Search

This paper provides a rationale for the commonly observed numerical efficiency of staggered C-grid discretizations for solving the inviscid shallow water equations. In particular, using the key concepts of nonstandard calculus, we aim to show that the grid staggering of the primitive variables (surface elevation and normal velocity components) is capable of dealing with flow discontinuities. After a brief introduction of hyperreals through the notion of infinitesimal increments, a nonstandard rendition of the governing equations is derived that essentially turns into a finite procedure and permits a convenient way of modeling the hydraulic jumps in open channel flow. A central result of this paper is that the discrete formulations thus obtained are distinguished by the topological structures of the solution fields and subsequently provide a natural framework for the staggered discretization of the governing equations. Another key of the present study is to demonstrate that the discretization naturally regularizes the solution of the inviscid flow passing through the hydraulic jump without the need of non-physical dissipation. The underlying justification is provided by analytically studying the distributions of the flow variables across an infinitesimal thin hydraulic jump along with the use of hyperreal Heaviside step functions. This main finding is shown to be useful to comprehend the importance of the application of staggered finite difference schemes to accurately predict rapidly varying free-surface flows. A numerical experiment is provided to confirm this result., Environmental Fluid Mechanics

The Simulating WAves Nearshore (SWAN) model has been extended with an infragravity module to predict the Wave-Group-Forced (WGF) infragravity response to a frequency-directional sea-swell spectrum at a mildly sloping alongshore uniform beach. To that end the SWAN model has been extended with an WGF-infragravity source term denoted Ssb where the subscript denotes surfbeat. The corresponding WGF infragravity energy model has been verified with a set of benchmark tests using the infragravity amplitude model of Reniers et al. (2002). Next the implementation of the energy balance in SWAN has been validated with both prototype-scale laboratory experiments and field observations, showing a good comparison with observations not affected by the nodal structure of the (partially) standing infragravity waves. This suggests that the model is capable of providing improved infragravity boundary conditions in relatively shallow water compared to the typical assumption of equilibrium forcing conditions using for instance Hasselmann's equilibrium theory (Hasselmann, 1962). These infragravity boundary conditions can subsequently can be used by other more sophisticated models to compute runup, overtopping and dune erosion., Environmental Fluid Mechanics

To calculate tsunami forces on coastal structures it is of great importance to determine the shape of the tsunami front reaching the coast. Based on literature reviews, analytical reasoning,video footage, and numerical modelling it is concluded that both the continental shelf slope and the bay geometry have a significant influence on the transformation of a tsunami wave near the coastline. After conducting 1D and 2DH wave simulations, a distinction is made between three types of tsunami waves; a non-breaking front (surging), a breaking front and an undular bore breaking front. Tsunami waves transform into these three wave types over a steep continental shelf, an intermediate sloped continental shelf, and a gentle sloped continental shelf, respectively. A new tsunami surf-similarityparameter is proposed to quantitatively predict the type of wave at the coastline, which was validated based on observations during the 2011 Tohoku Earthquake and Tsunami., Hydraulic Structures and Flood Risk, Environmental Fluid Mechanics

Analysis of the mean (wave-averaged) momentum balance is a common approach used to explain the physical forcing driving wave set-up and mean currents in the nearshore zone. Traditionally this approach has been applied to phase-averaged models but has more recently been applied to phase-resolving models using post-processing, whereby model output is used to calculate each of the momentum terms. While phase-resolving models have the advantage of capturing the nonlinear properties of waves propagating in the nearshore (making them advantageous to enhance understanding of nearshore processes), the post-processing calculation of the momentum terms does not guarantee that the momentum balance closes. We show that this is largely due to the difficulty (or impossibility) of being consistent with the numerical approach. If the residual is of a similar magnitude as any of the relevant momentum terms (which is common with post-processing methods as we show), the analysis is largely compromised. Here we present a new method to internally calculate and extract the depth-integrated, mean momentum terms in the phase-resolving non-hydrostatic wave-flow model SWASH in a manner that is consistent with the numerical implementation. Further, we demonstrate the utility of the new method with two existing physical model studies. By being consistent with the numerical framework, the internal method calculates the momentum terms with a much lower residual at computer precision, combined with greatly reduced calculation time and output storage requirements compared to post-processing techniques. The method developed here allows the accurate evaluation of the depth-integrated, mean momentum terms of wave-driven flows while taking advantage of the more complete representation of the wave dynamics offered by phase-resolving models. Furthermore, it provides an opportunity for advances in the understanding of nearshore processes particularly at more complex sites where wave nonlinearity and e, Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Environmental Fluid Mechanics

Joint effects of the dynamic sea-level rise projected changes in the large-scale atmosphere/ocean circulation, and wave climate on hurricane-induced extreme water levels in the Caribbean region are assessed. We use the 2D-depth integrated ADCIRC + SWAN wave-ocean model, baroclinically coupled to an ocean-eddying version of the Community Earth System Model, to compare impacts of the September 2017 hurricanes with projected impacts of similar hypothetical tropical storms occurring in the future. The model predicts only minor changes in the hurricane-induced extreme water levels for those Caribbean islands which were severely devastated by the 2017 tropical storms (Irma and Maria). That is, provided that the hurricane intensity remains at the present-day level, the global mean sea-level rise is the main future coastal flood risk factor., Hydraulic Engineering, Physical and Space Geodesy

