A Depth-Averaged Method for Estimating Velocity Profile Evolution in a Granular Flow*

We present a method for estimating the depth-dependent velocity profiles of free surface granular flows from evolving surface velocity and flow-depth data. We first derive a quasi-two-dimensional three-variable depth-averaged model for free surface flows that accommodates the inclusion of a varying basal boundary condition. This model is then used in conjunction with an ensemble Kalman Filter (enKF) and free surface data to examine the inverse problem: “What is the internal velocity field of the flow, given our model and free surface data?”. We demonstrate the capabilities of this method by applying our algorithm to the Blasius boundary-layer problem described in Tsang et al. (2018). Synthetic, evolving free surface data is generated from discrete particle model (DPM) simulations and then input into the enKF/depth-averaged algorithm in order to estimate the internal velocity. These estimates are then compared to the coarse-grained DPM velocity field and are shown to provide a good fit to the synthetic data. We believe our method has clear potential, not just in modelling free surface flows, but also as a powerful data-analysis tool for experimentally validating modelling work done within the granular community.