Abstract
The near-shore and estuary environment is characterized by complex natural processes. A prominent feature is the wind-generated waves, which transfer energy and lead to various phenomena not observed where the hydrodynamics is dictated only by currents. Over the past several decades, numerical models have been developed to predict the wave and current state and their interactions. Most models, however, have relied on the two-model approach in which the wave model is developed independently of the current model and the two are coupled together through a separate steering module. In this study, a new wave model is developed and embedded in an existing two-dimensional (2D) depth-integrated current model, SRH-2D. The work leads to a new wave–current model based on the one-model approach. The physical processes of the new wave model are based on the latest third-generation formulation in which the spectral wave action balance equation is solved so that the spectrum shape is not pre-imposed and the non-linear effects are not parameterized. New contributions of the present study lie primarily in the numerical method adopted, which include: (a) a new operator-splitting method that allows an implicit solution of the wave action equation in the geographical space; (b) mixed finite volume and finite difference method; (c) unstructured polygonal mesh in the geographical space; and (d) a single mesh for both the wave and current models that paves the way for the use of the one-model approach. An advantage of the present model is that the propagation of waves from deep water to shallow water in near-shore and the interaction between waves and river inflows may be carried out seamlessly. Tedious interpolations and the so-called multi-model steering operation adopted by many existing models are avoided. As a result, the underlying interpolation errors and information loss due to matching between two meshes are avoided, leading to an increased computational efficiency and accuracy. The new wave model is developed and verified using a number of cases. The verified near-shore wave processes include wave shoaling, refraction, wave breaking and diffraction. The predicted model results compare well with the analytical solution or measured data for all cases.
Highlights
The near-shore estuary and coastal environment is characterized by complex natural processes driven by tides, waves, currents, saline water and the interactions among them [1,2]
In terms of the physical processes, the current state of the art based on the third-generation wave modeling approaches is adopted: the governing equations largely follow the formulation adopted by SWAN to solve the wave action balance equation in which the spectrum shape is not pre-imposed and the non-linear effects are not parameterized [54]
The results show that wave propagation does not show any diffraction behind the semi-infinite plate if the diffraction treatment presented in Section 2.4 is not applied
Summary
The near-shore estuary and coastal environment is characterized by complex natural processes driven by tides, waves, currents, saline water and the interactions among them [1,2]. All early third-generation models employed the first- or second-order finite difference schemes and were limited to the structured mesh. Roland et al [40] reported the wind wave model (WWM) which employed finite element methods in geographical space. In terms of the physical processes, the current state of the art based on the third-generation wave modeling approaches is adopted: the governing equations largely follow the formulation adopted by SWAN to solve the wave action balance equation in which the spectrum shape is not pre-imposed and the non-linear effects are not parameterized [54]. The finite volume method is adopted in the geographical space with the unstructured polygonal mesh This is to conform to the mesh system adopted by SRH-2D; this way, the wave model may be embedded within SRH-2D using the one-model approach. As a result, underlying interpolation errors and information loss due to solution matching between different meshes are avoided, leading to an increased computational efficiency and accuracy
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