory model (LSM) and, provided the ratio of the upwind fetch of source to the Obukhov length is not too large ( | x / L | ≤ 10 ), agreement is very good. The Lagrangian model, in turn, is shown to be consistent with the Project Prairie Grass (PPG) dispersion data, subject only to the tuning of a flexible constant whose optimal value carries the implication that the ratio ( S c ) of the eddy viscosity to the (far field) eddy diffusivity is not unity in the neutral limit, but rather S c ≈0.64. It seems unlikely this calibration results from having neglected deposition of the PPG ‘tracer’ (sulphur dioxide) to the surface.