A framework for cost-effective modeling of nonlocal eddy diffusivities

New techniques, such as the Macroscopic Forcing Method (MFM) (Mani and Park (2019), arXiv:1905.08342), have quantified nonlocality as a missing ingredient in Reynolds-averaged Navier-Stokes (RANS) models. In contrast with the commonly used Boussinesq approximation, a purely local approximation, nonlocality allows an unclosed term at a given point to depend on mean field quantities at all points in space and at previous times. However, this dependence also causes implementation of nonlocality to be computationally expensive and impractical for many applications. Using passive scalar transport as an example, we present a framework for cost-effective modeling of spatiotemporal nonlocality with extension to inhomogeneous flows.