Quantifying Suspended Sediment Diffusion Through Direct \textit{in situ} Measurements of Turbulent Schmidt Number

In this study we investigate how the diffusion of suspended sediment differs from the diffusion of fluid momentum using both laboratory and \textit{in situ} field measurements. The most common model for turbulent diffusion considers eddy diffusivity ($D_{T})$ to be proportional to the eddy viscosity (\textit{$\nu $}$_{T})$ scaled by the turbulent Schmidt number (\textit{$\sigma $}$_{T})$. But accurate selection of \textit{$\sigma $}$_{T}$ values is challenging because sediment, by virtue of its inertia, is transported differently than either momentum or passive scalars. We directly measure \textit{$\sigma $}$_{T}$ over a variety of flow cases using a novel Volumetric Particle Imager (VoPI) developed for this purpose. VoPI is a field-deployable quantitative imaging device that can obtain three-component particle velocity records in a volume. By computing velocity variances and integral timescales from measured Lagrangian velocity records, we compute $D_{T}$ (for particles) and \textit{$\nu $}$_{T}$ (for tracers) directly using Taylor's (1921) formulation. We present the construction and calibration of the device as well as validation of its measurements. We also report the connections between the measured \textit{$\sigma $}$_{T}$ values and the flow conditions in which they occur and suggest predictive methods for when direct measurements are unavailable.