AN EFFICIENT PARAMETERIZATION OF SUBMERGED TURBULENT FLOWS INSIDE STREAM GRAVEL BEDS

Understanding of hyporehic exchange processes in gravel bed streams requires information on the transport mechanisms at the interface where stream water and subsurface water mix. Modeling the flow problem is often done by solving the Navier-Stokes equations in the stream and applying the porous media theory inside the gravel. When the flow is turbulent and the pore-scale Reynolds number is above unity, the Darcy Law is no longer valid. The drag forces inside the gravel are computed, under such conditions, by the Forchheimer Equation, -dh/dx=αq+βq², where h is the hydraulic head, x is the flow direction, q is the water flux (superficial velocity) and α and β are the two Forchheimer parameters. A major difficulty in using the Forchheimer Equation is in evaluating the actual value of α and β. This evaluation is difficult in the laboratory and even more so under field conditions.

We developed an efficient method for the parameterization of submerged turbulent flows which is based on an analytical solution of the steady state continuity equation and the Forchheimer Equation. The method was tested using four different porous media including pebbles, a random cylinders array, foam rubber, and insulation fiber material. The proposed analytical solution was used to calculate the value of α and β twice; an approximated representation of the analytical solution and a complete representation of the analytical solution which includes a non-linear curve fit scheme. The calculations where then compared with the results of a column experiment (as often used in the soil physics literature to obtain the hydraulic conductivity coefficient).

Most of the natural streams in semi-arid regions are either dry or deliver low flow rates. Discharge is often so low that the whole water flow disappears, before it reappears at some downstream sections (e.g., ‘mid-reach drying'). We will show that when the flow is submerged, as occur in mid-reach drying streams, the proposed method is very useful when the flow in gravel bed streams and the hyporehic exchange processes are to be analyzed.