Volume-averaged Reynolds-averaged Navier-Stokes Research Articles

Fully integrated modeling of surface water and groundwater in coastal areas

This paper presents an improved model based on a three-dimensional non-hydrostatic wave model NHWAVE to simulate the interactions between the surface water and the groundwater affected by tides or waves in coastal areas. With the model, both the surface water flow and the groundwater flow are calculated based on the well-balanced Volume-averaged Reynolds-averaged Navier-Stokes equations. The spatially varying porosity and hydraulic conductivity are used to identifiy the domains for the surface water and the groundwater. The model is calibrated and validated using a wide range of laboratory measurements reported in the literature, involving the tide propagation through a sandy embankment, the tide-induced groundwater table fluctuation in a sandy beach, and the wave setup in a sloping sandy beach. The interactions between the surface water and the groundwater are analyzed and the influencing factors on the groundwater flow are discussed. The phase lag between the surface water elevation and the groundwater table fluctuation is mainly influenced by the hydraulic conductivity of the porous media. The wave attenuation in the groundwater is proportional to its propagation distance. The computed wave setup elevationin the permeable beach is smaller than in the impermeable beach. It is shown that the fully integrated model is capable of simulating the interactions between the surface water and the groundwater affected by tides or waves in coastal areas. It can be an efficient tool to study the tide and wave dynamics in the permeable sandy beach.

Numerical assessment of tsunami attack on a rubble mound breakwater using OpenFOAM®

A numerical assessment study of tsunami attack on the rubble mound breakwater of Haydarpasa Port, located at the southern entrance of the Istanbul Bosphorus Strait in the Sea of Marmara, Turkey, is carried out in this study using a Volume-Averaged Reynolds-Averaged Navier-Stokes solver, IHFOAM, developed in OpenFOAM® environment. The numerical model is calibrated with and validated against the data from solitary wave and tsunami overflow experiments representing tsunami attack. Furthermore, attack of a potential tsunami near Haydarpasa Port is simulated to investigate effects of a more realistic tsunami that cannot be generated in a wave flume with the present state of the art technology. Discussions on practical engineering applications of this type of numerical modeling studies are given focusing on pressure distributions around the crown-wall of the rubble mound breakwater, and the forces acting on the single stone located behind the crown-wall at the rear side of the breakwater. Numerical modeling of stability/failure mechanism of the overall cross-section is studied throughout the paper.The present study shows that hydrodynamics along the wave flume and over the breakwater can be simulated properly for both solitary wave and tsunami overflow experiments. Stability of the overall cross-section can only be simulated qualitatively for solitary wave cases; on the other hand, the effect of the time elapsed during tsunami overflow cannot be reflected in the simulations using the present numerical tool. However, the stability of the overall cross-section under tsunami overflow is assessed by evaluating forces acting on the rear side armor unit supporting the crown-wall of the rubble mound breakwater as a practical engineering application in the present paper. Furthermore, two non-dimensional parameters are derived to discuss the stability of this armor unit; and thus, the stability condition of the overall cross-section. Approximate threshold values for these non-dimensional parameters are presented comparing experimental and numerical results as a starting point for engineers in practice. Finally, investigations on the solitary wave and tsunami overflow experiments/simulations are extended to the potential tsunami simulation in the scope of both representation of a realistic tsunami in a wave flume and stability of the rubble mound breakwater.

