= Solution
The three questions concern different statistics. <Taylor turbulent dispersion> follows the absolute displacement of one marked <fluid element> from its release position, or the spreading of the centre of a cloud. Its input is the <velocity> <autocorrelation> along a <Lagrangian trajectory>. It relates short-time ballistic motion to long-time effective <diffusion>. This is not the shear-flow mechanism ordinarily called <Taylor dispersion>.
<Richardson pair dispersion> instead follows the separation of two fluid elements, or the growth of a cloud relative to its moving centre. Common sweeping by an eddy much larger than the cloud contributes to absolute displacement but largely cancels from relative displacement. The relative diffusivity depends on separation; the classical inertial-range prediction is a $t^3$ mean-square separation regime after memory of the release separation is lost.
<Obukhov-Corrsin theory>, also called <Kolmogorov-Obukhov-Corrsin theory>, concerns spatial fluctuations of a <passive scalar>, their transfer across scales and their destruction by molecular <diffusion>. Its objects are <scalar structure functions> and scalar spectra, with an inertial-convective prediction controlled by scalar-variance flux and the turbulent energy supply. Thus \b[Taylor describes one-particle transport, Richardson describes relative spreading, and Obukhov-Corrsin describes scale-by-scale scalar mixing]. Following a cloud's location is not the same as predicting its internal concentration fluctuations.
Back to article page
