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Showing papers on "Breaking wave published in 2018"


Book
01 Mar 2018
TL;DR: In this paper, the authors provide a comprehensive treatment of the theory for small and large amplitude internal gravity waves. And they provide a single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.
Abstract: The study of internal gravity waves provides many challenges: they move along interfaces as well as in fully three-dimensional space, at relatively fast temporal and small spatial scales, making them difficult to observe and resolve in weather and climate models. Solving the equations describing their evolution poses various mathematical challenges associated with singular boundary value problems and large amplitude dynamics. This book provides the first comprehensive treatment of the theory for small and large amplitude internal gravity waves. Over 120 schematics, numerical simulations and laboratory images illustrate the theory and mathematical techniques, and 130 exercises enable the reader to apply their understanding of the theory. This is an invaluable single resource for academic researchers and graduate students studying the motion of waves within the atmosphere and ocean, and also mathematicians, physicists and engineers interested in the properties of propagating, growing and breaking waves.

275 citations


Journal ArticleDOI
TL;DR: In this paper, the authors focus on the most common type of IG waves, those induced by the presence of groups in incident short waves, and three related mechanisms explain their generation: (1) the development, shoaling and release of waves bound to the short-wave group envelopes (2) the modulation by these envelopes of the location where short waves break, and (3) the merging of bores (breaking wave front, resembling to a hydraulic jump) inside the surfzone.

149 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that most commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity.
Abstract: In previous computational fluid dynamics studies of breaking waves, there has been a marked tendency to severely over-estimate turbulence levels, both pre- and post-breaking. This problem is most likely related to the previously described (though not sufficiently well recognized) conditional instability of widely used turbulence models when used to close Reynolds-averaged Navier–Stokes (RANS) equations in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity. While this problem has been known for nearly 20 years, a suitable and fundamentally sound solution has yet to be developed. In this work it is demonstrated that virtually all commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in such regions. A new formulation of the is the dissipation.)

143 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated geometric, kinematic and energetic differences between maximally tall non-breaking waves and marginally breaking waves in focusing wave groups and showed that the initial breaking instability occurs within a very compact region centred on the wave crest.
Abstract: We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. Based on a fully nonlinear 3D boundary element model, our numerical simulations investigate geometric, kinematic and energetic differences between maximally tall non-breaking waves and marginally breaking waves in focusing wave groups. Our study focuses initially on unidirectional domains with flat bottom topography and conditions ranging from deep to intermediate depth (depth to wavelength ratio from 1 to 0.2). Maximally tall non-breaking (maximally recurrent) waves are clearly separated from marginally breaking waves by their normalised energy fluxes localised near the crest tip region. The initial breaking instability occurs within a very compact region centred on the wave crest. On the surface, this reduces to the local ratio of the energy flux velocity (here the fluid velocity) to the crest point velocity for the tallest wave in the evolving group. This provides a robust threshold parameter for breaking onset for 2D wave packets propagating in uniform water depths from deep to intermediate. Further targeted study of representative cases of the most severe laterally focused 3D wave packets in deep and intermediate depth water shows that the threshold remains robust. These numerical findings for 2D and 3D cases are closely supported by our companion observational results. Warning of imminent breaking onset is detectable up to a fifth of a carrier wave period prior to a breaking event.

73 citations


Journal ArticleDOI
TL;DR: In this paper, a buoyancy-modified turbulence model is proposed to simulate wave breaking in a numerical wave flume, where the density of the turbulent energy is explicitly included in the turbulence transport equations and the buoyancy term is added to the turbulent kinetic energy (TKE) equation.

72 citations


Journal ArticleDOI
TL;DR: In this paper, the performance of different wave generation and absorption methods in computational fluid dynamics (CFD)-based numerical wave tanks (NWTs) is analyzed, and sensitivity analysis has been conducted in order to quantify and compare the differences in terms of absorption quality between these methods.
Abstract: In this paper, the performance of different wave generation and absorption methods in computational fluid dynamics (CFD)-based numerical wave tanks (NWTs) is analyzed. The open-source CFD code REEF3D is used, which solves the Reynolds-averaged Navier–Stokes (RANS) equations to simulate two-phase flow problems. The water surface is computed with the level set method (LSM), and turbulence is modeled with the k-ω model. The NWT includes different methods to generate and absorb waves: the relaxation method, the Dirichlet-type method and active wave absorption. A sensitivity analysis has been conducted in order to quantify and compare the differences in terms of absorption quality between these methods. A reflection analysis based on an arbitrary number of wave gauges has been adopted to conduct the study. Tests include reflection analysis of linear, second- and fifth-order Stokes waves, solitary waves, cnoidal waves and irregular waves generated in an NWT. Wave breaking over a sloping bed and wave forces on a vertical cylinder are calculated, and the influence of the reflections on the wave breaking location and the wave forces on the cylinder is investigated. In addition, a comparison with another open-source CFD code, OpenFOAM, has been carried out based on published results. Some differences in the calculated quantities depending on the wave generation and absorption method have been observed. The active wave absorption method is seen to be more efficient for long waves, whereas the relaxation method performs better for shorter waves. The relaxation method-based numerical beach generally results in lower reflected waves in the wave tank for most of the cases simulated in this study. The comparably better performance of the relaxation method comes at the cost of larger computational requirements due to the relaxation zones that have to be included in the domain. The reflections in the NWT in REEF3D are generally lower than the published results for reflections using the active wave absorption method in the NWT based on OpenFOAM.

