A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model

The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for breaking waves and dry areas. The dispersive part is treated with a classical finite difference approach. Extensive numerical validations are then performed in one horizontal dimension, relying both on analytical solutions and experimental data. The results show that our approach gives a good account of all the processes of wave transformation in coastal areas: shoaling, wave breaking and run-up

Influence of convex and concave curvatures in a coastal dike line on wave run-up

Due to climatic change and the increased usage of coastal areas, there is an increasing risk of dike failures along the coasts worldwide. Wave run-up plays a key role in the planning and design of a coastal structure. Coastal engineers use empirical equations for the determination of wave run-up. These formulae generally include the influence of various hydraulic, geometrical and structural parameters, but neglect the effect of the curvature of coastal dikes on wave run-up and overtopping. The scope of this research is to find the effects of the dike curvature on wave run-up for regular wave attack by employing numerical model studies for various dike-opening angles and comparing it with physical model test results. A numerical simulation is carried out using DualSPHysics, a mesh-less model and OpenFOAM, a mesh-based model. A new influence factor is introduced to determine the influence of curvature along a dike line. For convexly curved dikes (ad = 210° to 270°) under perpendicular wave attack, a higher wave run-up was observed for larger opening angles at the center of curvature whereas for concavely curved dikes (ad = 90° to 150°) under perpendicular wave attack, wave run-up increases at the center of curvature as the opening angle decreases. This research aims to contribute a more precise analysis and understanding the influence of the curvature in a dike line and thus ensuring a higher level of protection in the future development of coastal structures.Peer ReviewedPostprint (published version

Numerical and experimental study on tsunami run-up and inundation influenced by macro roughness elements

This research study considers long wave run-up experimentally and numerically. At first, an alternative methodology in long wave physical modeling is presented by means of a set of pipe pumps forcing the inflow of a controlled volume of water into a wave channel mimicking a tsunami-like wave shape that is consistently contained by a proportional plus integral plus derivative controller (PID) controller. Arbitrary wave lengths are persistently generated by means of the proposed methodology. First results are compared to tsunami data stemming from conventional experimental configurations with solitary waves as well as with recent numerical modeling results. Comparisons are thoroughly discussed and - in a second step - numerical simulations are accomplished taking the interaction of long wave run-up and macro-roughness elements into account. Four different experimental configurations of macro-roughness elements are carried out while spacing between elements and numbers of obstacle rows are alternated. A fundamental correlation analysis reveals that a correlation of the number of macro-roughness rows, effective area of flow cross section and a grouping factor of different element configurations exists in principle

Model Coupling for Environmental Flows, with Applications in Hydrology and Coastal Hydrodynamics.

The aim of this paper is to present an overview of “model coupling” methods and issues in the area of environmental hydrodynamics, particularly coastal hydrodynamics and surface/subsurface hydrology. To this end, we will examine specific coupled phenomena in order to illustrate coupling hypotheses and methods, and to gain new insights from analyses of modelling results in comparison with experiments. Although this is to some extent a review of recent works, nevertheless, some of the methods and results discussed here were not published before, and some of the analyses are new. Moreover, this study is part of a more general framework concerning various types of environmental interactions, such as: interactions between soil water flow (above the water table) and groundwater flow (below the water table); interactions between surface and subsurface waters in fluvial environments (streams, floodplains); interactions between coastal flow processes and porous structures (e.g. sea‑driven oscillations and waves through sand beach or a porous dike); feedback effects of flow systems on the geo‑environmental media. This paper starts with a general review of conceptual coupling approaches, after which we present specific modelling and coupling methods for dealing with hydrological flows with surface water / groundwater interactions, and with coastal flows involving the propagation of seawater oscillations through a porous beach (vertically and horizontally). The following topics are treated. (1) Coupled stream‑aquifer plane flow in an alluvial river valley (quasi‑steady seasonal flow regime), assuming aquifer/stream continuity, and using in situ piezometric measurements for comparisons. (2) Water table oscillations induced by sea waves, and propagating through the beach in the cross‑shore direction: this phenomenon is studied numerically and experimentally using a wave canal with an inclined beach equipped with capacitive micro‑piezometers. (3) Tidally driven vertical oscillations of water flow and capillary pressure in a partially saturated / unsaturated sand beach column, studied numerically and experimentally via a “tide machine” contraption (described in some detail): the goal is to apprehend the role of capillary effects, and forcing frequency, on the hydraulic response of a beach column forced by tides from below. At the time of this writing, some of the results from the tide machine are being reinterpreted (ongoing work). We also point out a recent study of vertical flow in the beach, which focuses on the effect of intermittent waves in the swash zone, rather than tidal oscillations

A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system

A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low-order Lagrange finite element spaces, despite the fact that the system contains third order spatial partial derivatives for the depth averaged velocity of the fluid. After studying the efficacy and the conservation properties of the new numerical method, we proceed with the validation of the new numerical model and boundary conditions by comparing the numerical solutions with laboratory experiments and with available theoretical asymptotic results

Nonlinear evolution of wave groups in directional sea

Nonlinear wave-wave interaction behavior in deep and intermediate water depths and also on a sloping beach are investigated using third-order Zakharov equation which is known as a superior model to predict the evolution of wave group without restriction on spectra width. Transfer energy occurs between the waves components when resonant conditions satisfy. It has been found that nonlinear transfer of energy controls the shape of directional spectrum, including development of the peak and wave group evolution for wave steepness akp ??? 0.2. The comparison of wave group evolutions on directional spectra with unidirectional spectra indicates that evolution of wave groups in deep water and at intermediate water depths are significantly affected by nonlinear interactions between directional components. When directional effect is considered, transformation of wave groups in deep water is much more pronounced at akp = 0.2. The effects of wave interaction are enhanced in relatively shallow water; however, is reduced on a sloping beach, which decreases the maximum wave height

Modeling Nonlinear Dispersive Water Waves

An expository review is given on various theories of modeling weakly to strongly nonlinear, dispersive, time-evolving, three-dimensional gravity-capillary waves on a layer of water. It is based on a new model that allows the nonlinear and dispersive effects to operate to the same full extent as in the Euler equations. Its relationships with some existing models are discussed. Various interesting phenomena will be illustrated with applications of these models and with an exposition on the salient features of nonlinear waves in wave-wave interactions and the related processes of transport of mass and energy