Non-breaking Waves Research Articles

Hydraulic stability of rock armors in breaking wave conditions

Armor layers of mound breakwaters are usually designed with empirical formulas based on small-scale tests in non-breaking wave conditions. However, most rubble mound breakwaters are constructed in the depth-induced breaking zone, where they must withstand design storms having some percentage of large waves breaking before reaching the structure; in these cases, the design formulas for non-breaking wave conditions are not fully valid. To characterize double-layer rock armor damage in breaking wave conditions, 2D physical model tests were carried out with a bottom slope m = 1/50. In order to develop a simple method to determine the wave parameters in the depth-induced breaking zone, experimental wave measurements were compared to the numerical estimations given by the SwanOne model. An analysis was conducted to select the best characteristic wave height to estimate rock armor damage when dealing with depth-induced breaking waves; the spectral significant wave height, Hm0, estimated at a distance of 3hs seaward from the structure toe, was found to be the most adequate. A new hydraulic stability formula is proposed for double-layer rock armors in breaking wave conditions, considering the observed potential 6-power relationship between the equivalent dimensionless armor damage and the Hm0 at 3hs seaward distance from the structure toe.

The effect of pneumatophore density on turbulence: A field study in a Sonneratia-dominated mangrove forest, Vietnam

This paper examines the role of mangrove pneumatophore roots as a spatial control over the turbulent kinetic energy (TKE) dissipation rate within a natural mangrove forest. Measurements of turbulence at millimeter scales were compared with vegetation geometries reconstructed using a novel photogrammetric technique. These small-scale relationships were then averaged to show larger-scale patterns in turbulence across the mudflat and mangrove fringe-forest transition. Although turbulence estimates varied with across-shore position, TKE dissipation was always elevated in the fringe relative to mudflat and forest interior sample sites. The largest dissipation rates (4.5 × 10−3Wkg−1) were measured as breaking waves propagated over canopies in very shallow water. Dissipation was reduced, but often remained intense (10−5–10−4Wkg−1) under non-breaking waves at the fringe, likely indicating turbulent generation in pneumatophore wakes. Pneumatophore density was positively correlated with the spatial distribution of TKE dissipation. Turbulence was also correlated positively with wave height and negatively with water depth. Fringe sediments were more sandy and less muddy than sediments onshore and offshore, suggesting that the intense turbulence may lead to winnowing of fine-grained sediments at the fringe.

Numerical simulation of non-breaking solitary wave run-up using exponential basis functions

A meshless method based on exponential basis functions (EBFs) is developed to simulate the propagation of solitary waves and run-up on the slope. The presented method is a boundary-type meshless method applying the exponential basis functions with complex exponents. The solution of governing equations is considered as a series of these basis functions. Boundary conditions are satisfied through a point-wise collocation approach. Based on the presented EBF meshless method, a new formula is introduced for the maximum run-up height on different slopes, valuable for engineering applications. The results obtained through the numerical method in the prediction of solitary wave propagation and estimation of run-up are verified through the comparison with experimental data. The comparison with 159 experimental data indicates that this new formula is more accurate than the preceding formulas in predicting the maximum run-up of non-breaking solitary waves. Minimum calculation time and convenient performances are the other advantages of this method.

Nonbreaking wave‐induced mixing in upper ocean during tropical cyclones using coupled hurricane‐ocean‐wave modeling

AbstractThe effects of turbulence generated by nonbreaking waves have been investigated by testing and evaluating a new nonbreaking wave parameterization in a coupled hurricane‐ocean‐wave model. The MPI version of the Princeton Ocean Model (POM) with hurricane forcing is coupled with the WAVEWATCH‐III (WW3) surface wave model. Hurricane Ivan is chosen as the test case due to its extreme intensity and availability of field data during its passage. The model results are validated against field observations of wave heights and sea surface temperatures (SSTs) from the National Data Buoy Centre (NDBC) during Hurricane Ivan and against limited in situ current and bottom temperature data. A series of numerical experiments is set up to examine the influence of the nonbreaking wave parameterization on the mixing of upper ocean. The SST response from the modeling experiments indicates that the nonbreaking wave‐induced mixing leads to significant cooling of the SST and deepening of the mixed layer. It was found that the nondimensional constant b1 in the nonbreaking wave parameterization has different impacts on the weak and the strong sides of the storm track. A constant value of b1 leads to improved predictions on the strong side of the storm while a steepness‐dependent b1 provides a better agreement with in situ observations on the weak side. A separate simulation of the intense tropical cyclone Olwyn in north‐west Australia revealed the same trend for b1 on the strong side of the tropical cyclone.

