Deep-water Waves Research Articles

Beach narrowing on prograding coasts: Examples from the tropics to subtropics of eastern Australia

Subtropical to tropical sandy beaches are subject to a wide variety of processes that influence shoreline position, though they receive little research attention compared to temperate coastlines. This presents challenges to understanding the drivers of long-term coastal change, particularly in places like the sub/tropical margins of Australia, where there are significant differences in local to regional geologic, oceanographic, and climatic conditions. Here, we investigate changes in beach planform morphology for a number of beaches in Queensland, Australia, over a period of up to 90 years using high resolution (0.5–5 m pixel size) aerial photographs. In total, 945 images were orthorectified and bounding features for the subaerial beach (high water and dune vegetation lines) were digitised to extract shoreline change statistics for 15 beaches ranging from the tropics to subtropics, between 15°S and 28°S. Three beach types were identified, defined based on lateral boundary features and the scale of shoreline/beach width variability. These include low variability beaches with two bounding rocky headlands (type 1); beaches with one headland and one river boundary, with the most significant shoreline adjustment away from the headland (type 2); and highly variable beaches with two river boundaries (type 3). Our change analysis demonstrates overall seaward displacement of the high water and vegetation lines, but also net losses in beach width due to fast rates of seaward vegetation advance in a tropical setting. These changes are largely consistent along this coastline, despite differences in exposure to deep-water waves and large variation in tidal ranges. Long-term accretion persists here despite rising sea levels over the past century. This result suggests a long-term net positive sediment budget along this section of the coast that is likely a reflection of global adjustments to tropical climate, and associated increases in terrestrial sediment generation and dune vegetation growth rates. Overall, this study provides insights into a variety of coastal settings through the subtropics and tropics and highlights the importance of tracking change along both the landward and seaward edges of the subaerial beach, regardless of exposure and associated wave regimes.

Estimation of Wave-Breaking Index by Learning Nonlinear Relation Using Multilayer Neural Network

Estimating wave-breaking indexes such as wave height and water depth is essential to understanding the location and scale of the breaking wave. Therefore, numerous wave-flume laboratory experiments have been conducted to develop empirical wave-breaking formulas. However, the nonlinearity between the parameters has not been fully incorporated into the empirical equations. Thus, this study proposes a multilayer neural network utilizing the nonlinear activation function and backpropagation to extract nonlinear relationships. Existing laboratory experiment data for the monochromatic regular wave are used to train the proposed network. Specifically, the bottom slope, deep-water wave height and wave period are plugged in as the input values that simultaneously estimate the breaking-wave height and wave-breaking location. Typical empirical equations employ deep-water wave height and length as input variables to predict the breaking-wave height and water depth. A newly proposed model directly utilizes breaking-wave height and water depth without nondimensionalization. Thus, the applicability can be significantly improved. The estimated wave-breaking index is statistically verified using the bias, root-mean-square errors, and Pearson correlation coefficient. The performance of the proposed model is better than existing breaking-wave-index formulas as well as having robust applicability to laboratory experiment conditions, such as wave condition, bottom slope, and experimental scale.

A universal bifurcation mechanism arising from progressive hydroelastic waves

A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic nonlinearities, is an extension of the famous Whitham equation. The coefficients of the nonlinear terms are chosen to match with the key properties of the full Euler equations, precisely, the associated cubic nonlinear Schrödinger equation and the amplitude of the solitary wave at the bifurcation point. It is shown that the supercritical bifurcation, rich with Stokes, solitary, generalized solitary, and dark solitary waves in the vicinity of the phase speed minimum, is a universal bifurcation mechanism. The newly developed model can capture the essential features near the bifurcation point and easily be generalized to other nonlinear wave problems in hydrodynamics.

A combined approach to cliff characterization: Cliff Stability index

In this work, a combined multidisciplinary method to characterize coastal cliff environments is presented. It combined two complementary approaches – engineering and geomorphological. The first one is represented by the wave power values along the cliff face. For that purpose, the deep-water wave climate is statistically characterized, and high-energy sea states are numerically propagated to the cliff with a state-of-the-art model. The variations in wave power at the cliff face are controlled by the varying cliff orientation and by the irregular morphology, which influences wave propagation through refraction and shoaling processes. Based on wave power, four engineering exposure levels, from low to extreme, are defined and mapped onto the cliff. The geomorphological approach is based on an index developed ad hoc for this work, the Cliff Stability (CS) index, which takes into account the cliff geometry, lithology, structure and degradation state, as well as the hydrological conditions. Based on the CS index, four geomorphological exposure levels are defined and mapped, from low to extreme. The combined approach is shown through the application to a study site in NW Spain. The two perspectives, engineering and geomorphological, are found to yield similar results in some sections of the study area, but not all. It may be inferred that, despite the importance of wave action in shaping the cliff, the additional elements included in the CS index also play a significant role. In practical terms, the significance of these results is that the two approaches, engineering and geomorphological, should be combined to properly characterize coastal cliffs. This combined approach represents a multidisciplinary tool to define and characterize the exposure levels and, thus, prevent damages in cliff environments across the world.

