This paper reports the double-averaged (in space and in time) hydrodynamic equations for mobile-boundary conditions that are\udderived based on the refined double-averaging theorems, modified Reynolds decomposition, and improved definitions of the spatial and time\udbed porosities. The obtained double-averaged conservation equations provide a mathematical framework for studying mobile-boundary flows\udsuch as gravel bed rivers during flood events or flows over vegetated beds. These equations will help in designing measurement campaigns for\udobtaining mobile bed data and their interpretation and parameterization, eventually leading to improved and more robust predictive models.
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