Wave attenuation over porous seabeds: A numerical study

We investigate wave attenuation over porous seabeds by means of a phase- and depth- resolving numerical model that solves the Volume-Averaged Reynolds-Averaged Navier–Stokes (VARANS) equations. The numerical model is calibrated with laboratory data from Corvaro et al. (2010). The numerical model predicts the wave attenuation and the velocity field near the porous bed for different regular wave conditions. Subsequently, a parametric analysis on the physical characteristics of the porous media is made to investigate their relative role on wave attenuation. The results of the analysis indicate nonlinear dependencies of wave attenuation on both, total porosity and mean grain diameter. The widely used parabolic model in terms of the dispersiveness parameter predicts both types of dependencies, effectively. Hence, new parametric formulations are derived for the determination of the coefficients involved in the parabolic model for each type of dependence. On the other hand, the role of the spectral shape on the wave spectrum bulk dissipation is investigated. Numerical results for irregular waves show a clear dependence of the dissipation rate with the Ursell (Ur) parameter. The dissipation rate becomes sensitive to frequency spreading for Ur < 20. Moreover, forcing the model assuming an f − 5 tail in the incident wave spectrum underpredicts seabed attenuation with respect to an f − 4 formulation. Finally, bispectral analysis of irregular wave propagation allow us to investigate the mechanism of wave attenuation. The numerical results suggest that energy is directly dissipated at the peak frequency, whereas nonlinear energy transfer plays an important role in energy attenuation at higher harmonics.

NUMERICAL STUDY ON THE INFLUENCE OF INFILTRATION ON SWASH HYDRODYNAMICS AND SEDIMENT TRANSPORT IN THE SWASH ZONE

Infiltration and exfiltration processes have a significant influence on the hydrodynamics of the swash zone. Such processes need to be taken into account in the modelling of cross-shore sediment transport and the prediction of beach profile evolution. This paper presents a numerical study of the swash hydrodynamics using a 2D Volume-Averaged Reynolds-Averaged Navier-Stokes model, which was calibrated and validated against new experimental data. The model was used to simulate wave run-up from regular waves over permeable and impermeable fixed slopes. Swash flow velocities and water depth data were obtained from the simulations and used to estimate bed shear stresses at three different locations on the beach slope. The results show that infiltration can have opposing effects on the bed shear stress when compared to equivalent swash on an impermeable slope. During the uprush phase, stresses are directly increased due to boundary layer thinning, whereas, during the backwash phase, there is a significant reduction of flow leading to a decrease in the bed shear stresses.

Numerical study on loosely deposited foundation behavior around a composite breakwater subject to ocean wave impact

In this study, an integrated model is developed to investigate the potential risk for failure of caisson-type breakwaters caused by liquefaction in its loosely deposited sand foundations. In the present model, the Volume-Averaged Reynolds Averaged Navier-Stokes (VARANS) equations are used for solving flow inside and outside the porous media, while Biot's consolidation equation is used for linking the soil skeleton-pore fluids interactions. A new developed poro-elastoplastic model is implemented to reproduce the behavior of loose sand foundation under cyclic shearing. Verification of the present numerical framework includes (i) comparison with the laboratory experiments in terms of water surface levels around the structure, and the fluctuating component of the pore water pressure inside the rubble mound and seabed foundation; and (ii) comparison with the geotechnical centrifugal wave tests for the wave-induced residual component of pore water pressures in a porous seabed. Based on the present model, the hydrodynamic process and the associated dynamic foundation behavior involved in the interactions between the ocean waves, a composite breakwater and its loose sand foundations was performed and analyzed. Particular focus is put on the residual pore pressure development and the resulting liquefaction around the structure under combined actions of both wave and structure rocking motions. Based on the numerical examples presented, under combined actions of both wave and caisson motions, liquefaction starts on both edges of the breakwater and spreads sideways until reaching an equilibrium state where the maximum liquefaction depth can be observed. The liquefied zone around the breakwater is asymmetric in nature, and the maximum depth of soil liquefaction appears at the seaward side of the structure. Furthermore, the parametric study indicates that the maximum liquefaction depth around the composite breakwater increases with increasing wave steepness (H/L0) and relative water depth (d/L0) and decreasing soil permeability (ks).