66 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of wave age and wave steepness on wind turbulence over breaking waves based on direct numerical simulation (DNS) of two-fluid flows are investigated.
Abstract: We study wind turbulence over breaking waves based on direct numerical simulation (DNS) of two-fluid flows In the DNS, the air and water are simulated as a coherent system, with the interface captured using the coupled level-set and volume-of-fluid method Because the wave breaking is an unsteady process, we use ensemble averaging over 100 runs to define turbulence statistics We focus on analysing the turbulence statistics of the airflow over breaking waves The effects of wave age and wave steepness are investigated It is found that before wave breaking, the turbulence statistics are largely influenced by the wave age The vertical gradient of mean streamwise velocity is positive at small and intermediate wave ages, but it becomes negative near the wave surface at large wave age as the pressure force changes from drag to thrust Furthermore, wave-coherent motions make increasingly important contributions to the momentum flux and kinetic energy of velocity fluctuations (KE-F) as the wave age increases During the wave breaking process, spilling breakers do not influence the wind field significantly; in contrast, plunging breakers alter the structures of wind turbulence near the wave surface drastically It is observed from the DNS results that during wave plunging, a high pressure region occurs ahead of the wave front, which further accelerates the wind in the downstream direction Meanwhile, a large spanwise vortex is generated, which greatly disturbs the airflow around it, resulting in large magnitudes of Reynolds stress and turbulence kinetic energy (TKE) below the wave crest Above the crest, the magnitude of KE-F is enhanced during wave plunging at small and large wave ages, but at intermediate wave age, the transient enhancement of KE-F is absent The effect of wave breaking on the magnitude of KE-F is further investigated through the analysis of the KE-F production It is discovered that at small wave age, the transient enhancement of KE-F is caused by the appearance of a local maximum in the profile of total momentum flux; but at large wave age, it results from the change in the sign of the KE-F production from negative to positive, due to the sign change in the wave-coherent momentum flux At intermediate wave age, neither of these two processes is present, and the transient growth of KE-F does not take place

62 citations


Journal ArticleDOI
TL;DR: The physics ofinternal waves in shallow waters are reviewed and two commonalities among internal waves in the nearshore are identified: exposure to deep offshore waters and enhanced turbulence and mixing.
Abstract: Internal waves are widespread features of global oceans that play critical roles in mixing and thermohaline circulation. Similarly to surface waves, internal waves can travel long distances, ultimately breaking along continental margins. These breaking waves can transport deep ocean water and associated constituents (nutrients, larvae, and acidic low-oxygen waters) onto the shelf and locally enhance turbulence and mixing, with important effects on nearshore ecosystems. We are only beginning to understand the role internal waves play in shaping nearshore ecosystems. Here, I review the physics of internal waves in shallow waters and identify two commonalities among internal waves in the nearshore: exposure to deep offshore waters and enhanced turbulence and mixing. I relate these phenomena to important ecosystem processes ranging from extreme events to fertilization success to draw general conclusions about the influence of internal waves on ecosystems and the effects of internal waves in a changing climate.

59 citations


Journal ArticleDOI
TL;DR: In this article, the authors describe 2D numerical simulations of velocity and pressure fields generated by non-breaking waves on a vertical breakwater with a recurved parapet wall.

