Non-breaking Waves Research Articles

Evolution of Infragravity Waves Over a Shoal Under Nonbreaking Conditions

AbstractThe present paper aims to clarify the mechanism of infragravity wave (IGW) energy amplification over nearshore shoals reported in recent studies. Wave transformation and energy transfer between short waves (SWs) and IGWs were investigated using SWASH model for nonbreaking random waves propagating over trapezoid shoals with different bottom slopes. It was found that the time lag of IGWs relative to SW groups is the major mechanism for energy transfer from SWs to IGWs and the amplification of IGW energy over all segments of the shoal. The time lag is generated on the front slope and enlarged on the plateau of the shoal, decreases on the rear slope with higher decreasing rates on milder slopes. Over the rear slope, the evolution of IGWs depends on the relative importance of deshoaling and nonlinear energy transfer. It was found that nonlinear energy transfer dominates over the rear slope gentler than 1/60, causing the IGW energy to increase over the first half of the deshoaling process and decrease over the second half whereas deshoaling dominates for steeper rear slope and the IGW energy decay over the whole slope. It is demonstrated numerically and theoretically that the shoals with gentler bottom slopes amplify the IGW energy more effectively by providing longer distance for nonlinear energy transfer to build up. The persistent nonlinear energy transfer on the plateau indicates the important role of wave spatial evolution history in the subsequent IGWs evolution. Strong free IGWs were detected on leeward of the shoal, possibly due to release of topography‐induced additional bound IGWs.

Can Langmuir Circulations Solve the Problem of Insufficient Upper-Ocean Mixing?

Insufficient vertical mixing in the upper ocean during summer is a common problem of oceanic circulation and climate models. The turbulence associated with non-breaking waves is widely believed to effectively solve this problem. In many studies, non-breaking surface wave processes are attributed to the effects of Langmuir circulations (LCs). In the present work, the influences of LCs on the upper-ocean thermal structure are examined by using one-and three-dimensional ocean circulation, as well as climate, models. The results indicated that the effect of vertical mixing enhanced by LCs is limited to the upper ocean. The models evaluated, including those considering LC effects alone and the combined effects of LCs and wave breaking, failed to produce a reasonable summertime thermocline, resulting in a large cold bias in the subsurface layer. Therefore, while they can slightly reduce the biases of mixed layer depths and sea surface temperatures in models, LCs are insufficient to solve the problem of insufficient vertical mixing. Moreover, restriction of non-breaking surface wave-induced processes in LCs may be questionable.

Experimental investigation of higher harmonic wave loads and moments on a vertical cylinder by a phase-manipulation method

This paper considers wave loads on bottom mounted vertical cylinders in the regime relevant to offshore wind turbine monopiles, examining the higher harmonics of the loading from non-breaking waves which are important in engineering design. Although we consider measurements of total force, our focus is on the moments applied about the seabed which have received much less attention in the literature. We consider an empirical ‘Stokes-like’ model whereby the magnitude of the higher harmonics of force or moment are dependent on the linear force or moment time-series raised to an appropriate power and a fixed coefficient. We compare this representation to high quality wave flume measurements and fully non-linear potential flow simulations. In general we find good agreement for all of the harmonic structure except for the triple frequency component where there are significant discrepancies. We also extend the Stokes-like model and show that harmonics of moments can be robustly predicted from the force harmonic and an appropriate constant moment arm for each harmonic, so a more elaborate calculation is generally not necessary.