Numerical study of wave-induced soil response in a sloping seabed in the vicinity of a breakwater

In this study, a mathematical integrated model is developed to investigate the wave-induced sloping seabed response in the vicinity of breakwater. In the present model, the wave model is based on the Volume-Averaged/Reynolds Averaged Navier–Stokes (VARANS) equations, while Biot's consolidation equation is used to govern the soil model. The influence of turbulence fluctuations on the mean flow with respect to the complicated interaction between wave, sloping seabed and breakwater are obtained by solving the Volume-Averaged k−ϵ model. Unlike previous investigations, the phase-resolved absolute shear stress is used as the source of accumulation of residual pore pressure, which can link the oscillatory and residual mechanisms simultaneously. Based on the proposed model, parametric studies regarding the effects of wave and soil characteristics as well as bed slopes on the wave-induced soil response in the vicinity of breakwater are investigated. Numerical results indicate that wave-induced seabed instability is more likely to occur in a steep slope in the case of soil with low relative density and low permeability under large wave loadings. It is also found that, the permeability of breakwater significantly affect the potential for liquefaction, especially in the region below the breakwater.

Two-Dimensional Model for Accumulation of Pore Pressure in Marine Sediments

AbstractA two-dimensional (2D) porous model was developed to investigate the accumulation of pore pressure in marine sediments in which the volume-averaged Reynolds-averaged Navier-Stokes (VARANS) equations were used as the governing equations for the wave motion and the Biot consolidation theory was used for the porous seabed. Unlike most of the previous investigations on the accumulation of pore pressure in which the amplitude of the shear stress over the wave period was used in the source term, in this study, the source term was redefined as a time-dependent function using the phase-resolved oscillatory shear stresses. Overall good agreement of both the oscillatory and residual pore pressures with previous analytical solutions and experimental data demonstrated the reliability of the model for the prediction of wave-induced pore-pressure accumulation. For the case with progressive wave loadings, the liquefaction zone related to the initial incident of the wave phases was formed as a 2D pattern during t...

Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part I: Formulation and validation

In this paper and its companion (Higuera et al., 2014--this issue), the latest advancements regarding Volume-averaged Reynolds-averaged Navier–Stokes (VARANS) are developed in OpenFOAM® and applied. A new solver, called IHFOAM, is programmed to overcome the limitations and errors in the original OpenFOAM® code, having a rigorous implementation of the equations. Turbulence modelling is also addressed for k-ϵ and k-ω SST models within the porous media. The numerical model is validated for a wide range of cases including a dam break and wave interaction with porous structures both in two and three dimensions. In the second part of this paper the model is applied to simulate wave interaction with a real structure, using an innovative hybrid (2D–3D) methodology.

Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part II: Application

This paper and its companion Higuera et al. (2014--this issue) introduce the formulation of Volume-Averaged Reynolds-Averaged Navier–Stokes (VARANS) equations in OpenFOAM® to simulate two-phase flow through porous media. This new implementation, so-called IHFOAM, corrects the limitations of the original OpenFOAM® code. An innovative hybrid methodology (2D–3D) is presented to optimize the simulation time needed to assess the three-dimensional effects of wave interaction with coastal structures. The combined use of a 2D and a 3D model enables the practical application of the 3D VARANS code to simulate real cases, contributing to a significant speed-up. This is highly convenient and especially suitable for non-conventional structures, as it overcomes the limitations inherent to applying semi-empirical formulations out of their range or 2D simulations only. A detailed study of stability and overtopping for a 3D porous high-mound breakwater at prototype scale subjected to oblique irregular (random) waves is carried out. Pressure around the caissons, overtopping discharge rate and turbulent magnitudes are presented in three dimensions. The mean pressure laws present a high degree of accordance with the formulation provided by Goda–Takahashi. Furthermore, local effects due to three-dimensional processes play a significant role, especially close to the breakwater head.