58 citations


Journal ArticleDOI
TL;DR: In this article, a numerical simulation of a two-phase gas-liquid mixing layer that lies in the absolute instability regime is conducted, and the results obtained with the finest mesh are shown to be not far from converged results of turbulent dissipation.
Abstract: The two-phase mixing layer formed between parallel gas and liquid streams is an important fundamental problem in turbulent multiphase flows. The problem is relevant to many industrial applications and natural phenomena, such as air-blast atomizers in fuel injection systems and breaking waves in the ocean. The velocity difference between the gas and liquid streams triggers an interfacial instability which can be convective or absolute depending on the stream properties and injection parameters. In the present study, a direct numerical simulation of a two-phase gas-liquid mixing layer that lie in the absolute instability regime is conducted. A dominant frequency is observed in the simulation and the numerical result agrees well with the prediction from viscous stability theory. As the interfacial wave plays a critical role in turbulence transition and development, the temporal evolution of turbulent fluctuations (such as the enstrophy) also exhibits a similar frequency. In order to investigate the statistical response of the multiphase turbulence flow, the simulation has been run for a long physical time so that time-averaging can be performed to yield the statistically converged results for Reynolds stresses and the turbulent kinetic energy (TKE) budget. An extensive mesh refinement study using from 8 million to about 4 billions cells has been carried out. The turbulent dissipation is shown to be highly demanding on mesh resolution compared to other terms in TKE budget. The results obtained with the finest mesh are shown to be not far from converged results of turbulent dissipation which allow us to obtain estimations of the Kolmogorov and Hinze scales. The computed Hinze scale is significantly larger than the size of droplets observed and does not seem to be a relevant length scale to describe the smallest size of droplets formed in atomization.

53 citations


Journal ArticleDOI
TL;DR: In this article, a 3D phase-averaged modeling system using a vortex force formalism is applied to hindcast an unpublished field experiment, carried out at a dissipative beach under moderate to very energetic wave conditions (H m 0 = 6 m at breaking and T p = 22 s ).


Journal ArticleDOI
TL;DR: In this article, the authors show that wave breaking occurs with positive probability for the stochastic Camassa-Holm (SCH) equation with a positive probability, and conjecture that the time-asymptotic solutions of the SCH will consist of emergent wave trains of peakons moving along time paths.

Journal ArticleDOI
TL;DR: In this paper, a large-eddy simulation (LES) was used to simulate turbulent flow over strongly forced steep steady and unsteady waves, with time t and space x varying wave height h(x, t) imposed as a lower boundary condition.
Abstract: Turbulent flow over strongly forced steep steady and unsteady waves is simulated using large-eddy simulation (LES) with time t and space x varying wave height h(x, t) imposed as a lower boundary condition. With steady waves, h(x, t) is based on measurements of incipient and active breaking waves collected in a wind-wave flume, while a numerical wave code is used to generate an unsteady evolving wave packet (group). Highly intermittent airflow separation is found in the simulations, and the results suggest separation near a wave crest occurs prior to the onset of wave breaking. The form (pressure) drag is most sensitive to the wave slope, and the form drag can contribute as much as 74% to the total stress. Wind and scalar profiles from the LES display log-linear variations above the wave surface; the LES wind profiles are in good agreement with the measurements. The momentum roughness increases as the water surface changes from wind ripples to incipient breaking to active breaking. However, the sca...

Book
11 Sep 2018
TL;DR: In this paper, a laboratory experiment was conducted in a wave tank to examine macroscale features of wave breaking over bars and reefs, which included breaker type, height, and depth; plunge, splash, and penetration distance; breaker vortex area; wave decay; wave reflection; and wave runup.
Abstract: : A laboratory experiment was conducted in a wave tank to examine macroscale features of wave breaking over bars and reefs. Submerged triangular- shaped obstacles representing bars and reefs were installed on a 1/30 concrete slope to cause wave breaking. Seaward and shoreward slopes of the obstacles were varied, as was the deepwater wave steepness, which resulted in 108 monochromatic wave tests and 12 irregular wave tests. Empirical expressions were determined for the wave properties investigated, which included breaker type, height, and depth; plunge, splash, and penetration distance; breaker vortex area; wave decay; wave reflection; and wave runup. Additionally, data acquired from other studies involving plane slopes were reanalyzed to determine breaker indices and plunge distance. Differences were found between wave properties on plane slopes and barred profiles. Plunging and collapsing breakers were predominate for regular waves breaking over bars and reefs, whereas spilling breakers occurred on the plane slope. The strength of return flow altered the breaking wave form. Return flow was strongest if the bars were terraced or if the seaward slope was steep, and the deepwater wave steepness was small. The position of the break point was greatly influenced by return flow, which exerted control over the breaker depth. Breaker height was found to increase in the presence of strong return flow. Plunge distance normalized by breaking wave height was found to be shorter over irregular slopes than plane slopes.