Infragravity waves are low-frequency surface waves that can impact a variety of nearshore and oceanic processes. Recent measurements in the North Sea showed that significant bursts of infragravity energy occurred during storm events. Using a spectral wave model, we show that a substantial part of this energy was radiated from distant shorelines where it was generated by the incident sea-swell waves. These radiated infragravity waves can cross the North Sea basin and reach distant shorelines. The origin of the infragravity wave energy varied between the different storms, and particularly depends on where largest sea-swell waves made landfall. Along the coastlines of the North Sea, shoreward directed infragravity waves that originate from a remote source were non-negligible during storm events. This suggests that radiated infragravity waves can potentially contribute to coastal dynamics and hazards away from their region of generation., Environmental Fluid Mechanics

The weakly reflective wave generation is a wave generation and absorption method in phase-resolving models, based on the assumption that the waves propagating towards the wave generation boundary are small amplitude shallow water waves with direction perpendicular to the boundary. This assumption makes the method weakly reflective for dispersive and directional waves. The internal wave generation method was proposed by Vasarmidis et al. (2019b) as an alternative, for the non-hydrostatic wave model, SWASH, to avoid reflections. In this study, a comparison is made between the performance of the new internal wave generation method and the weakly reflective wave generation method. It is shown that using the internal wave generation leads to a significantly more accurate prediction of the resulting wave field in case of waves reflected back to the numerical boundary. Additionally, the internal wave generation method is extended to short-crested waves and SWASH is validated for the first time with experimental data for the cases of wave propagation over a shoal and wave diffraction around a wall. The proposed extended internal wave generation method increases the capability of SWASH towards the study of wave propagation of highly dispersive short-crested waves in coastal environments with minimal reflection from the boundaries., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Environmental Fluid Mechanics

This paper discusses the discretization methods that have been commonly employed to solve the wave action balance equation, and that have gained a renewed interest with the widespread use of unstructured grids for third-generation spectral wind-wave models. These methods are the first-order upwind finite difference and first-order vertex-centered upwind finite volume schemes for the transport of wave action in geographical space. The discussion addresses the derivation of these schemes from a different perspective. A mathematical framework for mimetic discretizations based on discrete calculus is utilized herein. A key feature of this algebraic approach is that the process of exact discretization is segregated from the process of interpolation, the latter typically involved in constitutive relations. This can help gain insight into the performance characteristics of the discretization method. On this basis, we conclude that the upwind finite difference scheme captures the wave action flux conservation exactly, which is a plus for wave shoaling. In addition, we provide a justification for the intrinsic low accuracy of the vertex-centred upwind finite volume scheme, due to the physically inaccurate but common flux constitutive relation, and we propose an improvement to overcome this drawback. Finally, by way of a comparative demonstration, a few test cases is introduced to establish the ability of the considered methods to capture the relevant physics on unstructured triangular meshes., Environmental Fluid Mechanics

We are concerned with the numerical solution of a linear transport problem with nonzero divergence velocity field that originates from the spectral energy balance equation describing the evolution of wind waves and swells in coastal seas. The discretization error of the commonly used first-order upwind finite difference and first-order vertex-centered upwind finite volume schemes in one space dimension is analyzed. Smoothness of nondivergent velocity field plays a crucial role in this. No such analysis has been attempted to date for such problems. The two schemes studied differ in the manner in which they treat the scalar flux numerically. The finite difference variant is shock captured, whereas the vertex-centered finite volume approximation employs an arithmetic mean of the velocity and appears not to be flux conservative. The methods are subsequently extended to two dimensions on triangular meshes. Numerical experiments are provided to verify the convergence analysis. The main finding is that the finite difference scheme displays optimal rates of convergence and offers higher accuracy over the finite volume scheme, regardless the regularity of the velocity field. The latter scheme notably yields convergence rates of 0.5 and 0 in L2-norm and L∞-norm, respectively, when the velocity field is not smooth. A test case illustrating wave shoaling and refraction over submerged shoals is also presented and demonstrates the practical importance of flux conservation., Environmental Fluid Mechanics

Sea-level rise poses severe threats to coastal and low-lying regions around the world, by exacerbating coastal erosion and flooding. Adequate sea-level projections over the next decades are important for both decision making and for the development of successful adaptation strategies in these coastal and low-lying regions to climate change. Ocean components of climate models used in the most recent sea-level projections do not explicitly resolve ocean mesoscale processes. Only a few effects of these mesoscale processes are represented in these models, which leads to errors in the simulated properties of the ocean circulation that affect sea-level projections. Using the Caribbean Sea as an example region, we demonstrate a strong dependence of future sea-level change on ocean model resolution in simulations with a global climate model. The results indicate that, at least for the Caribbean Sea, adequate regional projections of sea-level change can only be obtained with ocean models which capture mesoscale processes., Environmental Fluid Mechanics, Physical and Space Geodesy