Importance of Wave Non-linearity for 3D Morphodynamic Modelling

Mengual, B.; Bertin, X., and Martins, K., 2020. Importance of wave non-linearity for 3D morphodynamic modelling. In: Malvárez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1201-1205. Coconut Creek (Florida), ISSN 0749-0208.The effect of wave non-linearity on morphological changes of a sandbar is investigated through a realistic application at Duck Beach (North Carolina, USA) of a 3D state-of-the-art process-based morphodynamic model, which couples sediment transport, currents and waves (vortex force formalism). From simplified 1D/2DH models, previous studies highlighted that acceleration skewness of non-breaking waves over a sandbar could promote its progressive onshore migration. This process can counterbalance the offshore migration occurring under breaking waves through the development of strong offshore-directed “undertow” currents near the seabed. Based on the existing literature, an additional bedload flux associated to acceleration skewness of waves is implemented in the 3D model. Numerical experiments with and without this additional term clearly demonstrate the need to account for this supplementary wave-induced transport to reproduce onshore migration phases of the sandbar. Effectively, even a model integrating wave asymmetry effects on bedload flux estimates and 3D wave-current interactions fails to reproduce the observed onshore migration of the sandbar.

Numerical Study on Regular Wave Shoaling, De-Shoaling and Decomposition of Free/Bound Waves on Gentle and Steep Foreshores

Numerical tests are performed to investigate wave transformations of nonlinear nonbreaking regular waves with normal incidence to the shore in decreasing and increasing water depth. The wave height transformation (shoaling) of nonlinear waves can, just as for linear waves, be described by conservation of the mechanical energy flux. The numerical tests show that the mechanical energy flux for nonlinear waves on sloping foreshores is well described by stream function wave theory for horizontal foreshore. Thus, this theory can be used to estimate the shoaled wave height. Furthermore, the amplitude and the celerity of the wave components of nonlinear waves on mildly sloping foreshores can also be predicted with the stream function wave theory. The tests also show that waves propagating to deeper water (de-shoaling) on a very gentle foreshore with a slope of cot(β) = 1200 can be described in the same way as shoaling waves. For de-shoaling on steeper foreshores, free waves are released leading to waves that are not of constant form and thus cannot be modelled by the proposed approach.

Do Beach Profiles Under Nonbreaking Waves Minimize Energy Dissipation?

AbstractThe hypothesis that equilibrium beach profiles under nonbreaking waves minimize wave energy dissipation was considered by Larson et al. (1999 Coast. Eng. 36 59‐85). Larson et al. approached the hypothesis as a variational problem, assuming a priori that the solution (the extremal profile) followed a power law with a freely tunable exponent, which was varied so as to extremize the relevant functional. Here, we revisit this hypothesis and solve the associated variational problem approximately via analytical means, without a priori assumptions on the mathematical structure of the solution. We remark that for the solution to be realistic, the problem formulation must consider additional constraints; for example, the bed slope angle must not exceed the sediment's angle of repose. Incidentally, the solution we derive recovers the power law prescribed by Larson et al., which is in turn backed by a large body of empirical evidence. However, the exponent of the power in our solution is not an arbitrarily free parameter; it depends on the parametrization of the bed shear stress (the main mechanism by which nonbreaking waves dissipate energy), and predicted values of the exponent are supported by previous research. The power law curve derived here agrees well with empirical data from field and laboratory, suggesting that a principle of energy economy may indeed underpin the particular shape adopted by beach profiles under nonbreaking waves. This theoretical study aims at promoting and aiding further tests of this hypothesis.

On the Average Shape of the Largest Waves in Finite Water Depths

AbstractThis paper investigates the average shape of the largest waves arising in finite water depths. Specifically, the largest waves recorded in time histories of the water surface elevation at a single point have been examined. These are compared to commonly applied theories in engineering and oceanographic practice. To achieve this both field observations and a new set of laboratory measurements are considered. The latter concern long random simulations of directionally spread sea states generated using realistic Joint North Sea Wave Project (JONSWAP) frequency spectra. It is shown that approximations related to the linear theory of quasi-determinism (QD) cannot describe some key characteristics of the largest waves. While second-order corrections to the QD predictions provide an improvement, key effects arising in very steep or shallow water sea states are not captured. While studies involving idealized wave groups have demonstrated significant changes arising as a result of higher-order nonlinear wave–wave interactions, these have not been observed in random sea states. The present paper addresses this discrepancy by decomposing random wave measurements into separate populations of breaking and nonbreaking waves. The characteristics of average wave shapes in the two populations are examined and their key differences discussed. These explain the mismatch between findings in earlier random and deterministic wave studies.

