Advancements in nearshore wave modeling: A unified one-layer nonhydrostatic approach

Abstract

This work presents a novel one-layer nonhydrostatic formulation and model for nearshore waves. The proposed governing equations define velocities and pressures at arbitrary distances from the still water and only contain spatial derivatives of maximum second order. The formulation can be unified into the existing nonhydrostatic models by defining the variables at the middle depth and neglecting certain additional terms. A Stokes-type Fourier analysis was performed to analyze the formulations' properties and determine the location of variables. The proposed formulation exhibited a clear superiority in describing both the linear and nonlinear properties of the coastal waves. The equations were numerically solved using a hybrid-finite, volume-finite difference scheme. The resulting model accurately described the wave-breaking and runup processes that occurred due to the adoption of a shock-capturing scheme and seabed elevation reconstruction. The suggested novel numerical model was validated against two theoretical benchmark tests and three wave transformation experiments.