Journal ArticleDOI
TL;DR: In this article, the effects of the main influential parameters, including the incident wave height, wave frequency and PTO damping, on the maximum heave displacement, phase difference between the buoy velocity and wave elevation, and capture width ratio were quantitatively studied.

Journal ArticleDOI
TL;DR: In this paper, heat and momentum transfer across the wind-driven breaking air-water interface at extremely high wind speeds was experimentally investigated using a high-speed wind-wave tank.
Abstract: Heat and momentum transfer across the wind-driven breaking air–water interface at extremely high wind speeds was experimentally investigated using a high-speed wind-wave tank. An original m...

Journal ArticleDOI
TL;DR: Dual copolarized (VV and HH) Ka-band radar measurements of joint modulation of normalized radar cross section (NRCS) and Doppler velocity (DV) performed from a sea research platform are presented and an empirical MTF parameterization based on polynomial fitting as a function of observation geometry and wind is proposed.
Abstract: This paper presents dual copolarized (VV and HH) Ka-band radar measurements of joint modulation of normalized radar cross section (NRCS) and Doppler velocity (DV) performed from a sea research platform. NRCS and DV modulations are well correlated. NRCS modulations exhibit a spiky structure. HH modulations are stronger than VV ones leading to modulations of the polarization ratio. This suggests that an important portion of NRCS modulations is produced by nonpolarized radar returns from modulated wave breaking facets. DV modulations reveal that at incidence angles <50°, NRCS spikes are attributable to rather slow moving facets, which may be interpreted as short wave breaking disturbances embedded in the water at crests of modulating waves. Using the DV as a proxy for wave gauge, a modulation transfer function (MTF) is estimated for both polarizations. The hydrodynamics component of the total MTF, hydro-MTF, combines NRCS modulations supported by Bragg waves and wave breaking. The contribution of each type of facets to the hydro-MTF is weighted by its partial contribution to the NRCS, and thus, hydro-MTF becomes dependent on radar polarization. Using hydro-MTF for HH and VV, Bragg wave and wave breaking modulations are separated. Wave breaking modulations are significant, with MTF amplitude varying from 5 to about 30 depending on wind speed. Ka-band Bragg waves are strongly modulated at low winds, but their modulation almost vanishes at moderate winds. Finally, we propose an empirical MTF parameterization based on polynomial fitting as a function of observation geometry and wind.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the intensity of the load applied by non-breaking waves on the recurved parapet wall of vertical breakwaters under both regular and irregular waves.

Journal ArticleDOI
TL;DR: In this paper, a numerical study regarding the damaged ship cabin flooding in transversal regular waves is carried out based on a weakly compressible Smoothed Particle Hydrodynamics (WCSPH) method.

Journal ArticleDOI
TL;DR: In this paper, wave breaking closure for Boussinesq type models is considered, and two closure strategies are considered: an eddy viscosity approach and suppressing the dispersive terms in breaking regions.

Journal ArticleDOI
01 Nov 2018-Water
TL;DR: A series of numerical simulations were performed to explore the influences of filling level, excitation frequency and amplitude on liquid sloshing by using the OpenFOAM (Open Field Operation and Manipulation), which was fully validated by the experimental data as mentioned in this paper.
Abstract: A series of numerical simulations were performed to explore the influences of filling level, excitation frequency and amplitude on liquid sloshing by using the open source Computational Fluid Dynamics toolbox OpenFOAM (Open Field Operation and Manipulation), which was fully validated by the experimental data. The results show that the dynamic impact pressure is proportional to the external excitation amplitude only in non-resonance frequency ranges. Pressure-frequency response curves demonstrate a transition process from a ‘soft-spring’ response to a ‘hard-spring’ response following the changes of the filling level. Such a transition process is found to be dominated by the ratio of the filling level to tank length and the critical value can be obtained. It is also found that wave breaking influences the period of sloshing wave in tanks and ultimately alters the resonance frequency from the linear theory.

Journal ArticleDOI
TL;DR: In this paper, a wave-breaking mechanism is implemented into a nonlinear potential flow solver, which is used to solve for the free surface in a numerical wave tank using the high-order spectral (HOS) method.
Abstract: We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech https://arxiv.org/pdf/1508.06002.pdf , submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642–658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation successfully for a wide range of breaking conditions. The model is also able to successfully calculate the transfer of energy between frequencies due to wave focusing and wave breaking. This study is limited to unidirectional waves but provides a valuable basis for future application of the wave-breaking model to a multidirectional wave field. By including parameters for removing energy due to wave-breaking into a nonlinear potential flow solver, the risk of developing numerical instabilities due to an overturning wave is decreased, thereby increasing the application range of the model, including calculating more extreme sea states. A computationally efficient and accurate model for the generation of a nonlinear random wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures, and in the study of open ocean wave generation and propagation in a realistic environment.