Stability of seawalls using modified pseudo-dynamic method under earthquake conditions

By using the modified pseudo-dynamic method for submerged soils this paper explores the seismic stability of seawall for the active condition of earth pressure. Different forces such as seismic active earth pressure, seismic inertia forces of the wall, non-breaking wave pressure, hydrostatic and hydrodynamic pressures are considered in the stability analysis. Limit equilibrium has been used, and expressions for the factor of safety against sliding and overturning mode of failure have been proposed. The proposed methodology overcomes the limitations of existing pseudo-dynamic method for submerged soils. A detailed parametric study has been conducted by varying different parameters and results are presented in the form of design charts for computation of factor of safety against sliding and overturning mode of failures. It was noticed that the influences of soil friction angle, seismic acceleration coefficient, wall inclination and excess pore pressure are significant when compared to the other parameters. The value of factor of safety against the sliding mode of failure is increasing by about 62% when the value of soil frictional angle is increased from 30° to 40°. It was also found that the factor of safety against overturning mode of failure is decreasing by about 22% as the value of excess pore pressure ratio increases from 0 to 0.75. The proposed method with closed-form solutions can be used for the seismic design of seawalls.

Laboratory study on effects of submerged obstacles on tsunami wave and run-up

This paper presents laboratory experiments and numerical simulations of effects of submerged obstacles on tsunami-like solitary wave and its run-up. This study was carried out for the breaking and non-breaking solitary waves on 1:19.85 uniform slope which contains a submerged obstacle. New laboratory experiments are performed to describe the mitigation of tsunami amplitude and run-up under the effect of submerged obstacles. We are based on experimental results obtained to validate the numerical model. The numerical modeling using COULWAVE aims essentially to show the effect of the obstacle on the shape of solitary wave and the limit of this effect. Using a multiple nonlinear regression, we have determined a model to estimate height of run-up according to the amplitude of the wave and the obstacle peak depth.

Sensitivity of typhoon modeling to surface waves and rainfall

AbstractImproving intensity simulation and forecast of tropical cyclones has always been a challenge, although in recent years the track forecasts have been remarkably improved. In this study, we explore the sensitivity of typhoon simulation to three physical processes using a fully coupled atmosphere‐ocean‐wave model. Two storms, a strong and a weak one, have been chosen. The effects of wave breaking induced sea spray, ocean vertical mixing associated with nonbreaking surface waves, and sea surface cooling due to intense rainfall are assessed by means of a set of numerical experiments. The results show and confirm that sea spray leads to an increase of typhoon intensity by enhancing the air‐sea heat flux, while nonbreaking wave‐induced vertical mixing and rainfall lead to a decrease. Each process can be relevant, depending on wind and wave conditions. These can vary dramatically when typhoons interact with not sufficiently well‐defined coastal areas, typically an archipelago. Compared with the control runs, when all the three physical processes are considered, the (absolute) difference between the modeled sea level pressure and best track data is reduced from 26.05 to 0.70 hPa for typhoon Haiyan, and from −9.42 to −8.67 hPa for typhoon Jebi. We have found a steady overestimate of the dimensions of the typhoons. We have verified an extreme sensitivity to the initial conditions, especially when small differences in the typhoon track may imply different relevance of the physical processes, like the ones we have considered, governing the evolution of the storm.

