A depth-averaged 2D shallow water model for breaking and non-breaking long waves affected by rigid vegetation

Abstract

This paper presents a depth-averaged two-dimensional shallow water model for simulating long waves in vegetated water bodies under breaking and non-breaking conditions. The effects of rigid vegetation are modelled in the form of drag and inertia forces as sink terms in the momentum equations. The drag coefficient is treated as a calibrated bulk constant and also determined using two empirical formulas as functions of stem Reynolds number, Froude number, and vegetation volume fraction. The governing equations are solved using an explicit finite-volume method based on rectangular mesh with the Harten, Lax, and van Leer approximate Riemann solver with second-order piecewise linear reconstruction for the streamwise convection fluxes, a second-order upwind scheme for the lateral convection fluxes, and a stable centred difference scheme for the water surface gradient terms. The model was tested using five laboratory experiments, including steady flow in a flume with alternate vegetation zones, solitary wave in a vegetated flatbed flume, long-wave runup on a partially-vegetated sloping beach, the dam-break wave overtopping an obstacle, and breaking the solitary wave on a sloping beach. The computed water levels, flow velocities, wave heights, and runups are in generally good agreement with experimental observations. The model was then applied to assess the hydrodynamic effectiveness and limitations of vegetation in coastal and river protection. It is shown that vegetation along the coastal shoreline has a positive benefit in reducing wave runup on sloping beaches, whereas vegetation in open channels causes conflicting impacts: reducing inundation in the downstream areas, but increasing flood risk in a certain distance upstream.