Bulk drag coefficient of a subaquatic vegetation subjected to irregular waves: Influence of Reynolds and Keulegan-Carpenter numbers

Seagrass meadows are essential for protection of coastal erosion by damping wave and stabilizing the seabed. Seagrass are considered as a source of water resistance which modifies strongly the wave dynamics. As a part of EDF R & D seagrass restoration project in the Berre lagoon, we quantify the wave attenuation due to artificial vegetation distributed in a flume. Experiments have been conducted at Saint-Venant Hydraulics Laboratory wave flume (Chatou, France). We measure the wave damping with 13 resistive waves gauges along a distance L = 22.5 m for the “low” density and L = 12.15 m for the “high” density of vegetation mimics. A JONSWAP spectrum is used for the generation of irregular waves with significant wave height Hs ranging from 0.10 to 0.23 m and peak period Tp ranging from 1 to 3 s. Artificial vegetation is a model of Posidonia oceanica seagrass species represented by slightly flexible polypropylene shoots with 8 artificial leaves of 0.28 and 0.16 m height. Different hydrodynamics conditions (Hs, Tp, water depth hw) and geometrical parameters (submergence ratio α, shoot density N) have been tested to see their influence on wave attenuation. For a high submergence ratio (typically 0.7), the wave attenuation can reach 67% of the incident wave height whereas for a low submergence ratio (< 0.2) the wave attenuation is negligible. From each experiment, a bulk drag coefficient has been extracted following the energy dissipation model for irregular non-breaking waves developed by Mendez and Losada (2004). This model, based on the assumption that the energy loss over the species meadow is essentially due to the drag force, takes into account both wave and vegetation parameter. Finally, we found an empirical relationship for Cd depending on 2 dimensionless parameters: the Reynolds and Keulegan-Carpenter numbers. These relationships are compared with other similar studies.

Experimental Evidence of the Influence of Recurves on Wave Loads at Vertical Seawalls

The role of recurves on top of seawalls in reducing overtopping has been previously shown but their influence in the distribution and magnitude of wave-induced pressures and forces on the seawall remains largely unexplored. This paper deals with the effects of different recurve geometries on the loads acting on the vertical wall. Three geometries with different arc lengths, or extremity angles (αe), were investigated in large-scale physical model tests with regular waves, resulting in a range of pulsating (non-breaking waves) to impulsive (breaking waves) conditions at the structure. As the waves hit the seawall, the up-rushing flow is deflected seawards by the recurve and eventually, re-enters the underlying water column and interacts with the next incoming wave. The re-entering water mass is, intuitively, expected to alter the incident waves but it was found that the recurve shape does not affect wave heights significantly. For purely pulsating conditions, the influence of αe on peak pressures and forces was also negligible. In marked contrast, the mean of the maximum impulsive pressure and force peaks increased, even by a factor of more than two, with the extremity angle. While there is no clear relation between the shape of the recurve and the mean peak pressures and forces, interestingly the mean of the 10% highest forces increases gradually with αe and this effect becomes more pronounced with increasing impact intensity.

Numerical Simulation and Analysis of Phase-Focused Breaking and Non-Breaking Wave Impact on a Fixed Offshore Platform Deck

AbstractExtreme wave impact due to tsunamis and storm surge create large wave heights that cause destruction to coastal and offshore structures. Focused waves have been used to represent such extreme waves, and in the present study, its impact on offshore deck has been studied numerically. Numerical modeling has been carried out using open-source software reef3d, with the level set method to capture the air–water interface. Focused waves are generated by phase focusing a group of waves at a particular position and time. The nonlinearity of focused waves and its effect on the vertical impact force has been quantified for different airgaps and increasing wave heights. The wave steepness was increased to initiate phase-focused breaking in the numerical wave tank, which was then validated with the experimental results. This breaking-focused wave impact on offshore deck is then studied at different breaking locations. The results for different positionings of the deck with respect to breaker location show that the maximum horizontal impact force on the deck occurs when the plunging crest hits the deck side.