Modulation Instability of Hydro-Elastic Waves Blown by a Wind with a Uniform Vertical Profile

An interesting physical phenomenon was recently observed when a fresh-water basin is covered by a thin ice film that has properties similar to the property of a rubber membrane. Surface waves can be generated under the action of wind on the air–water interface that contains an ice film. The modulation property of hydro-elastic waves (HEWs) in deep water covered by thin ice film blown by the wind with a uniform vertical profile is studied here in terms of the airflow velocity versus wavenumber. The modulation instability of HEWs is studied through the analysis of coefficients of the nonlinear Schrödinger (NLS) equation with the help of the Lighthill criterion. The NLS equation is derived using the multiple scale method in the presence of airflow. It is demonstrated that the potentially unstable hydro-elastic waves with negative energy appear for relatively small wind speeds, whereas the Kelvin–Helmholtz instability arises when the wind speed becomes fairly strong. Estimates of parameters of modulated waves for the typical conditions are given.

Lump-periodic, some interaction phenomena and breather wave solutions to the (2+1)-rth dispersionless Dym equation

In this study, we successfully apply Hirota’s bilinear method (HBM) to retrieve the different wave structures of the general [Formula: see text]th dispersionless Dym equation by considering the test function approaches. The studied model is used to describe the dynamics of deep water waves. We formally retrieve some novel lump periodic, some other new interaction, and breather wave solutions. Moreover, the physical behavior of the reported results is sketched through several three-dimensional, two-dimensional and contour profiles with the assistance of suitable parameters. The acquired results are valuable in grasping the elementary scenarios of nonlinear fluid dynamics as well as the dynamics of engineering sciences in the related nonlinear higher-dimensional wave fields. The gained results are checked and found correct by putting them into the governing equation with the aid of Mathematica. Thus, our strategies through the fortress of representative calculations give a functioning and intense mathematical execution for tackling complicated nonlinear wave issues.

A new spectral parameter to predict dominant wave breaking based on the JONSWAP spectrum

Finding a robust and universal diagnostic parameter that determines the onset of deep-water breaking and its strength has been challenging in wave breaking research. In this paper, a new diagnostic parameter (wave-breaking spectral parameter, WSP) is defined based on the significant steepness of the spectral peak ϵp that was initially proposed by Banner et al. (2000) and Babanin et al. (2001). In addition, the WSP formula contains the spectral peakedness parameter Qp and spectral width ν for taking into account the effect of spectral shape on the value of breaking threshold. To derive the WSP formula and verify the prediction ability of this diagnostic parameter, multiple wave types including nonbreaking waves, critical waves, and single and multiple breaking wave trains were generated in our experiments. The wave trains were generated using a linear focusing theory with components following the JONSWAP distribution. Results show that the threshold value of the new WSP, which distinguishes single and multiple breaking events from non-breaking waves, is found to be 0.042. Furthermore, WSP is used in isolated deep-water spilling breaking packets, and its prediction accuracy is compared with that of the kinematic criterion parameter Bx. The results show that WSP has advantages in predicting the onset of wave breaking, especially for non-sharp wave conditions. Finally, the spatial variation of the total loss rate of the wave energy flux ΔFbrE¯¯ΔFbE¯¯ in deep-water unsteady breaking waves was investigated. It was found that the new WSP has a strong linear correlation with the total loss rate of the wave energy flux. Considering that WSP can be mathematically expressed directly using the spectrum, WSP will be parameterized into the dissipation term of the spectral wind-wave model in our future work. It is expected that the calculation accuracy of the dissipation term will be improved, and the wave model's prediction accuracy of wave parameters will be enhanced because WSP provides a reliable wave-breaking threshold value and has a strong linear relationship with the dissipation rate.