Shallow tropical bays in the Caribbean, like Orient Bay and Galion Bay in Saint Martin, are often sheltered by coral reefs. In the relatively calm environment behind the reefs, seagrass meadows grow. Together, these ecosystems provide valuable ecosystem services like coastal protection, biodiversity hotspots, nursery grounds for animals and enhancing tourism and fisheries. However, sea-level rise imperils these ecosystems and the services they provide because of changing hydrodynamic conditions, with potential effects on the interdependencies between these ecosystems. By means of a hydrodynamic model that accounts for the interaction with vegetation (Delft3D Flexible Mesh), the impact of sea-level rise (0.87 m in 2100) is investigated for three scenarios of future reef development (i.e. keep-up, give-up and catch-up). If coral reefs cannot keep up with sea-level rise, the wave height and flow velocity increase significantly within associated bays, with the wave height doubling locally in case of eroding reefs in our model simulations. Since the presence of seagrass strongly depends on the hydrodynamic conditions, the response of seagrass to the future hydrodynamic conditions is projected using a habitat suitability model that is based on a logistic regression. The spatial character of the bays determines the response of seagrass. In Orient Bay, which is deeper and partly exposed to higher waves, the seagrass will likely migrate from the deeper parts to shallow areas that become suitable for seagrass because of the surf zone moving landward. In contrast, the conditions for seagrass worsen in Galion Bay for the catch-up and give-up scenario; due to the shallowness of this bay, the seagrass cannot escape to more suitable areas, resulting in significant seagrass loss. It is shown that healthy coastal ecosystems are able to limit the change in hydrodynamic conditions due to sea-level rise. Therefore, preserving these ecosystems is key for ensuring the resilience of sh, Environmental Fluid Mechanics, Physical and Space Geodesy

This paper aims to present the extension of the non-hydrostatic wave-flow model SWASH with the covolume method to build discretization schemes on unstructured triangular grids. Central to this method that is free of spurious pressure modes, is the use of dual pairs of meshes that are mutually orthogonal, such as the Delaunay-Voronoi mesh systems. The approximants sought are the components of the flow velocity vector normal to the cell faces of the primal mesh. In addition to the covolume approach, a novel upwind difference scheme for the horizontal advection terms in the momentum equation is proposed. This scheme obeys the Rankine-Hugoniot jump relations and prevents the odd-even decoupling of the velocity field accordingly. Moreover, cases with flow discontinuities, such as steady bores and broken waves, are properly treated. In spite of the low-order accuracy of the proposed method, unstructured meshes easily allow for local refinement in a way that retains the desired accuracy. The unstructured-grid version of SWASH is applicable to a wide range of 2DH wave-flow problems to investigate the nonlinear dynamics of free surface waves over varying bathymetries. Its efficiency and robustness is tested on a number of these problems employing unstructured triangular meshes., Environmental Fluid Mechanics

Wave forecasting in ocean and coastal waters commonly relies on spectral models based on the spectral action balance equation. These models assume that different wave components are statistically independent and as a consequence cannot resolve wave interference due to statistical correlation between crossing waves, as may be found in, for instance, a focal zone. This study proposes a statistical model for the evolution of wave fields over non-uniform currents and bathymetry that retains the information on the correlation between different wave components. To this end, the quasi-coherent model (Smit & Janssen, J. Phys. Oceanogr., vol. 43, 2013, pp. 1741-1758) is extended to allow for wave-current interactions. The outcome is a generalized action balance model that predicts the evolution of the wave statistics over variable media, while preserving the effect of wave interferences. Two classical examples of wave-current interaction are considered to demonstrate the statistical contribution of wave interferences: (1) swell field propagation over a jet-like current and (2) the interaction of swell waves with a vortex ring. In both examples cross-correlation terms lead to development of prominent interference structures, which significantly change the wave statistics. Comparison with results of the SWAN model demonstrates that retention of cross-correlation terms is essential for accurate prediction of wave statistics in shear-current-induced focal zones., Environmental Fluid Mechanics

The purpose of this work is to point out the relevance of the Rankine-Hugoniot jump relations regarding the numerical solution of the inviscid shallow water equations. To arrive at physically relevant solutions in rapidly varied flow, it is of crucial importance that continuity of mass flux and momentum flux across a steady discontinuity is fulfilled at the discrete level. By adopting this viewpoint, finite difference schemes can be studied that may be well suited to solve shallow water flow problems involving discontinuities, while they are not based on a characteristic decomposition of the governed hyperbolic equations. Three schemes on staggered grids with either the water level or the water depth at the cell centre and the flow velocity or the depth-integrated velocity at the cell interface are examined. They differ in (1) the character of the transport velocity to bias the discretization of the advective acceleration term in the upwind direction, and (2) the determination of the water depth at the cell face with which the depth-integrated velocity must be linked to the flow velocity. A detailed analysis is provided and aimed at highlighting the necessity of fulfilling the Rankine-Hugoniot jump conditions for preventing the odd-even decoupling problem. The accuracy and robustness of three selected schemes is assessed by means of convergence tests, three idealized 1D test problems with exact solutions and a 1D laboratory experiment of the breaking, runup and rundown of a solitary wave on a sloping beach. Numerical results reveal that schemes satisfying exactly the jump conditions display improved performance over schemes which do not share this property. Also, these results support strong evidence on the link between not fulfilling the jump conditions and the appearance of odd-even oscillations., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Environmental Fluid Mechanics

