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

Abstract

SUMMARYNon‐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 non‐hydrostatic 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. Copyright © 2012 John Wiley & Sons, Ltd.