On the Formation of Coherent Vortices beneath Nonbreaking Free-Propagating Surface Waves

AbstractNumerical simulations of monochromatic surface waves freely propagating over an initially quiescent flow field are conducted and found to reveal an array of quasi-streamwise vortices of alternating orientation in a manner akin to that of Langmuir circulation beneath wind-driven surface waves. A linear instability analysis of the wave-averaged Craik–Leibovich (CL) equation is then conducted to determine whether the structures in the simulations can be explained by the Craik–Leibovich type 2 (CL2) instability, which requires the presence of spanwise-independent drift and mean shear of the same sign. There is no imposed shear in the simulations, but they confirm the theoretical analysis of Longuet-Higgins that an Eulerian-mean shear with a magnitude comparable to that of Lagrangian Stokes drift occurs at the edge of the surface boundary layer in the otherwise irrotational oscillatory flow. The spanwise wavelength of the least stable disturbance is found to be close to the spacing between predominant vortex pairs, which likely are excited by the CL2 instability.

Effects of a Macro-Roughness Element on Tsunami Wave Amplification, Pressures, and Loads: Physical Model and Comparison to Japanese and US Design Equations

Experiments were conducted at a 1:20 length scale in a large tsunami flume to measure wave evolution and pressures on and around structural elements. The water surface profiles of waves propagating across a bare beach were compared with those recorded in front of an onshore obstacle representing an urban macro-roughness element. The addition of a structure significantly changed the water surface profile for broken waves: the water surface amplification in the presence of a macro-roughness element reached seven times the bare-earth water surface elevation. Estimated pressures from design equations were calculated using recommended inputs and compared with pressures recorded by gauges installed on the structural elements. Design equations showed good agreement for non-breaking wave pressures but underestimated peak pressures for breaking waves. Likewise, force integrations of measured pressures on the experimental specimen indicated that design equations may underestimate loads due to waves that break offshore and propagate across a beach as a turbulent bore. The time-integrated pressure impulse was shown to be less sensitive to wave characteristics than the peak recorded pressures. Time-averaged loading curves were also developed for different average periods.

On steady non-breaking downstream waves and the wave resistance – Stokes’ method

In this work, we have obtained explicit analytical formulae expressing the wave resistance of a two-dimensional body in terms of geometric parameters of nonlinear downstream waves. The formulae have been constructed in the form of high-order asymptotic expansions in powers of the wave amplitude with coefficients depending on the mean depth. To obtain these expansions, the second Stokes method has been used. The analysis represents the next step of the research carried out in Maklakov & Petrov (J. Fluid Mech., vol. 776, 2015, pp. 290–315), where the properties of the waves have been computed by a numerical method of integral equations. In the present work, we have derived a quadratic system of equations with respect to the coefficients of the second Stokes method and developed an effective computer algorithm for solving the system. Comparison with previous numerical results obtained by the method of integral equations has been made.

Localization for spatial–spectral implementations of 1D Analytic Boussinesq equations

Accurate simulations of waves in oceanic and coastal areas should take dispersive effects over a large range of frequencies into account in the relevant order of nonlinearity of the equation. Taking the exact Hamiltonian–Boussinesq formulation of surface waves as starting point, a fully Hamiltonian consistent spatial–spectral approximation of the kinetic energy leads to a model that has exact dispersion above constant depth and can deal with arbitrary depth, for nonlinearity in second, third and fourth order of the surface elevation (Kurnia and van Groesen, 2014). In this paper we describe and show with simulations of various 1D cases of breaking and non-breaking waves how localized effects of partially or fully reflective walls, run-up on a coast and the dam-break problem can be dealt with in the implementation with global Fourier integral operators; a dynamic or post-processing step will show the interior flow properties.