Journal ArticleDOI
TL;DR: In this paper, the authors present a theory which analytically predicts the reflection coefficients and which can be used to optimally select the source term parameters before running the simulation, which is given in a general form so that it is applicable to many existing implementations.

Journal ArticleDOI
TL;DR: In this paper, the analysis of a challenging free surface flow problem involving a surface vessel moving at high speeds, or planing, is performed using a general purpose high Reynolds free surface solver developed at CNR-INSEAN.
Abstract: This paper focuses on the analysis of a challenging free surface flow problem involving a surface vessel moving at high speeds, or planing. The investigation is performed using a general purpose high Reynolds free surface solver developed at CNR-INSEAN. The methodology is based on a second order finite volume discretization of the unsteady Reynolds-averaged Navier–Stokes equations (Di Mascio et al. in A second order Godunov—type scheme for naval hydrodynamics, Kluwer Academic/Plenum Publishers, Dordrecht, pp 253–261, 2001; Proceedings of 16th international offshore and polar engineering conference, San Francisco, CA, USA, 2006; J Mar Sci Technol 14:19–29, 2009); air/water interface dynamics is accurately modeled by a non standard level set approach (Di Mascio et al. in Comput Fluids 36(5):868–886, 2007a), known as the single-phase level set method. In this algorithm the governing equations are solved only in the water phase, whereas the numerical domain in the air phase is used for a suitable extension of the fluid dynamic variables. The level set function is used to track the free surface evolution; dynamic boundary conditions are enforced directly on the interface. This approach allows to accurately predict the evolution of the free surface even in the presence of violent breaking waves phenomena, maintaining the interface sharp, without any need to smear out the fluid properties across the two phases. This paper is aimed at the prediction of the complex free-surface flow field generated by a deep-V planing boat at medium and high Froude numbers (from 0.6 up to 1.2). In the present work, the planing hull is treated as a two-degree-of-freedom rigid object. Flow field is characterized by the presence of thin water sheets, several energetic breaking waves and plungings. The computational results include convergence of the trim angle, sinkage and resistance under grid refinement; high-quality experimental data are used for the purposes of validation, allowing to compare the hydrodynamic forces and the attitudes assumed at different velocities. A very good agreement between numerical and experimental results demonstrates the reliability of the single-phase level set approach for the predictions of high Froude numbers flows.

Journal ArticleDOI
TL;DR: In this paper, a wave-current coupled model was calibrated and validated against observational data, and then applied to investigate the complex dynamics in the Maryland Coastal Bays during Hurricane Irene (2011).

Journal ArticleDOI
TL;DR: In this article, the shape of the wave spectrum plays a substantial role in the breaking of steep wave groups, and their associated kinematic field, and the effect of the underlying focussing mechanism is investigated.

Journal ArticleDOI
TL;DR: In this article, the authors validate a two-phase Reynolds Averaged Navier-Stokes (RANS) solver with experimental results for the propagation of steep focused wave groups, using a newly developed methodology based on the separation of harmonics.

Journal ArticleDOI
TL;DR: In this paper, the authors focused on the hydrodynamic simulation of wave run-up and mainly sought to evaluate the importance of wave scattering types identified by Swanet al. (2005) and lateral progressive edge waves on nonlinear wave amplification around a single fixed cylinder.

Journal ArticleDOI
TL;DR: In this paper, a scaling law for energy dissipation in the inner surf zone was proposed, which achieves satisfactory results at both the time-averaged and wave-by-wave scales.
Abstract: The spatial and temporal variation of energy dissipation rates in breaking waves controls the mean circulation of the surf zone. As this circulation plays an important role in the morphodynamics of beaches, it is vital to develop better understanding of the energy dissipation processes in breaking and broken waves. In this paper, we present the first direct field measurements of roller geometry extracted from a LiDAR data set of broken waves to obtain new insights into wave energy dissipation in the inner surf zone. We use a roller model to show that most existing roller area formulations in the literature lead to considerable overestimation of the wave energy dissipation, which is found to be close to, but smaller than, the energy dissipation in a hydraulic jump of the same height. The role of the roller density is also investigated, and we propose that it should be incorporated into modified roller area formulations until better knowledge of the roller area and its link with the mean roller density is acquired. Finally, using previously published results from deepwater wave breaking studies, we propose a scaling law for energy dissipation in the inner surf zone, which achieves satisfactory results at both the time‐averaged and wave‐by‐wave scales.