An Analytical Approach to Shear Dispersion and Tracer Age |
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Authors: | Email author" target="_blank">Ronald?B?SmithEmail author |
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Institution: | (1) Department of Geology and Geophysics, Yale University, 208109, New Haven, CT, U.S.A., 06520-8109 |
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Abstract: | Solutions to the sheared Fickian advection–diffusion equation in a half-space with arbitrary surface source are given using
a ‘transfer function’ method. The method uses Fourier transforms in two horizontal coordinates and time, along with complex
Airy functions in the vertical coordinate. Surface deposition and tracer decay are included in the formulation. ‘Puff’ and
steady ‘plume’ solutions are compared with Saffman’s moment formulae. The inclusion of a decay rate factor (α) allows the
average tracer age to be computed from steady state solutions for concentration C(x, y, z) according to Age = − dln C/dα. A comparison between the puff centroid formula of Saffman and plume Age computations confirms that shear causes tracer puffs
to accelerate horizontally as they diffuse upward into a different wind regime. In forward shear, tracer ages are younger
than in unsheared flow but the range of ages is greater due to the existence of a high fast pathway and a low slow pathway.
In reverse shear, concentrations, ages and the range of ages all rise markedly near the source. Large tracer age suggests
that some tracer has taken a very distant path involving a low-level outbound trip and a high-level return. The effect of
surface deposition is to reduce the influence of the distant path. In the case of reverse shear, deposition makes the tracer
younger. In a turning wind, the time needed to reach a given radius increases due to the curved path of the plume. |
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Keywords: | Deposition Diffusion Dispersion Pollution Shear Tracer |
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