Determination of River Ecological Discharge from Navier-Stokes-Forchheimer Equation

River water is one of the major resources serving the water needs in food production, economic development, and ecological systems. As the world population grows, optimal use of this water resource is particularly important for sustainable development. For example, if river water is heavily used for irrigation and hydropower by building dams, the downstream ecosystem loses its natural balance and thus limits economic development. Therefore, a minimum water depth must be maintained for river habitats. The objective of this research is therefore to present a scientific method for determining river ecological discharge over a gravel bed river, given a flow depth. Specifically, for a river with porous media bed, we first specify a minimum flow depth to meet habitat requirements; we next solve the flow velocity distributions for both within and above the porous bed, which lead to the minimum discharge. The flow above the porous bed is solved from the classic Navier-Stokes equation; the flow within the porous bed is solved from the Navier-Stokes-Forchheimer equation. The results of this research are useful for reservoir management and operations.