Breaking Solitary Wave Research Articles

A numerical model for solitary wave breaking based on the phase-field lattice Boltzmann method

This study presents a numerical investigation of a solitary wave breaking over a slope by using the phase-field lattice Boltzmann method. The incompressible two-phase flow equations are solved by using a velocity-based formulation of the two-phase lattice Boltzmann method with a central-moment collision model to accurately simulate wave breaking problems. For interface capture, a phase-field lattice Boltzmann method that ensures mass conservation is employed. The validity of the proposed method is confirmed through solitary wave propagation and transformation problems, and the obtained results are in good agreement with the experimental and calculated results. The proposed method is then employed to analyze wave breaking on a slope, demonstrating strong concordance with experimental data and existing computational findings. By analyzing the instantaneous flow characteristics and the temporal evolution of the variation in kinetic, potential, and total energy from deep to shallow water, the model can reveal the macroscopic characteristics of solitary wave breaking. Because the phase-field model effectively simulates wave breaking and air entrainment, it can depict wave energy dissipation more accurately than the single-phase lattice Boltzmann method with free surface tracking.

Effects of solitary wave breaking on the hydrodynamic performance of a submerged horizontal plate: A physical modeling study

A series of physical model tests were conducted to investigate the solitary wave control performance of a submerged horizontal plate (SHP). Hydrodynamic coefficients were analyzed for a wide range of SHP specifications, placement conditions, and dimensionless factors. Three wave breaking types on the SHP were identified: non-breaking, collapsing breaker, and plunging breaker. Their correlation with modified wave breaking classification parameters and dimensionless factors was investigated. Indirect reflected waves resulting from backflow were found to take precedence over direct reflected waves generated by the fluid resistance of the SHP. The dissipation coefficient increased as the friction and shoaling effects of the SHP, along with the nonlinearity of the solitary wave, grew more pronounced. The indirect reflection coefficient and the transmission coefficient exhibited an inverse relationship. The reflection coefficient achieved its peak value, while the transmission coefficient attained its minimum value within specific ranges. Based on the modified parameters, the hydrodynamic coefficients exhibited similar distributions. The modified surf-similarity parameter was found to be more suitable for classifying wave breaking types and predicting dissipation coefficients than the other two parameters. These experimental results can be utilized as foundational data for the optimal design of SHPs in controlling solitary waves.

A Three-Dimensional Fully-Coupled Fluid-Structure Model for Tsunami Loading on Coastal Bridges

A three-dimensional (3D) fully-coupled fluid-structure model has been developed in this study to calculate the impact force of tsunamis on a flexible structure considering fluid-structure interactions. The propagation of a tsunami is simulated by solving the 3D Navier–Stokes equations using a finite volume method with the volume-of-fluid technique. The structure motion under the tsunami impact force is simulated by solving the motion equation using the generalized alpha method. The structure motion is fed back into the fluid solver via a technique that combines a sharp-interface immersed boundary method with the cut-cell method. The flow model predicts accurate impact forces of dam-break flows on rigid blocks in three experimental cases. The fully coupled 3D flow-structure model is tested with experiments on a large-scale (1:5) model bridge under nonbreaking and breaking solitary waves. The simulated wave propagation and structure restoring forces generally agree well with the measured data. Then, the fully-coupled fluid-structure model is compared with an uncoupled model and applied to assess the effect of flexibility on structure responses to tsunami loading, showing that the restoring force highly depends on the dynamic characteristics of the structure and the feedback coupling between fluid and structure. The maximum hydrodynamic and restoring forces decrease with increasing structure flexibility.

Vertical Mixing in The Onshore Region of The Northwestern Maluku Sea, Indonesia

Spatio-temporal dynamics of vertical mixing in the northwestern Maluku Sea were quantified using the Thorpe Method from archived CTD datasets collected during the expedition of Baruna Jaya VIII RCO-LIPI on November 12–13, 2000. The turbulent kinetic energy (TKE) dissipation rate and vertical eddy diffusivity values inspected the variability of mixing properties. Higher values for both parameters were found at the shallower bathymetry, which is less than 1000 m deep. This suggests that the water column is vertically unstable as a result of being often subjected to internal solitary wave (ISW) breaking events. The strong temporal variability observed from the density profile also indicated a strong impact on internal tide activity. There was temporal fluctuation of the TKE dissipation rate as well as vertical eddy diffusivity values following semidiurnal periodicity, with typical variability up to one order of magnitude for both the dissipation and diffusivity. The range of fluctuation is [6.8×10-8 ? 9.3×10-7] W kg-1 and [1.5×10-5 – 5.4×10-3] m2s-1, respectively in the upper 200 m depth. This water generated a high dissipation rate and vertical diffusivity when regularly exposed to internal solitary waves breaking from the Lifamatola Passage.Keywords: mixing properties, CTD data, turbulent kinetic energy, vertical eddy diffusivity

The combined KdV-mKdV equation: Bilinear approach and rational solutions with free multi-parameters

In this paper, we investigate the combined KdV-mKdV equation which serves as a valuable tool in the study of water waves, enabling researchers to understand and predict the behaviour of various wave phenomena, including solitary waves, wave breaking, turbulence, wave-structure interactions, and tsunamis. Using the bilinear approach, its rational solutions with free multi-parameters and N-soliton solutions in the determinant form are obtained. The novel idea in this paper is that we develop the bilinear approach allowing free multi-parameters in rational solutions. The dynamics of rational solutions are presented by selecting appropriate parameters. By the bilinear approach, different to the Darboux transformation method, there are no limiting techniques involved on the spectrum parameters to obtain rational solutions. The approach can be extended to obtain other types of solutions if outside the framework of polynomials.

