fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

, Erdogan–Chatwin equation refers to a nonlinear

diffusion equation The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's l ...

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 equation in 1967. The equation for the scalar field

\varphi(x,t)

readsSmith, 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. :

\varphi_t = (\varphi_x+a\varphi_x^3)_x,

where

a

is a positive constant. For

a\ll 1

, the equation reduces to the linear

heat equation In mathematics and physics (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quanti ...

\varphi_t = \varphi_

and for

a\gg 1

, the equation reduces to

\varphi_t = 3a\varphi_x^2\varphi_

References

{{DEFAULTSORT:Erdogan-Chatwin equation Equations of fluid dynamics Fluid dynamics Partial differential equations

See also

References