A Numerical Model for Offshore Mound Evolution

A numerical model was developed to simulate the evolution of a mound placed in the offshore (i.e., outside the zone of wave breaking), exposed to varying non-breaking waves and water levels. The net sediment transport rate is assumed to be mainly dominated by bed load transport, where wave asymmetry plays an important role. The net transport over a wave cycle is expressed with reference to an equilibrium profile, which ensures model reliability and robustness. In order to validate the model, data collected at two field sites, Cocoa Beach and Perdido Key Beach in Florida, USA, were employed. The numerical results show good agreement with the measured data from the two sites in terms of the profile evolution. It demonstrates that the model has the capability to simulate the evolution of mounds placed in the offshore. In addition, several scenarios with different mound volume and location designs were investigated to indicate potential uses for the model. The results illustrate how the mound evolution is influenced by the volume and location of the mound placement.

A 3D Hybrid Model Coupling SPH and QALE-FEM for Simulating Nonlinear Wave-structure Interaction

This paper presents a three-dimensional (3D) hybrid model, which couples the weakly compressible smoothed particle hydrodynamics (SPH) and the Quasi Arbitrary Langangian-Eulerian Finite Element Method (QALE-FEM), for modelling the wave-structure interaction (WSI) in extreme sea states. The former is a fully Lagrangian mesh-free approach, which solves the one-phase incompressible Navier-Stokes model, and has shown a satisfactory performance in simulating the WSI. The latter is an arbitrary Lagrangian Eulerian approach based on the fully nonlinear potential theory and can accurately simulate highly-nonlinear non-breaking water waves in a large scale with a high computational efficiency. These two models are coupled using a one-way zonal approach, in which the SPH uses a small computational domain near the structure, whereas the QALE-FEM covers the rest of the computational domain and provides wave conditions at the inlet of the SPH domain. The present hybrid model is validated against the experimental results and applied to the CCP-WSI blind test on modelling wave energy converters subjected to extreme focusing waves. The accuracy and convergence of the presented model are discussed.

Dynamic hydroelastic response of a surface-piercing strut in waves and ventilated flows

The objective of this work is to study the effects of waves and ventilation on the dynamic hydroelastic response of a surface-piercing strut via towing tank studies. The experimental studies are especially designed to test the hypothesis that flow conditions affect the modal response and hence structural dynamics, which in turn affect the hydrodynamic response through fluid–structure interaction, particularly near regions of mode localization such as frequency coalescence. The results showed that the modal frequencies decrease with increasing submergence, and are higher in fully ventilated flow compared to fully wetted flow. Regular, non-breaking waves lead to simple harmonic oscillations about the mean values at the encountered wave frequency for the slowly varying component of the hydrodynamic loads and tip deformations. The spectral response of the fast fluctuating component of the hydrodynamic loads and tip deformations showed peaks at the modal frequencies and vortex shedding frequencies (off the blunt trailing edge of the strut). Significant dynamic load amplifications and flow-induced vibrations were observed when the second and third modal frequencies coalesced at a submerged aspect ratio of two in fully wetted flow. In fully ventilated flow, the second and third modes separated enough to result in drastically reduced dynamic load fluctuations and flow-induced vibrations. When the submergence decreased, the separation between the modal frequencies increased, which avoided frequency coalescence in both fully wetted and fully ventilated flows. The results suggest that for cases where the wave encountered frequency is well separated from the modal frequencies, the spectral response of the fast fluctuating component of the hydrodynamic loads and tip deformations are governed by the structural response, and not by wave conditions.