Breaking wave-induced response of composite breakwater and liquefaction in seabed foundation

In the practice of engineering, breaking wave is much more dangerous for the stability of composite breakwater built on porous seabed than non-breaking wave in offshore area. In previous investigations or design codes, the empirical formulations generally were adopted to estimate the wave impact acting on the lateral side of caisson. The interaction between breaking wave, seabed foundation and composite breakwater is not taken into consideration. In this study, adopting the integrated numerical model PORO-WSSI 2D developed by (Ye, 2012a) and (Jeng et al., 2013), the interaction mechanism between breaking wave, seabed foundation and composite breakwater is investigated numerically. In PORO-WSSI 2D,the Volume-Averaged Reynolds Averaged Navier–Stokes (VARANS) equations govern the wave motion and the porous flow in seabed foundation and in rubble mound; and the dynamic Biot's equations (known as “u-p” approximation) govern the dynamic behaviors of seabed foundation and composite breakwater under breaking wave loading. Numerical analysis indicates that the turbulent energy of breaking wave is significant, and the wave impact on caisson applied by breaking wave is much greater than non-breaking wave. The composite breakwater and its seabed foundation respond to the breaking wave loading intensively. The maximum horizontal vibration magnitude of the composite breakwater is up to 5mm; the maximum liquefaction depth in the seabed in front of the composite breakwater reaches up to 1.2 to 1.6m. The parametric study shows that the permeability and saturation of seabed, wave height are three dominant factors for the wave-induced liquefaction in seabed foundation.

Numerical study on the interaction between waves and twin pipelines in sandy seabed

ABSTRACT Zhang, J., Zheng, J., Zhang, C., Jeng, D. and Guo, Y., 2013. Numerical study on the interaction between waves and twin pipelines in sandy seabed In offshore engineering practice, the construction of an identical cylinder close to the existing pipeline may largely affect the near flow field and hydrodynamic forces on the pipelines. The interaction between incident ocean wave and twin pipelines in sandy seabed plays an important role in the design of submarine pipelines. A mathematical model based on the Volume-Averaged Reynolds-Averaged Navier-Stokes (VARANS) equations, a two-equation k-e turbulence closure and an internal source term wave maker is adopted to describe this complex phenomenon. The sandy bed where the pipelines are partly buried is treated as a rigid porous material, and its impact on wave-pipeline interaction is considered in the VARANS model in terms of porosity and equivalent mean diameter of porous material. The impacts of burial depth and distance between the centers of twin pi...

SOLITARY WAVE INTERACTION WITH A SUBMERGED PERMEABLE BREAKWATER: EXPERIMENT AND NUMERICAL MODELING

We study the interactions between a non-breaking solitary wave and a submerged permeable breakwater experimentally and numerically. The particle image velocimetry (PIV) technique was employed to measure instantaneous free surface displacements and velocity fields in the vicinity of the porous media. The porous media, consisted of uniform glass-made spheres, was mounted on the seafloor. Quantitative mean properties were obtained by ensemble averaging 30 repeated instantaneous measurements. In addition, two different numerical considerations are taken to simulate the experiments. One is to model an idealized volume-averaged porous media using a two-dimensional (2D) volume of fluid (VOF)-type model. This model is based on the Volume-Averaged Reynolds-Averaged Navier–Stokes (VARANS) equations coupled with the non-linear k-ε turbulence closure solver. The other is to model the real porous breakwater constructed by spheres using a three-dimensional (3D) VOF-type model. This model solves 3D incompressible Navier–Stokes equations with Large-eddy-simulation (LES) model. The comparisons were performed between measurements, 2D and 3D numerical results for the time histories of the free surface elevation, instantaneous free surface displacements and corresponding velocity properties around the permeable object. Fairly good agreements were obtained. The verified 3D numerical results were used to trace the trajectories of fluid particle around the porous media to help understand the possible sediment movements in suspended loads. Also, the 2D numerical model is used to estimate the energy reflection, transmission and dissipation using the energy integral method by varying the aspect ratio and the grain size of the permeable obstacle.

