Dunes, turbulent eddies, and interfacial exchange with permeable sediments

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Abstract

[1] Interfaces between a water column and underlying porous media are ubiquitous in nature. Turbulent flow over an irregular interface separating a water column and underlying porous media drives advective-fluid exchange between the two domains. We investigate the dynamics of this coupled system for unidirectional flow in the water column and a triangular interface modeled on dunes. Numerical simulations solve the Reynolds-averaged Navier-Stokes equations for the water column and then Darcy's Law and the continuity equation for the porous media. The two sets of equations are coupled via the pressure distribution along the interface. The pressure maximum and minimum along the interface, which are tied to the presence of an eddy, dominantly control the configuration of and flux through the interfacial exchange zone (IEZ) in the porous media. Since the length of eddies for fully developed turbulent flow is insensitive to the Reynolds numbers (Re), the configuration of the IEZ remains stable across a range of Re, although flux through the IEZ is strongly dependent on the Re. The flux is a power function of Re and a linear function of the current-topography induced pressure gradient along the interface. Mean residence times for fluids in the IEZ follow an inverse-power relationship with Re since the volume of the IEZ is insensitive to Re. The IEZ depths and fluxes can be predicted via equations fitted to the simulated IEZ depths and fluxes, scaled by the dune steepness, for different Re, granted that other systems maintain close dynamic similitude with those studied here.

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