An ISPH with k–ε closure for simulating turbulence under solitary waves

In this paper an Incompressible Smoothed Particle Hydrodynamics (ISPH) method solving the 2D RANS (Reynolds Averaged Navier-Stokes) equations with the k–ε turbulence closure is constructed. In the present model, the concept of “massless ISPH” utilizing the definition of “particle density” (number of computational particles within unit volume) is stressed. The skills of this numerical model are tested by applying to two laboratory experiments: (1) A non-breaking solitary wave propagating over a bottom-mounted barrier and (2) a solitary wave breaking on a 1 on 50 slope. In the former case flow separation occurs behind the barrier as the wave crest passes by and a vortex is generated, which later interacts with free surface causing breaking. In the latter case wave breaking and bottom friction both generate significant turbulence. For both cases, the effects of initial seeding of turbulent kinetic energy, required in the k–ε model, are studied and it is concluded that initial values of O (10−10) to O (10−8) m2/s2 should be used. An adaptive wall boundary condition for k–ε turbulence model is employed to avoid the unrealistic production of turbulence near the wall boundary. The numerical results, in terms of free surface profile, mean velocity field, vorticity field, turbulent kinetic energy and turbulent shear stress, are compared with experimental data. Very reasonable agreement is observed. This paper presents the first comprehensively validated 2D ISPH model with the k–ε turbulence closure, which can be applied to transient free surface wave problems.

A non-breaking-wave-generated turbulence mixing scheme for a global ocean general circulation model

A novel vertical mixing scheme to describe the influence of the non-breaking surface waves in ocean general circulation models is proposed based on the second-order turbulence closure model and a mathematical relationship fitted between the in situ observations of the turbulence kinetic energy dissipation rate and the calculated velocity shear module of non-breaking surface waves. The non-breaking-wave-generated turbulence mixing coefficients can be calculated empirically in terms of the wave spectral parameters including ΦSW, K, and ω, where ΦSW is the wave number spectrum of the significant wave height, K is the wave number, ω is the surface wave frequency. The effect of the new mixing scheme on global ocean circulation simulation was tested using the MArine Science and NUmerical Modeling ocean model. The results indicate significant improvement in the upper-ocean temperature structure and the mixed layer depth, i.e., the non-breaking-wave-generated turbulence mixing plays an important role in the upper ocean at high latitudes in summer for both hemispheres compared with traditional Mellor-Yamada 2.5 scheme.

Numerical Simulations of Non-Breaking, Breaking and Broken Wave Interaction with Emerged Vegetation Using Navier-Stokes Equations

Coastal plants can significantly dissipate water wave energy and services as a part of shoreline protection. Using plants as a natural buffer from wave impacts remains an attractive possibility. In this paper, we present a numerical investigation on the effects of the emerged vegetation on non-breaking, breaking and broken wave propagation through vegetation over flat and sloping beds using the Reynolds-average Navier-Stokes (RANS) equations coupled with a volume of fluid (VOF) surface capturing method. The multiphase two-equation k-ω SST turbulence model is adopted to simulate wave breaking and takes into account the effects enhanced by vegetation. The numerical model is validated with existing data from several laboratory experiments. The sensitivities of wave height evolution due to wave conditions and vegetation characteristics with variable bathymetry have been investigated. The results show good agreement with measured data. For non-breaking waves, the wave reflection due to the vegetation can increase wave height in front of the vegetation. For breaking waves, it is shown that the wave breaking behavior can be different when the vegetation is in the surf zone. The wave breaking point is slightly earlier and the wave height at the breaking point is smaller with the vegetation. For broken waves, the vegetation has little effect on the wave height before the breaking point. Meanwhile, the inertia force is important within denser vegetation and is intended to decrease the wave damping of the vegetation. Overall, the present model has good performance in simulating non-breaking, breaking and broken wave interaction with the emerged vegetation and can achieve a better understanding of wave propagation over the emerged vegetation.