The mesoscale variability in the Caribbean Sea is dominated by anticyclonic eddies that are formed in the eastern part of the basin. These anticyclones intensify on their path westward while they pass the coastal upwelling region along the Venezuelan and Colombian coast. In this study, we used a regional model to show that this westward intensification of Caribbean anticyclones is steered by the advection of cold upwelling filaments. Following the thermal wind balance, the increased horizontal density gradients result in an increase in the vertical shear of the anticyclones and in their westward intensification. To assess the impact of variations in upwelling on the anticyclones, several simulations were performed in which the northward Ekman transport (and thus the upwelling strength) is altered. As expected, stronger (weaker) upwelling is associated with stronger (weaker) offshore cooling and a stronger (weaker) westward intensification of the anticyclones. Moreover, the simulations with weaker upwelling show farther advection of the Amazon and Orinoco River plumes into the basin. As a result, in these simulations the horizontal density gradients were predominantly set by horizontal salinity gradients. The importance of the horizontal density gradients driven by temperature, which are associated with the upwelling, increased with increasing upwelling strength. The results of this study highlight that both upwelling and the advection of the river plumes affect the life cycle of mesoscale eddies in the Caribbean Sea., Environmental Fluid Mechanics, Physical and Space Geodesy

In this work, internal wave generation techniques are developed in an open source non-hydrostatic wave model (SimulatingWAves till SHore, SWASH) for accurate generation of regular and irregular long-crested waves. Two different internal wave generation techniques are examined: a source term addition method where additional surface elevation is added to the calculated surface elevation in a specific location in the domain and a spatially distributed source functionwhere a spatially distributed mass is added in the continuity equation. These internal wave generation techniques in combination with numerical wave absorbing sponge layers are proposed as an alternative to the weakly reflective wave generation boundary to avoid re-reflections in case of dispersive and directional waves. The implemented techniques are validated against analytical solutions and experimental data including water surface elevations, orbital velocities, frequency spectra and wave heights. The numerical results show a very good agreement with the analytical solution and the experimental data indicating that SWASH with the addition of the proposed internal wave generation technique can be used to study coastal areas and wave energy converter (WEC) farms even under highly dispersive and directional waves without any spurious reflection from the wave generator., Environmental Fluid Mechanics

Wave attenuation through mangrove forests has received more and more attention, especially in the context of increasing coastal erosion and sea-level-rise. Numerous studies have focused on studying the reduction of wave height in a mangrove forest. However, the understanding of this attenuation process is still in its infancy. In order to obtain more insight, a laboratory experiment, mimicking the processes of wave attenuation by coastal mangroves in the Mekong Delta, Vietnam was conducted. The reduction of wave height for different scenarios of mangrove densities and wave conditions was investigated. A new method to quantify vegetation attenuation induced by vegetation is presented. The wave height reduction is presented over a relative length scale (viz. the number of wavelengths), instead of an absolute length scale of the forest (e.g per meter or per 100 m). The effects of wave non-linearity on the wave height attenuation over the mangrove forest were investigated using the Ursell number. It is suggested that the non-linear character of waves has a strong influence on the attenuation of the waves inside the mangrove forest. A numerical model, mimicking the experiment was constructed in SWASH and validated using the experimental data. Finally, the data set was extended through numerical modelling so that a larger ranging relationship between wave attenuation per wave length and the Ursell number could be formulated., Coastal Engineering, Environmental Fluid Mechanics, Structural Integrity & Composites

A new wave-vegetation model is implemented in an open-source code, SWASH (Simulating WAves till SHore). The governing equations are the nonlinear shallow water equations, including non-hydrostatic pressure. Besides the commonly considered drag force induced by vertical vegetation cylinders, drag force induced by horizontal vegetation cylinders in complex mangrove root systems, as well as porosity and inertia effects, are included in the vegetation model, providing a logical supplement to the existing models. The vegetation model is tested against lab measurements and existing models. Good model performance is found in simulating wave height distribution and maximum water level in vegetation fields. The relevance of including the additional effects is demonstrated by illustrative model runs. We show that the difference between vertical and horizontal vegetation cylinders in wave dissipation is larger when exposed to shorter waves, because in these wave conditions the vertical component of orbital velocity is more prominent. Both porosity and inertia effects are more pronounced with higher vegetation density. Porosity effects can cause wave reflection and lead to reduced wave height in and behind vegetation fields, while inertia force leads to negative energy dissipation that reduces the wave-damping capacity of vegetation. Overall, the inclusion of both effects leads to greater wave reduction compared to common modeling practice that ignores these effects, but the maximum water level is increased due to porosity. With good model performance and extended functions, the new vegetation model in SWASH code is a solid advancement toward refined simulation of wave propagation over vegetation fields., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Environmental Fluid Mechanics, Hydraulic Structures and Flood Risk, Coastal Engineering

In this paper, the ability of the numerical phase resolving model SWASH (Simulating WAves till SHore) to hindcast wave-induced longshore currents is evaluated. Using default settings for all processes modelled, highly accurate results are found for wave heights, mean water levels and longshore currents. While wave current interaction is intrinsically modelled, insights into the spatial variation of wave driven longshore currents are found. Additionally, vertical variations of modelled longshore currents have been compared. Depth uniform profiles of longshore current within surf zone are noted on plane beaches under regular waves, except for minor deviations near the shoreline. The apparent validity of a depth-uniform longshore current encourages the use of a depth-averaged moment balance equation to compute the longshore current. A simpler model is shown to also be able to predict a proper magnitude of longshore current, although the cross-shore distribution – in contrast with SWASH - needs tuning for the eddy viscosity and the bottom friction coefficient, since the distribution of the wave-induced longshore current heavily depends on lateral mixing., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Coastal Engineering, Environmental Fluid Mechanics

