A systematic approach for obtaining and modeling a nonlocal eddy diffusivity.

We consider nonlocal eddy diffusivities for passive scalar transport phenomena and show how to exactly obtain them using the macroscopic forcing method (MFM), a technique introduced by Mani and Park (2021). While for many flows the nonlocal eddy diffusivity is more accurate than the commonly used Boussinesq eddy diffusivity, the nonlocal eddy diffusivity is often too computationally cost-prohibitive to obtain and use in practice. We develop a systematic and more cost-effective approach for approximating the nonlocal eddy diffusivity using matched moment inverse (MMI) operators. These operators require only a few moments of the nonlocal eddy diffusivity which can be computed more easily using inverse MFM and the resulting model can be written as a partial differential equation rather than a nonlocal integral.