Some properties of generalized age-distribution equations in fluid dynamics

The concept of age in fluid dynamics is analyzed in the case of a tracer ad vection-diffusion equation. From the general solution in a uniform velocity field, it is shown that unexpected symmetry properties arise for the age f ield. In particular, for a point release, the age field is isotropic, regar dless of the direction of the ow and the value of the diffusion coefficient . The analysis is then extended to situations with time-varying currents, w here 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 stationa ry concentration distribution function, providing details about the propaga tion of younger and older material at a given location.