Shear dispersion

This review of shear dispersion emphasizes that the usual one-dimensional diffusion equation, derived by Taylor [Proc. R. Soc. London Ser. A 219, 186 (1953)], is an asymptotic result that is valid only at large time. One route to earlier validity is a systematic wave-number expansion based on the center manifold theorem. This procedure captures much of the early behavior but it does discard exponentially decaying transients. However, in some cases of practical importance, such as tracer release experiments in rivers, the observation of ‘‘anomalous diffusion’’ (i.e., tracer variance growing nonlinearly with time) is at odds with this asymptotic reduction. Alternative approximations and models, which account for exponential transients using a description that is nonlocal in time are reviewed. A secondary theme of this review is the application of shear dispersion to mixing of passive and active scalars in rivers and estuaries. An example is shear dispersion of salt in which the shear flow is created by salinity gradients. Other examples include fixed flux convection.