Initial Stage of the Finite-Amplitude Cauchy–Poisson Problem

The nonlinear Cauchy–Poisson problem for an incompressible inviscid fluid to start flowing under gravity is investigated analytically. The general nonlinear initial/boundary-value problem is formulated, including both an initial surface deflection and an initial velocity generated by a pressure impulse on the surface. Two subproblems are: (1) a finite-amplitude surface deflection released from rest; (2) the fluid is forced into motion by a pressure impulse on the initially horizontal surface. Solutions for these two subproblems are given to the leading order. One exact solution is given for the fully nonlinear initial-value problem, where a surface pressure impulse is applied on a surface with finite initial deflection. The concept of the highest non-breaking wave is illustrated by dipole acceleration fields at a state of gravitational release from rest. This is done for two phenomena: run-up of a non-breaking solitary wave on a sloping beach, and free nonlinear sloshing in an open container.

The effects of slab geometries and wave directions on the steep wave-induced soil response and liquefaction around gravity-based offshore foundations

ABSTRACT Gravity-based offshore foundations generally consist of a bottom slab and one or more cylindrical shafts on top of it. The slab geometry can strongly affect the surrounding flow pattern, dynamic wave pressure distribution and further momentary soil liquefaction. In the present study, the effects of the slab geometry and the incoming wave angle to the foundations on the surrounding soil response are investigated. Gravity-based foundations with bottom slabs of cylindrical shape and hexagonal prismatic shape are considered. For the hexagonal foundation, two different incoming wave angles, i.e. propagating to the hexagon corner and the edge, are simulated. The waves are fully nonlinear steep non-breaking waves. The wave-structure interaction is validated against an existing experiment. Soil consolidation behaviour underneath the foundations is investigated. It is found that both the slab geometry and the incoming wave angle can affect the distributions of pore pressure and momentary liquefaction depth in the surrounding soil.

Flow Depths and Velocities across a Smooth Dike Crest

This contribution proposes a systematic analysis of the overtopping process at dikes, focused on the statistical description of the extreme flow characteristics across the dike crest. The specific objective of the analysis is the investigation of structures subjected to high run-up levels and low freeboards, under severe or extreme conditions that are likely to occur in the future due to climate change. The adopted methodology is based on the collection of new experimental and numerical tests of wave overtopping at smooth dikes at various crest levels. The reliability of the new data is checked in terms of average overtopping discharge and wave reflection coefficient, against consolidated predicting methods from the literature. An update and refitting of the existing formulae for the prediction of the extreme flow depths and velocities at the dike off-shore edge is proposed based on the experimental and numerical outcomes. The dynamics of the overtopping flow propagation along the dike crest under breaking and non-breaking waves, in emerged and submerged conditions, is investigated. Guidelines to update the state-of-the-art formulae for a more cautious estimation of the water depths and the velocities of propagation of the flow in the landward area are provided.

Decomposing Infrared Images of Wind Waves for Quantitative Separation Into Characteristic Flow Processes

An image processing method utilizing multi-dimensional empirical mode decomposition is developed to decompose wind-wave surface imageries attributed to various flow processes governing interfacial transport, including gravity waves, capillary ripples, Langmuir cells, and quasi-streamwise turbulent eddies. The decomposition and combination strategies are based on the characteristic length scales and directionalities of the signatures induced by the flow processes. The decomposed imagery thus provides quantification of the contribution partition to the interfacial signatures by individual flow processes. Analyses of infrared images taken in the wind wave facility Aeolotron at Heidelberg University reveal: quasi-streamwise eddies, which arise from the turbulent shear layer, dominate the contribution to interfacial signatures at low wind speeds. For nonbreaking waves at intermediate wind speeds, the contribution partitions to interfacial signatures by the four flow processes are of the same order of magnitude. For microscale breaking waves, the dominant contribution is attributed to boundary layer disruption in the wake of spilling breakers. For breaking waves at high wind speeds, transverse turbulent eddies, which induce similar surface signatures as those by capillary ripples, and streamwise vortices caused by breaking also contribute to the transport; the decomposed imageries are thus induced by multiple flow processes.