Prediction of scour depth at breakwaters due to non-breaking waves using machine learning approaches

Coastal structures may cease to function properly due to seabed scouring. Hence, prediction of the maximum scour depth is of great importance for the protection of these structures. Since scour is the result of a complicated interaction between structure, sediment, and incoming waves, empirical equations are not as accurate as machine learning schemes, which are being widely employed for the coastal engineering modeling. In this paper, which can be regarded as an extension of Pourzangbar et al. (2016), two soft computing methods, a support vector regression (SVR), and a model tree algorithm (M5′), have been implemented to predict the maximum scour depth due to non-breaking waves. The models predict the relative scour depth (Smax/H0) on the basis of the following variables: relative water depth at the toe of the breakwater (htoe/L0), Shields parameter (θ), non-breaking wave steepness (H0/L0), and reflection coefficient (Cr). 95 laboratory data points, extracted from dedicated experimental studies, have been used for developing the models, whose performances have been assessed on the basis of statistical parameters. The results suggest that all of the developed models predict the maximum scour depth with high precision, the M5′ model performed marginally better than the SVR model and also allowed to define a set of transparent and physically sound relationships. Such relationships, which are in good agreement with the existing empirical findings, show that the relative scour depth is mainly affected by wave reflection.

Propagation of 3D nonlinear waves over an elliptical mound with a High-Order Spectral method

The scattering of nonlinear and non-breaking surface gravity waves propagating over a three-dimensional varying bathymetry is considered in this paper. In a recent study (Gouin et al., 2016) two numerical schemes for propagating waves over a variable bottom in an existing High-Order Spectral (HOS) model have been introduced. Both the computational effort and the accuracy of the model were shown to be conserved with the introduction of these new schemes. Moreover, they have been extensively validated in 2D, but the propagation of regular and irregular waves over 3D varying bottoms remains to be addressed with such spectral methods. In this paper, the three-dimensional formalism is introduced as well as the practical implementation of 3D configurations. Then the method is applied to a three-dimensional varying bathymetry consisting of an elliptical lens, as used in the Vincent and Briggs (1989) experiment. Incident waves passing across the lens are transformed and a strong convergence region is observed after the elliptical mound. The wave amplification depends on the incident wave. Numerical results for regular waves, unidirectional and directional irregular waves are analysed and compared with experimental data, demonstrating the efficiency and practical applicability of the present approach to treat the nonlinear propagation of various sea states over a varying bathymetry.

Prediction of non-breaking wave induced scour depth at the trunk section of breakwaters using Genetic Programming and Artificial Neural Networks

Scour may act as a threat to coastal structures stability and reduce their functionality. Thus, protection against scour can guarantee these structures’ intended performance, which can be achieved by the accurate prediction of the maximum scour depth. Since the hydrodynamics of scour is very complex, existing formulas cannot produce good predictions. Therefore, in this paper, Genetic Programming (GP) and Artificial Neural Networks (ANNs) have been used to predict the maximum scour depth at breakwaters due to non-breaking waves (Smax/Hnb). The models have been built using the relative water depth at the toe (htoe/Lnb), the Shields parameter (θ), the non-breaking wave steepness (Hnb/Lnb), and the reflection coefficient (Cr), where in the case of irregular waves, Hnb=Hrms, Tnb=Tpeak and Lnb is the wavelength associated with the peak period (Lnb=Lp). 95 experimental datasets gathered from published literature on small-scale experiments have been used to develop the GP and ANNs models. The results indicate that the developed models perform significantly better than the empirical formulas derived from the mentioned experiments. The GP model is to be preferred, because it performed marginally better than the ANNs model and also produced an accurate and physically-sound equation for the prediction of the maximum scour depth. Furthermore, the average percentage change (APC) of input parameters in the GP and ANNs models shows that the maximum scour depth dependence on the reflection coefficient is larger than that of other input parameters.

