Some properties of generalized age-distribution equations in fluid dynamics

Beckers, JM.;Delhez, E;Deleersnijder, Eric
(2001) SIAM Journal on Applied Mathematics — Vol. 61, n° 5, p. 1526-1544 (2001)

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Abstract
The concept of age in fluid dynamics is analyzed in the case of a tracer advection-diffusion equation. From the general solution in a uniform velocity field, it is shown that unexpected symmetry properties arise for the age field. In particular, for a point release, the age field is isotropic, regardless of the direction of the ow and the value of the diffusion coefficient. The analysis is then extended to situations with time-varying currents, where the symmetry can be broken under some circumstances. Finally, we show a method by which a time-dependent problem can be used to assess a stationary concentration distribution function, providing details about the propagation of younger and older material at a given location.
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Beckers, JM., Delhez, E., & Deleersnijder, E. (2001). Some properties of generalized age-distribution equations in fluid dynamics. SIAM Journal on Applied Mathematics, 61(5), 1526-1544. https://doi.org/10.1137/S0036139999363810 (Original work published 2001)