The Yucatan Channel connects the Caribbean Sea with the Gulf of Mexico and is the main outflow region of the Caribbean Sea. Moorings in the Yucatan Channel show high-frequent variability in kinetic energy (50–100 days) and transport (20–40 days), but the physical mechanisms controlling this variability are poorly understood. In this study, we show that the short-term variability in the Yucatan Channel transport has an upstream origin and arises from processes in the North Brazil Current. To establish this connection, we use data from altimetry and model output from several high resolution global models. A significant 40–70 day variability is found in the sea surface height in the North Brazil Current retroflection region with a propagation toward the Lesser Antilles. The frequency of variability is generated by intrinsic processes associated with the shedding of eddies, rather than by atmospheric forcing. This sea surface height variability is able to pass the Lesser Antilles, it propagates westward with the background ocean flow in the Caribbean Sea and finally affects the variability in the Yucatan Channel volume transport., Physical and Space Geodesy, Environmental Fluid Mechanics

The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model set-up. This article applies the Reynolds-averaged Navier–Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature- and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to double-diffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required., Water Resources, Environmental Fluid Mechanics

Wave-induced currents are an ubiquitous feature in coastal waters that can spread material over the surf zone and the inner shelf. These currents are typically under resolved in non-hydrostatic wave-flow models due to computational constraints. Specifically, the low vertical resolutions adequate to describe the wave dynamics – and required to feasibly compute at the scales of a field site – are too coarse to account for the relevant details of the three-dimensional (3D) flow field. To describe the relevant dynamics of both wave and currents, while retaining a model framework that can be applied at field scales, we propose a two grid approach to solve the governing equations. With this approach, the vertical accelerations and non-hydrostatic pressures are resolved on a relatively coarse vertical grid (which is sufficient to accurately resolve the wave dynamics), whereas the horizontal velocities and turbulent stresses are resolved on a much finer subgrid (of which the resolution is dictated by the vertical scale of the mean flows). This approach ensures that the discrete pressure Poisson equation – the solution of which dominates the computational effort – is evaluated on the coarse grid scale, thereby greatly improving efficiency, while providing a fine vertical resolution to resolve the vertical variation of the mean flow. This work presents the general methodology, and discusses the numerical implementation in the SWASH wave-flow model. Model predictions are compared with observations of three flume experiments to demonstrate that the subgrid approach captures both the nearshore evolution of the waves, and the wave-induced flows like the undertow profile and longshore current. The accuracy of the subgrid predictions is comparable to fully resolved 3D simulations – but at much reduced computational costs. The findings of this work thereby demonstrate that the subgrid approach has the potential to make 3D non-hydrostatic simulations feasible at the scale of a rea, Environmental Fluid Mechanics

The Dutch Caribbean consists of two island groups, the Leeward Antilles off the Venezuelan coast separated from the Windward Islands east of Puerto Rico over distances of the scale of the Caribbean Sea itself. Climate change in the Caribbean Sea is predicted to lead to rising sea levels, warming waters and changing eddy fields. Warming waters lead to an increase in the intensity and occurrence of tropical storms and hurricanes, and are linked to an increased risk of surge flooding. Changing eddy fields are likely to affect the path of storm tracks. All of which further influence the environment of the Caribbean, and hence the stability of its ecosystems., Environmental Fluid Mechanics

This paper presents a numerical model to simulate the evolution of waves and their interactions with a restrained ship that is moored in coastal waters. The model aims to be applicable at the scale of a harbour or coastal region, while accounting for the key physical processes that determine the hydrodynamic loads on the ship. Its methodology is based on the non-hydrostatic wave-flow model SWASH, which provides an efficient tool to simulate the nonlinear dynamics that govern the nearshore wave field. In this work, we propose a new numerical algorithm that accounts for the presence of a non-moving floating body, to resolve the wave impact on a restrained ship. The model is validated through comparisons with an analytic solution, a numerical solution, and two laboratory campaigns. The results of the model-data comparison demonstrate that the model captures the scattering of waves by a restrained body. Furthermore, it gives a reasonable prediction of the hydrodynamic loads that act on a restrained container ship for a range of wave conditions. Importantly, the model captures these dynamics efficiently, which demonstrates that it retains this favourable property of the non-hydrostatic approach when a floating body is included. The findings of this study suggest that the model provides a promising new alternative to simulate the nonlinear evolution of waves and their impact on a restrained ship at the scale of a realistic harbour or coastal region., Environmental Fluid Mechanics

The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In systems that approach axisymmetry around a central location, computation times can be reduced by applying a quasi 3-D axisymmetric model setup. This article applies the Navier-Stokes equations described in cylindrical coordinates, and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite volume model can be easily extended to this quasi 3-D framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature and salinity dependent densities, molecular diffusivities, and kinematic viscosity. Four qualitative case studies demonstrate a good behaviour with respect to expected density and diffusivity driven flow and stratification in shallow water bodies. A fifth case study involves a new validation method that quantifies the radial expansion of a dense water layer developing from a central inflow at the bottom of a shallow water body., Water Resources, Environmental Fluid Mechanics

Distributed temperature sensing has proven a useful technique for geoscientists to obtain spatially distributed temperature data. When studies require high-resolution temperature data in three spatial dimensions, current practices to enhance the spatial resolution do not suffice. For example, double-diffusive phenomena induce sharp and small-scale temperature patterns in water bodies subject to thermohaline gradients. This article presents a novel approach for a 3-D dense distributed temperature sensing setup, the design of which can be customized to the required spatial resolution in each dimension. Temperature is measured along fiber-optic cables that can be arranged as needed. In this case, we built a dense cage of very thin (1.6 mm) cables to ensure that interference with flow patterns was minimal. Application in water bodies with double-diffusion-induced sharp temperature gradients shows that the setup is well able to capture small-scale temperature patterns and even detects small unsuspected seeps and potential salt-fingers. However, the potential effect of the setup on the flow patterns requires further study., Water Resources, Environmental Fluid Mechanics

