Depth-integrated free-surface flow with a two-layer non-hydrostatic formulation

摘要

This paper presents the derivation of a depth-integrated wave propagation and runup model from a system of governing equations for two-layer non-hydrostatic flows. The governing equations are transformed into an equivalent, depth-integrated system, which separately describes the flux-dominated and dispersion dominated processes. The depth-integrated system reproduces the linear dispersion relation within a 5% error for water depth parameter up to kd=11, while allowing direct implementation of a momentum conservation scheme to model wave breaking and a moving-waterline technique for runup calculation. A staggered finite-difference scheme discretizes the governing equations in the horizontal dimension and the Keller box scheme reconstructs the non-hydrostatic terms in the vertical direction. An semi-implicit scheme integrates the depth-integrated flow in time with the non-hydrostatic pressure determined from a Poisson-type equation. The model is verified with solitary wave propagation in a channel of uniform depth and validated with previous laboratory experiments for wave transformation over a submerged bar, a plane beach, and fringing reefs.