Erdogan–Chatwin equation explained

In fluid dynamics, Erdogan–Chatwin equation refers to a nonlinear diffusion equation for the scalar field, that accounts for shear-induced dispersion due to horizontal buoyancy forces. The equation was named after M. Emin Erdogan and Phillip C. Chatwin, who derived the equaiton in 1967.^[1] The equation for the scalar field

reads^{[2] [3] [4]}

where

is a positive constant. For , the equation reduces to the linear heat equation, and for , the equation reduces to .

Notes and References

1. Erdogan, M. E., & Chatwin, P. C. (1967). The effects of curvature and buoyancy on the laminar dispersion of solute in a horizontal tube. Journal of Fluid Mechanics, 29(3), 465-484.
2. Smith, R. (1978). Asymptotic solutions of the Erdogan-Chatwin equation. Journal of Fluid Mechanics, 88(2), 323-337.
3. Barton, N. G. (1976). The dispersion of a buoyant solute in laminar flow in a straight horizontal pipe. Part 1. Predictions from Erdogan & Chatwin's (1967) paper. Journal of Fluid Mechanics, 74(1), 81-89.
4. Smith, R. (1982). Similarity solutions of a non-linear diffusion equation. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 28(2), 149-149.