Civil Engineering and Geosciences, Hydraulic Engineering

This paper presents a comprehensive numerical study into the infragravity-wave dynamics at a field site, characterized by a gently sloping barred beach. The nonhydrostatic wave-flow model SWASH was used to simulate the local wavefield for a range of wave conditions (including mild and storm conditions). The extensive spatial coverage of the model allowed us to analyze the infragravity-wave dynamics at spatial scales not often covered before. Overall, the model predicted a wavefield that was representative of the natural conditions, supporting the model application to analyze the wave dynamics. The infragravity-wave field was typically dominated by leaky waves, except near the outer bar where bar-trapped edge waves were observed. Relative contributions of bar-trapped waves peaked during mild conditions, when they explained up to 50% of the infragravity variance. Near the outer bar, the infragravity-wave growth was partly explained by nonlinear energy transfers from short waves. This growth was strongest for mild conditions, and decreased for more energetic conditions when short waves were breaking at the outer bar. Further shoreward, infragravity waves lost most of their energy, due to a combination of nonlinear transfers, bottom friction, and infragravity-wave breaking. Nonlinear transfers were only effective near the inner bar, whereas near the shoreline (where losses were strongest) the dissipation was caused by the combined effect of bottom friction and breaking. This study demonstrated the model's potential to study wave dynamics at field scales not easily covered by in situ observations., Hydraulic Engineering, Civil Engineering and Geosciences

Civil Engineering and Geosciences, Hydraulic Engineering

This paper presents a comprehensive numerical study into the infragravity-wave dynamics at a field site, characterized by a gently sloping barred beach. The nonhydrostatic wave-flow model SWASH was used to simulate the local wavefield for a range of wave conditions (including mild and storm conditions). The extensive spatial coverage of the model allowed us to analyze the infragravity-wave dynamics at spatial scales not often covered before. Overall, the model predicted a wavefield that was representative of the natural conditions, supporting the model application to analyze the wave dynamics. The infragravity-wave field was typically dominated by leaky waves, except near the outer bar where bar-trapped edge waves were observed. Relative contributions of bar-trapped waves peaked during mild conditions, when they explained up to 50% of the infragravity variance. Near the outer bar, the infragravity-wave growth was partly explained by nonlinear energy transfers from short waves. This growth was strongest for mild conditions, and decreased for more energetic conditions when short waves were breaking at the outer bar. Further shoreward, infragravity waves lost most of their energy, due to a combination of nonlinear transfers, bottom friction, and infragravity-wave breaking. Nonlinear transfers were only effective near the inner bar, whereas near the shoreline (where losses were strongest) the dissipation was caused by the combined effect of bottom friction and breaking. This study demonstrated the model's potential to study wave dynamics at field scales not easily covered by in situ observations., Hydraulic Engineering, Civil Engineering and Geosciences

This paper presents the application of new source terms in SWAN for the dominant water wave physics in the coastal zone: depth-induced breaking and triad wave-wave interactions. We present results demonstrating increased modelling skill in the prediction of bulk wave parameters e.g. significant wave height and of the spectral shape compared to currently used defaults, particularly in cases with horizontal bathymetries. These preliminary results suggest a greater range of applicability of these source terms for operational applications., Hydraulic Engineering, Civil Engineering and Geosciences

This paper presents the application of the open source non-hydrostatic wave-flow model SWASH to propagation of irregular waves in a barred surf zone, and the model results are discussed by comparing against an extensive laboratory data set. This study focus not only on wave transformation in the surf zone, but also on the numerical prediction of undertow and vertical distribution of turbulence levels under broken waves. Present simulations demonstrate the overall predictive capabilities of the model in computing breaking surf zone waves., Hydraulic Engineering, Civil Engineering and Geosciences

A more detailed understanding of porous flow inside a rubble-mound structure may have potential benefits in breakwater design. Numerical models are expected to be a useful additional research tool in this field, provided that their calculation results can be validated against measurements. This paper presents the results of a systematic effort to validate a set of different numerical models for a strongly simplified model set-up. The results of this effort will be used to select models for a next stage in which the complexity of the model set-up is increased. By means of this step-by-step approach a good insight in the capabilities and limitations of the various models is achieved., Hydraulic Engineering, Civil Engineering and Geosciences

The determination of wave conditions in partly sheltered areas is a challenging task for coastal engineers. Knowledge about these conditions is important for the design of coastal structures, the planning and operation of ports. Numerical models play an important role in the assessment of these conditions. Various types of models have been proposed of which phase averaged and phase resolving models are the most widely used. Here, we present the non-hydrostatic phase resolving SWASH model as a tool to determine wave conditions in partly sheltered areas. Examples are shown of wave diffraction behind a semi-infinite breakwater, and the penetration of waves into the harbour of Limassol, Cyprus. The computational results show good agreement with theoretical and experimental results, indicating that the SWASH model can be used as a tool to determine wave conditions in partly sheltered areas., Hydraulic Engineering, Civil Engineering and Geosciences

