Author(s): Junke Guo; Jianmin Zhang
Keywords: Laminar flow; porous media; turbulent flow; vegetated flow; velocity distribution
Abstract: Vegetated flows are typical in many aquatic systems such as natural and man-made wetlands, and therefore attract significant attention of researchers and engineers. This study first solves the Navier–Stokes–Forchheimer (NSF) equation for laminar vegetated flow and then modifies the obtained velocity distribution for turbulent flow. It demonstrates that (i) for flows through emergent and over submerged vegetation, the laminar velocity distributions are expressed by the Jacobi elliptic functions for which the parabolic law is recovered for zero vegetation; (ii) for flow through emergent vegetation, the laminar velocity distribution exhibits a typical boundary-layer profile, while its turbulent counterpart is simply uniform; and (iii) for flow over submerged vegetation, both laminar and turbulent velocity distributions are similar to those in conventional channel flows for the water layer, but both are approximated by hyperbolic sine laws for the vegetation layer. The laminar solutions meet the NSF equation and all boundary conditions; and the turbulent solutions agree with laboratory and field data.