Numerical simulation of the surface water – groundwater interaction in high mountain riverbeds (2017)
Abstract: Several recent advances have been made on the development of numerical simulations for the flow dynamics on the hyporheic zone of rivers, and generally, for the interaction of a channel flow over a permeable bed, where the mixing of surface and subsurface water is evident. This work has taken into account a revision of the different conceptual, numerical and experimental applications of these advances, identifying their different assumptions and simplifications, such as one-dimensional models of velocity fluctuation and coupled models of turbulent and laminar flow regimes. Special interest is shown in i) how the interface between the turbulent surface flow and the laminar flow in the porous media is managed, ii) the impacts of the imposed boundary conditions on the velocity and pressure fields and iii) the implementation of this model to idealized geometries for high-mountain river-beds. Consequently, a numerical model has been proposed and implemented in OpenFOAM® adopting the existence of pressure and velocity fluctuations coming from the turbulent surface flow of an idealized river, assuming a continuous computational domain containing both surface and porous flows, and characterizing the porous river bed using an apparent viscosity as a continuous space that represents the tortuosity of the flow inside the porous matrix. With this configuration, these simulations executed: 1) a flow over a permeable bed in order to visualize and quantify the dissipation of the velocity when entering into the porous bed, as well as to characterize the flow path within the hyporheic zone; 2) a multiphase flow simulation finding the free surface location of a flow in a flume with a permeable bed with sand river geometries, adapting a transport equation simulating a dye tracer that penetrates the porous bed. For both cases, the results suggest that, in order to correctly represent the flow over a permeable bed, the values of the apparent viscosity must be higher than the value calculated from Higashino’s deduction by at least three orders of magnitude. In addition, results suggest that the calculated velocity and pressure fields are clearly affected by the location and type of the boundary conditions imposed to the computational domain on the zone. From the multiphase flow simulation, the transport simulation of the dyed surface water was compared to a laboratory physical model reported in the literature. The results from this comparison insinuate that the proposed model is able to represent the interaction between the turbulent surface water flow and the groundwater inside a porous bed, finding that for the same orders of magnitude of the previous case, an hyporheic zone can be identified between 0.07cm and 0.12cm under the streambed dunes top.