  This study considers advective and diffusive transport of passive scalar
fields by spatially-varying incompressible flows. Prior studies have shown that
the eddy diffusivities governing the mean field transport in such systems can
generally be nonlocal in space and time. While for many flows nonlocal eddy
diffusivities are more accurate than commonly-used Boussinesq eddy
diffusivities, nonlocal eddy diffusivities are often computationally
cost-prohibitive to obtain and difficult to implement in practice. We develop a
systematic and more cost-effective approach for modeling nonlocal eddy
diffusivities using matched moment inverse (MMI) operators. These operators are
constructed using only a few leading-order moments of the exact nonlocal eddy
diffusivity kernel, which can be easily computed using the inverse macroscopic
forcing method (IMFM) (Mani and Park (2021)). The resulting reduced-order
models for the mean fields that incorporate the modeled eddy diffusivities
often improve Boussinesq-limit models since they capture leading-order nonlocal
effects. But more importantly, these models can be expressed as partial
differential equations that are readily solvable using existing computational
fluid dynamics capabilities rather than as integro-partial differential
equations.