Energy transfer due to shoaling and decomposition of breaking and non-breaking waves over a submerged bar

ABSTRACTWave propagation over a submerged bar is simulated using the open source CFD model REEF3D with various incident wave heights to study shoaling, wave breaking features and the process of wave decomposition into higher harmonics for relatively long waves of kd=0.52. The computed free surface elevations are compared with experimental data and good agreement is obtained for both non-breaking and spilling breaking waves for both the wave phase and free surface elevation, which has been difficult to obtain in current literature. The differences in the mode of wave shoaling over the weather side slope and the wave decomposition over the lee side slope of the submerged bar are discussed. The evolution of spilling breakers and plunging breakers over the bar crest is also studied. It is found that the free surface elevation continuously increases due to shoaling in the case of non-breaking waves, whereas breaking waves propagate with much lower free surface elevations after breaking over the bar crest. The power spectra of the free surface elevations at various locations indicate that the wave energy in the fundamental frequency is reduced by 76 for the non-breaking wave with kA=0.015 and by about 90 in other cases with higher incident wave heights with kA=0.023−0.034 due to energy dissipation and energy transfer to higher harmonic components as the wave propagates over the submerged bar.

Intrawave sand suspension in the shoaling and surf zone of a field‐scale laboratory beach

AbstractShort‐wave sand transport in morphodynamic models is often based solely on the near‐bed wave‐orbital motion, thereby neglecting the effect of ripple‐induced and surface‐induced turbulence on sand transport processes. Here sand stirring was studied using measurements of the wave‐orbital motion, turbulence, ripple characteristics, and sand concentration collected on a field‐scale laboratory beach under conditions ranging from irregular nonbreaking waves above vortex ripples to plunging waves and bores above subdued bed forms. Turbulence and sand concentration were analyzed as individual events and in a wave phase‐averaged sense. The fraction of turbulence events related to suspension events is relatively high (∼50%), especially beneath plunging waves. Beneath nonbreaking waves with vortex ripples, the sand concentration close to the bed peaks right after the maximum positive wave‐orbital motion and shows a marked phase lag in the vertical, although the peak in concentration at higher elevations does not shift to beyond the positive to negative flow reversal. Under plunging waves, concentration peaks beneath the wavefront without any notable phase lags in the vertical. In the inner‐surf zone (bores), the sand concentration remains phase coupled to positive wave‐orbital motion, but the concentration decreases with distance toward the shoreline. On the whole, our observations demonstrate that the wave‐driven suspended load transport is onshore and largest beneath plunging waves, while it is small and can also be offshore beneath shoaling waves. To accurately predict wave‐driven sand transport in morphodynamic models, the effect of surface‐induced turbulence beneath plunging waves should thus be included.

Impacts on a storm wall caused by non-breaking waves overtopping a smooth dike slope

Will coastal towns survive the rising pressure, or better, the rising sea level in future decades? Waves overtop dikes, and the overtopping flow on the crest of the dike can cause damage. Wave impacts from these overtopping flows already became of interest in coastal engineering the past few years, but very little literature and almost no design formulae are available yet for irregular waves. This paper gives such design formulae for practical use. Experimental modeling at three different scales (small, middle and large scale) has been carried out to measure such impacts. The tested geometry was a smooth sloping dike (only non-breaking waves) with a promenade at crest level and a storm wall at the end of this promenade.The outcome of this paper are three methodologies to a) calculate wave impact forces on such a storm wall as a function of the hydraulic parameters; b) determine the (Weibull) distribution of all impacts in one test, with the shape and scale parameters also linked to the hydraulic parameters; and c) to provide an indirect approach to calculate the impact forces on the storm wall. In this last approach, the (distribution of the) individual overtopping waves are linked to the (distribution of the) overtopping flow parameters, which are then linked to the (distribution of the) impact forces.Finally, the empirical formulae from the aforementioned three methodologies are compared; analogies and differences are discussed, and guidance is provided to design storm walls against post overtopping impact forces.Results show that forces from waves overtopping the dikes are in the order of 20 to 40kN/m prototype scale in the dimensionless freeboard (Rc/Hm0) range of 1 to 2. This is (much) lower compared to impact forces on vertical walls as calculated by the Shore Protection Manual.

