Approximate solution of boundary layer problems with injection or suction

Schetz, Joseph A.; Oh, Sin K.

doi:10.1007/bf01603279

Cited by 4 publications

(1 citation statement)

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“…By exploiting a suggestion of Shwetz (; see also Panchev et al, ) and thereby retaining the MO profiles of

(\overset{u}{false}, K_{c})

, Wilson () gave an approximate solution of Eq. for a finite ground‐level area source in the stably (or neutrally) stratified surface layer.…”

Section: Introductionmentioning

confidence: 99%

Dispersion from an area source in the unstable surface layer: an approximate analytical solution

Wilson

2015

Quart J Royal Meteoro Soc

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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.

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“…By exploiting a suggestion of Shwetz (; see also Panchev et al, ) and thereby retaining the MO profiles of