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Advection Maps for Closed Flows

Advection refers to the variation of a scalar field, induced by the effects of a superposed vector field, for example, the transport of pollutants to a river. A simple periodically repeating model of sinusoidal shear in a square region of size is considered, assuming velocities with inversion symmetry.

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For the velocity field, we choose
, , if ,
, , if ,
where is the maximum velocity and is the period, generating the mapping
where
.
Reference
[1] T. Tél and M. Gruiz, Chaotic Dynamics: An Introduction Based on Classical Mechanics, Cambridge, UK: Cambridge University Press, 2006.

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