In this paper, a numerical wave-flow model SWASH, based on non-linear shallow water equation with non- hydrostatic pressure, is applied to the estimation of wave overtopping over a dike in shallow foreshores. First sensitivity analysis is conducted to see the influence of wave generation, grid size, time window and bottom friction by one-dimensional calculations. After that the SWASH model is validated by comparing results from field measurements in Petten dike in the Netherlands. Due to the stability of the computation, the desired calculation could not be achieved, but an alternative way to calculate wave overtopping including two-dimensional effects is proposed., Hydraulic Engineering, Civil Engineering and Geosciences

This paper presents the application of new source terms in SWAN for the dominant water wave physics in the coastal zone: depth-induced breaking and triad wave-wave interactions. We present results demonstrating increased modelling skill in the prediction of bulk wave parameters e.g. significant wave height and of the spectral shape compared to currently used defaults, particularly in cases with horizontal bathymetries. These preliminary results suggest a greater range of applicability of these source terms for operational applications., Hydraulic Engineering, Civil Engineering and Geosciences

A more detailed understanding of porous flow inside a rubble-mound structure may have potential benefits in breakwater design. Numerical models are expected to be a useful additional research tool in this field, provided that their calculation results can be validated against measurements. This paper presents the results of a systematic effort to validate a set of different numerical models for a strongly simplified model set-up. The results of this effort will be used to select models for a next stage in which the complexity of the model set-up is increased. By means of this step-by-step approach a good insight in the capabilities and limitations of the various models is achieved., Hydraulic Engineering, Civil Engineering and Geosciences

The determination of wave conditions in partly sheltered areas is a challenging task for coastal engineers. Knowledge about these conditions is important for the design of coastal structures, the planning and operation of ports. Numerical models play an important role in the assessment of these conditions. Various types of models have been proposed of which phase averaged and phase resolving models are the most widely used. Here, we present the non-hydrostatic phase resolving SWASH model as a tool to determine wave conditions in partly sheltered areas. Examples are shown of wave diffraction behind a semi-infinite breakwater, and the penetration of waves into the harbour of Limassol, Cyprus. The computational results show good agreement with theoretical and experimental results, indicating that the SWASH model can be used as a tool to determine wave conditions in partly sheltered areas., Hydraulic Engineering, Civil Engineering and Geosciences

In this paper, a numerical wave-flow model SWASH, based on non-linear shallow water equation with non- hydrostatic pressure, is applied to the estimation of wave overtopping over a dike in shallow foreshores. First sensitivity analysis is conducted to see the influence of wave generation, grid size, time window and bottom friction by one-dimensional calculations. After that the SWASH model is validated by comparing results from field measurements in Petten dike in the Netherlands. Due to the stability of the computation, the desired calculation could not be achieved, but an alternative way to calculate wave overtopping including two-dimensional effects is proposed., Hydraulic Engineering, Civil Engineering and Geosciences

This paper presents the application of the open source non-hydrostatic wave-flow model SWASH to propagation of irregular waves in a barred surf zone, and the model results are discussed by comparing against an extensive laboratory data set. This study focus not only on wave transformation in the surf zone, but also on the numerical prediction of undertow and vertical distribution of turbulence levels under broken waves. Present simulations demonstrate the overall predictive capabilities of the model in computing breaking surf zone waves., Hydraulic Engineering, Civil Engineering and Geosciences

Hurricane Ike (2008) made landfall near Galveston, Texas, as a moderate intensity storm. Its large wind field in conjunction with the Louisiana-Texas coastline's broad shelf and large scale concave geometry generated waves and surge that impacted over 1000 km of coastline. Ike's complex and varied wave and surge response physics included: the capture of surge by the protruding Mississippi River Delta; the strong influence of wave radiation stress gradients on the Delta adjacent to the shelf break; the development of strong wind driven shore-parallel currents and the associated geostrophic setup; the forced early rise of water in coastal bays and lakes facilitating inland surge penetration; the propagation of a free wave along the southern Texas shelf; shore-normal peak wind-driven surge; and resonant and reflected long waves across a wide continental shelf. Preexisting and rapidly deployed instrumentation provided the most comprehensive hurricane response data of any previous hurricane. More than 94 wave parameter time histories, 523 water level time histories, and 206 high water marks were collected throughout the Gulf in deep water, along the nearshore, and up to 65 km inland. Ike's highly varied physics were simulated using SWAN?+?ADCIRC, a tightly coupled wave and circulation model, on SL18TX33, a new unstructured mesh of the Gulf of Mexico, Caribbean Sea, and western Atlantic Ocean with high resolution of the Gulf's coastal floodplain from Alabama to the Texas-Mexico border. A comprehensive validation was made of the model's ability to capture the varied physics in the system., Hydraulic Engineering, Civil Engineering and Geosciences

The effects of wind input parameterizations on wave estimations under hurricane conditions are examined using the unstructured grid, third-generation wave model, Simulating WAves Nearshore (SWAN). Experiments using Hurricane Ike wind forcing, which impacted the Gulf of Mexico in 2008, illustrate that the default and recommended setting for the wind input parameterization tends to overestimate the maximum significant wave heights in the deep Gulf of Mexico by about 2 m when comparing with observations. The overestimation can be remedied either by adjusting the maximum value of the surface drag coefficient or by substituting a high wind speed formula for the default low to moderate wind speed. Because of added dissipative effects in the shallow coastal areas, the overestimations found in deep water have limited effect on the waves in the near shore shallower waters. Thus, previous wave model results using a low to moderate wind speed bulk formula may still be reliable in waters shallower than about 20–30 m even while overestimating significant wave heights in deeper waters under hurricane conditions., Hydraulic Engineering, Civil Engineering and Geosciences