Preliminary Results of Modelling Simulation for High-resolution Hydrodynamic Fields for Central Vietnam's Water

This paper presents the development of hydrodynamic simulation models (waves, currents) for the Vietnam East Sea and nestingto coastal area (applied in the coastal area of ​​Phu Yen province). The COAWST modeling system has been used. This is an open source system which supports optimal parallel calculation and allows solving large-scale simulation problems. The model has been calibrated and verified by deep water wave data at the stations of Bach Long Vi, Con Co, Phu Quy and Phu Quoc for good results. Along with that, with the goal of having high resolution for the central Vietnam water, the model has been set up with coastal wave data in Phu Yen for very good results, the correlation coefficient between calculation and measurement is up to 0.95. The results of the current field, surface temperature from the model of the ocean shows the similarity with the verification data, especially simulating the typical rising water phenomenon in Ninh Thuan - Binh Thuan area. However, some stages have complicated movements, the model has not been closely simulated, for example in the area of Phu Quy island.

Emergence of Solitons from Irregular Waves in Deep Water

Numerical simulations were performed to study the long-distance evolution of irregular waves in deep water. It was observed that some solitons, which are the theoretical solutions of the nonlinear Schrödinger equation, emerged spontaneously as irregular wave trains propagated in deep water. The solitons propagated approximately at a speed of the linear group velocity. All the solitons had a relatively large amplitude and one detected soliton’s height was two times larger than the significant wave height of the wave train, therefore satisfying the rogue wave definition. The numerical results showed that solitons can persist for a long distance, reaching about 65 times the peak wavelength. By analyzing the spatial variations of these solitons in both time and spectral domains, it is found that the third-and higher-order resonant interactions and dispersion effects played significant roles in the formation of solitons.

Numerical Modeling of Wave Reflection from Sloped Impermeable Seawalls Using the SPH Method: Case Study of Chabahar Port

In this research, a comprehensive study is performed to investigate the interaction of regular waves with the impermeable seawall of the Chabahar port. First, a MIKE 21 SW model is used to transform the deep-water wave data to the nearshore zone. Then, the interaction of waves with the seawall is simulated using a well-known numerical smoothed particle hydrodynamics model named DualSPHysics. After validating the numerical results with the experimental data, a parametric study is performed to evaluate the effects of the wave height, wave period, and the slope of the seawall on the water level fluctuations and the wave reflection coefficient. The results showed that increasing the wave height slightly decreases the reflection coefficient. Meanwhile, a direct relationship was found between the wave height and the water level fluctuations near the wall. Generally, increasing the wave period resulted in higher reflection coefficients and water level fluctuations. Both the reflection coefficient and the water level fluctuations are greatly dependent on the slope of the seawall. Steeper slopes resulted in higher reflection coefficients and lower water level fluctuations near the seawall.

Numerical study on breaking solitary wave force on box-girder bridge

Solitary wave is often used to simulate tsunami propagating in deep water and breaking solitary wave is often used to simulate tsunami bore propagating in shallow water or on land. The breaking solitary wave force on box-girder, which has been widely used in bridge engineering in coastal areas of China, receives few attentions. This study aims to investigate characteristics and generation mechanism of breaking solitary wave force on box-girder numerically. A numerical wave flume with a 1:20 slope was built firstly, then the solitary wave generation ability, wave deformation and wave breaking on the slope, as well as wave force calculation precision, are validated. The water depth 0.6 m, the slope gradient 1:20 and the distance between slope top and box-girder 2.0 m remain unchanged, while the wave height and clearance changes in different cases. The time histories of horizontal force and vertical force on box-girder can be divided into three and four stages respectively according to their characteristics. The surface of box-girder is decomposed into a series of panels to facilitate exploring tsunami bore force generation mechanism. Results show horizontal force is dominated by static pressure on upstream vertical panels and vertical force is mainly contributed by static pressure on upstream horizontal panels and on panels in the chambers. Tsunami bore overtopping the box-girder deck impacts the top panel vigorously and results in the peak value of negative vertical force.

Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current

This paper describes a numerical investigation of ripples generated on the front face of deep-water gravity waves progressing on a vertically sheared current with the linearly changing horizontal velocity distribution, namely parasitic capillary waves with a linear shear current. A method of fully nonlinear computation using conformal mapping of the flow domain onto the lower half of a complex plane enables us to obtain highly accurate solutions for this phenomenon with the wide range of parameters. Numerical examples demonstrated that, in the presence of a linear shear current, the curvature of surface of underlying gravity waves depends on the shear strength, the wave energy can be transferred from gravity waves to capillary waves and parasitic capillary waves can be generated even if the wave amplitude is very small. In addition, it is shown that an approximate model valid for small-amplitude gravity waves in a linear shear current can reasonably well reproduce the generation of parasitic capillary waves.

