Leo Maas
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Miscellaneous: Diffusion in strained flow
A steady non-central source is emitting a substance into a strained flow field. The concentration contours are described by solving an advection-diffusion equation which is related to Schrodinger's equation for a parabolic potential function, subject to a non-central, local source field. The problem appears solvable in terms of incomplete (integral representations of) Bessel functions.
For a localized source at approximately (x,y)=(6,1) contourlines of concentration (solid) are computed and displayed in plan view. Also shown are streamlines (dashed) of the advecting strain-flow.
Publications:
Maas, L.R.M. (1989) A closed form Green's function describing diffusion in a strained flow field.  SIAM Journal on Applied Mathematics, 49: 1359-1373.