Numerical simulation of three-dimensional breaking waves on a gravel slope using a two-phase flow Navier–Stokes model

Wave breaking is mainly a three-dimensional flow problem characterized by wave energy dissipation due to turbulence. The understanding of the wave breaking mechanism on a beach is essential in studying coastal processes. The complexity of the wave-induced turbulence flow is also increased by the presence of a two-phase flow, which introduces buoyancy effects. In this work a set of numerical experiments is carried out on wave breaking on a gravel slope. The influence of a one-phase and two-phase flow and the permeability effect of the beach are investigated numerically by means of a Navier–Stokes model known as IH-3VOF, which considers the volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equations (del Jesus, 2011 [3]) to characterize the flow within the porous media. The accuracy of the VARANS equations is demonstrated by means of comparisons with laboratory data. The results are found to be within a 2% error in terms of wave height prior to the broken wave, and up to a 10% error after then, and in the order of 0.20 s in the time domain for the worst case. A further analysis of wave evolution on a permeable beach with alongshore variation of porosity is studied. Three-dimensional wave breaking and post-breaking wave transformations alongshore are analysed according to porosity values.

An integrated model for the wave-induced seabed response around marine structures: Model verifications and applications

In this study, an integrated model (PORO-WSSI II) for wave–seabed–structure interactions (WSSI) is developed by combining (i) the Volume-Averaged Reynolds-Averaged Navier–Stokes (VARANS) equations for wave motions in a fluid domain and the porous media flows in porous structures, and (ii) the dynamic Biot's equations for a porous elastic seabed. The effects of the porous flow in seabed and marine structures, and the fluid exchange at the interface between the fluid domain and solid domain on wave characteristics are considered. The finite difference two-step projection method and the forward time difference method are adopted to solve the VARANS equations. The volume of fluid (VOF) method is applied to track water free-surface. The finite element method and the Generalized Newmark method are respectively adopted for the space discretization and time discretization of the dynamic Biot's equations. A one-way integrating method is developed to integrate the VARANS equations with the dynamic Biot's equations. Several experimental data available in the literature are used to validate the integrated model. An overall agreement between the numerical results and the experiment data indicates that the integrated model developed for the WSSI problem is highly reliable. The integrated model is then applied to investigate the dynamic response of a large-scale composite breakwater on a seabed, and the mechanism of WSSI. Numerical results indicate that there are intensive fluid exchanges between the water body and the seabed and strong seepage forces in the seabed under the ocean wave loading. The excessive upward seepage force leads to the liquefaction of the seabed in the region under wave trough. There is a liquefaction zone in the seabed close to the bottom corner of the rubble mound, which may lead to foundation instability of the composite breakwater. The parametric study indicates that the wave characteristics have a significant impact on the liquefaction properties (depth, width and area).

Response of a porous seabed to water waves over permeable submerged breakwaters with Bragg reflection

An integrated model is developed for the investigation of wave motion and seabed response around multiple permeable submerged breakwaters subject to different levels of Bragg reflection. In this study, the Volume-Averaged Reynolds-Averaged Navier–Stokes (VARANS) equations are used to describe the non-linear interaction between waves and permeable structures, while Biot's “u−p” approximation theory is adopted for predicting the wave-induced seabed response. The numerical results show that the reflection coefficient is highly dependent on the wave period and the configuration/number of arrayed breakwaters. Wave motion and its induced seabed response (in terms of pore fluid pressure, vertical effective stress and liquefaction potential) around breakwaters can be largely changed due to Bragg reflection and energy dissipation of permeable structures. With the same incident wave conditions, the maximum liquefaction area decreases in size with an increasing soil permeability or degree of saturation.

