Determination of the leading order eddy diffusivity in a turbulent wake using PIV data and the Macroscopic Forcing Method

Dispersion of passive scalars, e.g., contaminants or heat, in turbulent wake flows is often mathematically modeled using a gradient diffusion model via the so-called eddy diffusivity. Such models assume locality and isotropy in dispersion closure operators and are often tuned to match reference data, but the validity of those assumptions is rarely assessed for realistic flow fields. In this study, we consider planar space-time resolved velocity fields measured via PIV in a turbulent wake flow behind a triangular wedge to quantitatively assess the eddy diffusivity closure for such flows. The measured velocity data are used to numerically solve the passive scalar transport equation using the Macroscopic Forcing Method (MFM). We will present the leading coefficients of the Kramers-Moyal expansion of the eddy diffusivity operator. The quantified leading order coefficients represent a local but anisotropic eddy diffusivity tensor field. Using a priori and a posteriori analyses of scalar transport against DNS solutions, we will present an assessment of the relative importance of nonlocality versus anisotropy in such flows.