The SWAN model is a third-generation spectral wave prediction model developed by Delft University of Technology. Since its initial release in 1998 this model has become a widely used and reliable tool for offshore and near shore wave predictions. Its main field of application is the coastal zone where, by virtue of its implicit numerical scheme, it can be considered as a very efficient tool for high resolution coastal applications. Besides this field of application it is also appropriate for open ocean conditions., Hydraulic Engineering, Civil Engineering and Geosciences

The effects of wind input parameterizations on wave estimations under hurricane conditions are examined using the unstructured grid, third-generation wave model, Simulating WAves Nearshore (SWAN). Experiments using Hurricane Ike wind forcing, which impacted the Gulf of Mexico in 2008, illustrate that the default and recommended setting for the wind input parameterization tends to overestimate the maximum significant wave heights in the deep Gulf of Mexico by about 2 m when comparing with observations. The overestimation can be remedied either by adjusting the maximum value of the surface drag coefficient or by substituting a high wind speed formula for the default low to moderate wind speed. Because of added dissipative effects in the shallow coastal areas, the overestimations found in deep water have limited effect on the waves in the near shore shallower waters. Thus, previous wave model results using a low to moderate wind speed bulk formula may still be reliable in waters shallower than about 20–30 m even while overestimating significant wave heights in deeper waters under hurricane conditions., Hydraulic Engineering, Civil Engineering and Geosciences

Hurricane Ike (2008) made landfall near Galveston, Texas, as a moderate intensity storm. Its large wind field in conjunction with the Louisiana-Texas coastline's broad shelf and large scale concave geometry generated waves and surge that impacted over 1000 km of coastline. Ike's complex and varied wave and surge response physics included: the capture of surge by the protruding Mississippi River Delta; the strong influence of wave radiation stress gradients on the Delta adjacent to the shelf break; the development of strong wind driven shore-parallel currents and the associated geostrophic setup; the forced early rise of water in coastal bays and lakes facilitating inland surge penetration; the propagation of a free wave along the southern Texas shelf; shore-normal peak wind-driven surge; and resonant and reflected long waves across a wide continental shelf. Preexisting and rapidly deployed instrumentation provided the most comprehensive hurricane response data of any previous hurricane. More than 94 wave parameter time histories, 523 water level time histories, and 206 high water marks were collected throughout the Gulf in deep water, along the nearshore, and up to 65 km inland. Ike's highly varied physics were simulated using SWAN?+?ADCIRC, a tightly coupled wave and circulation model, on SL18TX33, a new unstructured mesh of the Gulf of Mexico, Caribbean Sea, and western Atlantic Ocean with high resolution of the Gulf's coastal floodplain from Alabama to the Texas-Mexico border. A comprehensive validation was made of the model's ability to capture the varied physics in the system., Hydraulic Engineering, Civil Engineering and Geosciences

The SWAN model is a third-generation spectral wave prediction model developed by Delft University of Technology. Since its initial release in 1998 this model has become a widely used and reliable tool for offshore and near shore wave predictions. Its main field of application is the coastal zone where, by virtue of its implicit numerical scheme, it can be considered as a very efficient tool for high resolution coastal applications. Besides this field of application it is also appropriate for open ocean conditions., Hydraulic Engineering, Civil Engineering and Geosciences

This paper presents the application of the open source non-hydrostatic wave-flow model SWASH to wave propagation over a fringing reef, and the results are discussed and compared with observations obtained from a laboratory experiment subjected to various incident wave conditions. This study focus not only on wave breaking, bottom friction, and wave-induced setup and runup, but also on the generation and propagation of infragravity waves beyond the reef crest. Present simulations demonstrate the overall predictive capabilities of the model for a typical coral reef with steep slopes and extended reef flats., Hydraulic Engineering, Civil Engineering and Geosciences

Hydraulic Engineering, Civil Engineering and Geosciences

In this paper, the effect of beach nourishment on wave overtopping in shallow foreshores is investigated with the nonhydrostatic wave-flow model SWASH. Firstly, the applicability of SWASH to model wave overtopping is tested by comparing results with a physical model setup with different storm wall heights on top of an impermeable sea dike. The numerical results show good agreement with the physical model. After validation, sensitivity analysis of the effect of beach nourishment on wave overtopping is conducted by changing bottom configurations with the SWASH model. From the sensitivity analysis, it becomes clear that wave overtopping discharge in shallow foreshores is characterized by the bores generated in surf zone due to wave breaking. To reduce wave overtopping discharge in shallow foreshore, it is important to reduce the horizontal momentum of the bores., Hydraulic Engineering, Civil Engineering and Geosciences

This paper presents the application of the open source non-hydrostatic wave-flow model SWASH to wave propagation over a fringing reef, and the results are discussed and compared with observations obtained from a laboratory experiment subjected to various incident wave conditions. This study focus not only on wave breaking, bottom friction, and wave-induced setup and runup, but also on the generation and propagation of infragravity waves beyond the reef crest. Present simulations demonstrate the overall predictive capabilities of the model for a typical coral reef with steep slopes and extended reef flats., Hydraulic Engineering, Civil Engineering and Geosciences