The role of bandwidth in setting the breaking slope threshold of deep-water focusing wave packets

We examine the role of wave packet bandwidth in modulating the breaking slope threshold for focusing deep-water surface gravity wave packets. Using a fully nonlinear potential flow solver and laboratory experiments, we show that the slope threshold may be strongly modulated by the wave packet bandwidth. We propose a new breaking threshold parameterization that shows that the slope threshold may be modulated by more than a factor of two by changes in the bandwidth. This has implications for parameterizations of the properties of the breaking induced flow (e.g., the energy dissipation) as they do not currently account for these effects.

Formulating Wave Overtopping at Vertical and Sloping Structures with Shallow Foreshores Using Deep-Water Wave Characteristics

The state-of-The-Art formulas for mean wave overtopping (q) assessment typically require wave conditions at the toe of the structure as input. However, for structures built either on land or in very shallow water, obtaining accurate estimates of wave height and period at the structure toe often proves difficult and requires the use of either physical modeling or high-resolution numerical wave models. Here, we follow Goda's method to establish an accurate prediction methodology for both vertical and sloping structures based entirely on deep-water characteristics-where the influence of the foreshore is captured by directly incorporating the foreshore slope and the relative water depth at the structure toe (htoe/Hm0,deep). Findings show that q decreases exponentially with htoe/Hm0,deep due to the decrease of the incident wave energy; however, the rate of reduction in q decreases for structures built on land or in extremely shallow water (htoe/Hm0,deep ≤ 0.1) due to the increased influence of wave-induced setup and infragravity waves-which act as long-period fluctuations in mean water level-generated by nonlinear wave transformation over the foreshore.

On an eddy viscosity model for energetic deep-water surface gravity wave breaking

We present an investigation of the fundamental physical processes involved in deep-water gravity wave breaking. Our motivation is to identify the underlying reason causing the deficiency of the eddy viscosity breaking model (EVBM) in predicting surface elevation for strongly nonlinear waves. Owing to the limitation of experimental methods in the provision of high-resolution flow information, we propose a numerical methodology by developing an EVBM enclosed standalone fully nonlinear quasi-potential (FNP) flow model and a coupled FNP plus Navier–Stokes flow model. The numerical models were firstly verified with a wave train subject to modulational instability, then used to simulate a series of broad-banded focusing wave trains under non-, moderate- and strong-breaking conditions. A systematic analysis was carried out to investigate the discrepancies of numerical solutions produced by the two models in surface elevation and other important physical properties. It is found that EVBM predicts accurately the energy dissipated by breaking and the amplitude spectrum of free waves in terms of magnitude, but fails to capture accurately breaking induced phase shifting. The shift of phase grows with breaking intensity and is especially strong for high-wavenumber components. This is identified as a cause of the upshift of the wave dispersion relation, which increases the frequencies of large-wavenumber components. Such a variation drives large-wavenumber components to propagate at nearly the same speed, which is significantly higher than the linear dispersion levels. This suppresses the instant dispersive spreading of harmonics after the focal point, prolonging the lifespan of focused waves and expanding their propagation space.

Genesis and evolution of large-scale sediment waves in submarine canyons since the Penultimate Glacial Maximum (ca. 140 ka), northern South China Sea margin

Sediment waves are common on the seafloor, but large-scale ones developed in submarine canyons are rarely reported. In this study, we document for the first time the Quaternary deep-water canyon-confined large-scale sediment waves developed on the northern South China Sea margin based on the analysis of a high-quality 3-D seismic reflection volume combined with a 2-D multichannel seismic reflection profile and three wells. Results show that the onset of these canyon-confined large-scale sediment waves can be dated back to the Penultimate Glacial Maximum (PGM)(ca.140 ka). This was the last period for the Pearl River Delta to prograde over the shelf edge. And these sediment waves have continued to develop and migrate upslope until present. The large-scale sediment waves pertaining to the PGM have a dominant down-slope asymmetrical 2-D morphology with wavelengths of 1.059–6.090 km and wave heights of 3.3–32.5 m. The present large-scale sediment waves show an up-slope asymmetrical 2-D morphology with dimensions of 0.667–5.628 km wavelength and 2.7–14.0 m wave height, which are smaller relative to those at the PGM. Grain sizes of the sediment waves at the PGM and present are interpreted to be coarse, inferred from seismic reflection data by high amplitude reflections (HARs). After a comprehensive analysis of the types of sediment-laden flows, the sediment provenances, the seafloor topography and the features of the sediment waves, these large-scale sediment waves might be interpreted as cyclic steps generated by the down-slope flowing supercritical turbidity currents and associated internal hydraulic jumps along high gradient (approximately greater than 1.28°) canyon thalwegs characterized by numerous slope breaks. The evolution of the large-scale sediment waves from partially depositional at the PGM to erosion-dominated at the present is controlled by variations of the sediment supply and the submarine slope accommodation along the canyon thalweg, which is manifested in the co-evolution of the sediment waves with the canyon. The findings of this study tell us that in addition to axial channels and mass-transport complexes, large-scale sediment waves can also develop on the canyon floor, which helps to improve our understanding of the complex canyon processes. The ‘large-scale sediment waves’ described here may be a new potential deepwater-reservoir element for the deep-water hydrocarbon exploration associated with submarine canyons.