Coherent motions and time scales that control heat and mass transfer at wind-swept water surfaces

Forecast of the heat and chemical budgets of lakes, rivers and oceans requires improved predictive understanding of air-water interfacial transfer coefficients. Here we present laboratory observations of the coherent motions that occupy the air-water interface at wind speeds (U10) 1.1 to 8.9 m/s. Spatio-temporal near-surface velocity data and interfacial renewal data are made available by a novel flow tracer method. The relative activity, velocity scales and time scales of the various coherent interfacial motions are measured, namely for Langmuir circulations, streamwise streaks, non-breaking wind waves, parasitic capillary waves, non-turbulent breaking wind waves, and turbulence-generating breaking wind waves. Breaking waves exhibit a sudden jump in streamwise interfacial velocity wherein the velocity jumps up to exceed the wave celerity and destroys nearby parasitic capillary waves. Four distinct hydrodynamic regimes are found to exist between U10 = 0 and 8.9 m/s, each with a unique population balance of the various coherent motions. The velocity scales, time scales and population balance of the different coherent motions are input to a first-principles gas transfer model to explain the waterside transfer coefficient (kw) as well as experimental patterns of temperature and gas concentration. The model mixes concepts from surface renewal and divergence theories, and requires surface divergence strength (β), the Lagrangian residence time inside the upwelling zone (tLu), and the total lifetime of new interface before it is downwelled (tLT). The model's output agrees with time-averaged measurements kw, patterns of temperature in infrared photographs, and spatial patterns of gas concentration and kw from direct numerical simulations. Several non-dimensional parameters, e.g. βtLu and τstLT where τs is the interfacial shear rate, determine the effectiveness of a particular type of coherent motion for affecting kw. This article is protected by copyright. All rights reserved.

Investigation of breaking and non-breaking solitary waves and measurements of swash zone dynamics on a 5° beach

This study presents an experimental investigation of plunging breakers on a sloping beach with an inclination of 5.1°. The incident waves are solitary waves with various amplitudes from non-breaking waves to plunging breakers, and the area investigated is the swash zone. PIV (Particle Image Velocimetry) is performed on images captured at four different field of views (FOV). Shoreline position and maximum runup are measured, and are repeatable in both time and height, although cross-sectional variations of the shoreline shape are observed at maximum runup. For non-breaking waves the runup and fluid flow is computed by a boundary integral technique combined with a boundary layer model. Then, there is excellent agreement between the experimental and the computed velocity profiles at the lower region of the beach, while the boundary integral technique overpredicts the maximum runup height severely. For breaking waves the experiments indicate that the motion becomes more irregular as we move further up the beach. In addition, there are more irregularities present for waves with larger amplitude. Length and velocity of air bubbles entrapped by the plunging breakers are extracted from an image series captured with a large FOV. The images showed that a large air bubble remains intact for a time period during runup for the breaking waves.

Modelling of liquid sloshing using CLSVOF method and very large eddy simulation

Two interface capturing methods, the volume of fluid (VOF) and the coupled level set (LS) and VOF (CLSVOF), coupled with four turbulence modelling strategies, laminar flow assumption, RANS k–ε model, very large eddy simulation (VLES) and large eddy simulation (LES), are employed to simulate sloshing flows in a rectangular tank. The new VLES model is developed in this paper to overcome some of the apparent deficiencies of RANS and LES. The CLSVOF method, which combined the LS and VOF methods, was proposed by Sussman and Puckett. Two filling levels, 18.3% and 43.7%, are considered in the present analysis. Some complicated sloshing phenomena, including the plunging wave breaking, wave impact on the sidewall and the roof and the beating phenomenon can be observed in the present sloshing cases. The computational velocity fields, wave profiles and pressure data are compared with experimental results from Delorme and Souto–Iglesias. It must be emphasized that the analysis of the velocity amplitude and the free surface evolution are mainly focused on non-breaking wave and violent breaking wave, respectively. The specific objectives are: to evaluate the performance of the CLSVOF method and VLES model for modelling of liquid sloshing; (ii) to investigate the influence of interface capturing method and turbulence model on sloshing simulation results. This study will demonstrate that, contrary to the commonly held view, turbulence modelling and free surface tracking in violent and non–violent sloshing simulation play a dominant role and a secondary role, respectively.