The mean advective and eddy transport of a passive scalar property is examined. Using a theory based on rational approximation of Lagrangian particle statistics, a transport equation relating the mean eddy flux and the mean concentration field Θ is developed. The transport equation is an elaborated advection-diffusion model in which the mean eddy flux is determined by the recent history of the gradient of Θ. The flux law involves an eddy diffusivity which depends on time lag and is defined in terms of fluid particle trajectories. Particle trajectories in simulated geophysical turbulence are used to test the applicability of the restrictions upon which the model is based. Examples are given of how Θ fields are affected by the difference between an advection-diffusion model and its elaborated relative.
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