Numerical Modeling of Tsunami Waves Interaction with Porous and Impermeable Vertical Barriers

Tsunami wave interaction with coastal regions is responsible for very important human and economic losses. In order to properly design coastal defenses against these natural catastrophes, new numerical models need to be developed that complement existing laboratory measurements and field data. The use of numerical models based on the Navier‐Stokes equations appears as a reasonable approach due to their ability to evaluate complex flow patterns around coastal structures without the inherent limitations of the classical depth‐averaged models. In the present study, a Navier‐Stokes‐based model, IH‐3VOF, is applied to study the interaction of tsunami waves with porous and impermeable structures. IH‐3VOF is able to simulate wave flow within the porous structures by means of the volume‐averaged Reynolds‐averaged Navier‐Stokes (VARANS) equations. The equations solved by the model and their numerical implementation are presented here. A numerical analysis of the interaction of a tsunami wave with both an impermeable and porous vertical breakwater is carried out. The wave‐induced three‐dimensional wave pattern is analysed from the simulations. The role paid by the porous media is also investigated. Finally, flow around the breakwater is analyzed identifying different flow behaviors in the vicinity of the breakwater and in the far field of the structure.

Numerical Simulation of Solitary Wave Induced Flow Motion around a Permeable Submerged Breakwater

This paper presents a numerical model for the simulation of solitary wave transformation around a permeable submerged breakwater. The wave‐structure interaction is obtained by solving the Volume‐Averaged Reynolds‐Averaged Navier‐Stokes governing equations (VARANS) and volume of fluid (VOF) theory. This model is applied to understand the effects of porosity, equivalent mean diameter of porous media, structure height, and structure width on the propagation of a solitary wave in the vicinity of a permeable submerged structure. The results show that solitary wave propagation around a permeable breakwater is essentially different from that around impermeable one. It is also found that the structure porosity has more impact than equivalent mean diameter on the wave transformation and flow structure. After interacting with the higher structure, the wave has smaller wave height behind the structure with a lower travelling speed. When the wave propagates over the breakwater with longer width, the wave travelling speed is obviously reduced with more wave energy dissipated inside porous structure.

Numerical study for waves propagating over a porous seabed around a submerged permeable breakwater: PORO-WSSI II model

The phenomenon of the wave, seabed and structure interactions has attracted great attentions from coastal geotechnical engineers in recent years. Most previous investigations have based on individual approaches, which focused on either flow region or seabed domain. In this study, an integrated model (PORO-WSSI II), based on the Volume-Averaged/Reynolds-Averaged Navier–Stokes (VARANS) equations and Biot's poro-elastic theory, is developed to investigate the mechanism of the wave–permeable structure–porous seabed interactions. The new model is verified with the previous experimental data. Based on the present model, parametric studies have been carried out to investigate the influences of wave, soil and structure parameters on the wave-induced pore pressure. Numerical results indicated: (i) longer wave period and larger wave height will obviously induce a higher magnitude of pore pressure at the leading edge of a breakwater; (ii) after a full wave–structure interaction, the magnitude of pore pressure below the lee side of a breakwater decreases with an increasing structure porosity while it varies dramatically with a change of structure height; and (iii) the seabed thickness, soil permeability and the degree of saturation can also significantly affect the dynamic soil behaviour.

A numerical model for wave motions and turbulence flows in front of a composite breakwater

A mathematical model based on the Volume-Averaged/Reynolds Averaged Navier-Stokes (VARANS) equations is developed to describe surface wave motions in the vicinity of a coastal structure, which could be either a rigid solid structure or a permeable structure or a combination of both. In the VARANS equations, the volume-averaged Reynolds stress is modeled by adopting the nonlinear eddy viscosity assumption. The model equations for the volume-averaged turbulent kinetic energy and its dissipation rate are derived by taking the volume-average of the standard k− ϵ equations. Because of the volume-averaging process, the effects of the small-scale turbulence in porous media are introduced. The performance of the model is checked by comparing numerical solutions with the experimental data related to a composite breakwater reported by Sakakiyama and Liu [Coast. Eng. 121 (2001) 117].