Spatial deterministic wave forecasting for nonlinear sea–states

We derive a simple algebraic form of the nonlinear wavenumber correction of unidirectional surface gravity waves in deep water, based on temporal measurements of the water surface and the spatial Zakharov equation. This allows us to formulate an improvement over linear deterministic wave forecasting with no additional computational cost. Our new formulation is used to forecast both synthetically generated as well as experimentally measured seas and shows marked improvements over the linear theory.

Computational Fluid Dynamics Simulation of Deep-Water Wave Instabilities Involving Wave Breaking

Abstract Instabilities of deep-water wave trains subject to initially small perturbations (which then grow exponentially) can lead to extreme waves in offshore regions. The present study focuses on the two-dimensional Benjamin–Feir (or modulational) instability and the three-dimensional crescent (or horseshoe) waves, also known as Class I and Class II instabilities, respectively. Numerical studies on Class I and Class II wave instabilities to date have been mostly limited to models founded on potential flow theory; thus, they could only properly investigate the process from initial growth of the perturbations to the initial breaking point. The present study conducts numerical simulations to investigate the generation and development of wave instabilities involving the wave breaking process. A computational fluid dynamics (CFD) model solving Reynolds-averaged Navier–Stokes (RANS) equations coupled with a turbulence closure model in terms of the Reynolds stress model is applied. Wave form evolutions, Fourier amplitudes, and the turbulence beneath the broken waves are investigated.

Laboratory studies of the role of bandwidth in surface transport and energy dissipation of deep-water breaking waves

This paper presents laboratory measurements of surface transport due to non-breaking and breaking deep-water focusing surface wave packets and examines the dependence of the transport on the wave packet bandwidth, $\varDelta$ . This extends the work of Deike et al. (J. Fluid Mech., vol. 829, 2017, pp. 364–391) and Lenain et al. (J. Fluid Mech., vol. 876, 2019, p. R1), where similar numerical and laboratory experiments were conducted, but the bandwidth was held constant. In this paper, it is shown that the transport is strongly affected by the bandwidth. A model for the horizontal length scale of the breaking region is proposed that incorporates the bandwidth, central frequency, the linear prediction of the slope at focusing and the breaking threshold slope of the wave packet. This is then evaluated with data from archived and new laboratory experiments, and agreement is found. Furthermore, the horizontal length scale of the breaking region implies modifications to the model of the energy dissipation rate from Drazen et al. (J. Fluid Mech., vol. 611, 2008, pp. 307–332). This modification accounts for differing trends in the dissipation rate caused by the bandwidth in the available laboratory data.

Three-dimensional surface gravity waves of a broad bandwidth on deep water

A new nonlinear Schrödinger equation (NLSE) is presented for ocean surface waves. Earlier derivations of NLSEs that describe the evolution of deep-water waves have been limited to a narrow bandwidth, for which the bound waves at second order in wave steepness are described in leading-order approximations. This work generalizes these earlier works to allow for deep-water waves of a broad bandwidth with large directional spreading. The new NLSE permits simple numerical implementations and can be extended in a straightforward manner in order to account for waves on water of finite depth. For the description of second-order waves, this paper proposes a semianalytical approach that can provide accurate and computationally efficient predictions. With a leading-order approximation to the new NLSE, the instability region and energy growth rate of Stokes waves are investigated. Compared with the exact results based on McLean (J. Fluid Mech., vol. 511, 1982, p. 135), predictions by the new NLSE show better agreement than by Trulsen et al. (Phys. Fluids, vol. 12, 2000, pp. 2432–2437). With numerical implementations of the new NLSE, the effects of wave directionality are investigated by examining the evolution of a directionally spread focused wave group. A downward shift of the spectral peak is observed, owing to the asymmetry in the change rate of energy in a more complex manner than that for uniform Stokes waves. Rapid oblique energy transfers near the group at linear focus are observed, likely arising from the instability of uniform Stokes waves appearing in a narrow spectrum subject to oblique sideband disturbances.