Depth-integrated free-surface flow with parameterized non-hydrostatic pressure

摘要

Non-hydrostatic free-surface models can provide better descriptions of dispersive waves by increasing the number of layers at the expense of computational efficiency. This paper proposes a parameterized nonhydrostatic pressure distribution in a depth-integrated two-layer formulation to reduce computational costs and to maintain essential dispersion properties for modeling of coastal processes. The non-hydrostatic pressure at mid flow depth is expressed in terms of the bottom pressure with a free parameter, which is determined to match the exact linear dispersion relation for the water depth parameter up to kd = 3. This reduces the depth-integrated two-layer formulation to a hybrid system with a tridiagonal matrix in the pressure Poisson equation. Linear dispersion relations and shoaling gradients derived from the present model as well as conventional one-layer and two-layer models provide a baseline for performance evaluation. Results from these three models are compared with previous laboratory experiments for wave transformation over a submerged bar, a plane beach, and a fringing reef. The present model provides comparable results as the two-layer model but at the computational requirements of a one-layer model.