Numerical Simulations and an Updated Parameterization of the Breaking Internal Solitary Wave Over the Continental Shelf

AbstractThe breaking of internal solitary waves (ISWs) over slope‐shelf topography induces energy dissipation and enhances mixing. In this work, high‐resolution, laboratory‐scale simulations are employed to investigate the instability mechanisms and dissipation of ISWs. We find that the increasing nonhydrostatic pressure during deformation contributes to an adverse pressure gradient, which induces plunging flow for overturning. Shear instability and convective instabilities trigger wave breaking. Wave‐induced vortexes induce strong shearing and enhance the dissipation of energy by 1–2 orders of magnitude larger than that which occurs under stable conditions. Furthermore, based on laboratory results, we evaluate two commonly used parameterizations (Pacanowski & Philander, 1981, https://doi.org/10.1175/1520-0485(1981)011<1443:povmin>2.0.co;2, i.e., PP81; Klymak & Legg, 2010, https://doi.org/10.1016/j.ocemod.2010.02.005, i.e., KL10) in coarser‐resolution global ocean models by modifying the horizontal resolution from 100 grids every wavelength to approximately 30. The results show that PP81 and KL10 can both improve the estimation of the energy loss, but can only depict strong shear within the pycnocline and bottom boundary regions, respectively. Finally, an updated parameterization is presented that can effectively describe the strong shear in two regions during wave breaking. The flow field and dissipation are more consistent with the laboratory results using the new parameterization. This study improves the understanding of the mixing parameterizations in simulating the continuous processes of strong internal wave breaking.

PYCNOCLINE THICKNESS EFFECT ON INTERNAL WAVE BREAKING OVER A UNIFORM SLOPE

Internal waves play a significant role in the resuspension and transport of fine sediment adjacent to the sea bottom in the coastal region. Inall (2009) found the horizontal current and diffusion of mass due to the breaking of internal waves in the Fjord by using a fluorescent tracer. Internal waves have been shown to cause crucial mass transport and affect the ecological system. In particular, an internal solitary wave that progresses without changing the profile contributes to mass transport on a sloping bottom. Therefore, it is essential to clarify how an internal solitary wave breaks over a slope and transports mass. When pycnocline thickness is negligible in a twolayer fluid, an internal solitary wave breaking over a slope can be categorized into four breaker types by applying the latest classification based on wave slope, bottom slope gradient and an internal Reynolds number. Aghsaee et al. (2010) demonstrated that an internal solitary wave breaking over a slope can be categorized into four breaker types: surging, collapsing, plunging, and fission breakers using three-dimensional numerical simulations. They used wave slope and bottom slope gradient. However, some plunging and collapsing breakers were not appropriately categorized. Nakayama et al. (2019) solved the classification problem by introducing an internal Reynolds number based on the Korteweg–De Vries equation. However, it remains unsolved if this classification can categorize the breaking of an internal solitary wave under thick pycnocline conditions. This study uses numerical simulations to investigate the applicability of the classification under changing pycnocline thickness (Nakayama et al., 2021).

Wave propagation and evolution in a (1+1)-dimensional spatial-temporal domain: A comprehensive study

In this investigation, we utilize two recent analytical schemes to unveil novel solitary wave solutions for the [Formula: see text]-dimensional Mikhailov–Novikov–Wang integrable equation. The said equation serves as a mathematical model that captures specific physical phenomena, albeit lacking a direct physical interpretation. Nevertheless, it finds relevance in various systems within the realm of nonlinear waves in physics. Through the application of the aforementioned analytical schemes, we derive fresh solutions and evaluate their accuracy by employing the variational iteration method. The congruence observed between the analytical and numerical solutions of the investigated model serves as validation for the constructed solutions. Furthermore, we delve into exploring the implications of obtaining precise and ground breaking solitary wave solutions on the practical applications associated with the studied model.

On Solitary Wave Breaking and Impact on a Horizontal Deck

The impact of waves and bores generated by broken solitary waves on horizontal decks of coastal structures was studied by solving the Navier–Stokes equations. Solitary waves of different amplitudes were considered, and submerged ramps were used to bring the waves to the breaking point. The horizontal fixed deck was located downwave of the ramp and placed at various elevations above and below the still-water level. The results include the surface elevation of the wave and the bore-induced horizontal and vertical forces on the deck. The results were compared with laboratory measurements and those due to the bore generated by breaking a reservoir, and a discussion is provided on the relative magnitude of the loads. It is found that breaking solitary waves and dam-break provide reasonable loading conclusions for tsunamis events.

Numerical investigation of solitary wave breaking over a slope based on multi-phase smoothed particle hydrodynamics

This study presents a numerical investigation of the solitary wave breaking over a slope by using the multi-phase smoothed particle hydrodynamics (SPH) method. Four different computational models are proposed to solve the gas-related far-field boundary conditions, and the model with the least disturbance to the internal flow field is selected. Since the artificial viscous coefficient can greatly affect the wave-breaking location, an empirical equation is fitted to quickly determine the optimal value of the artificial viscous coefficient. In addition, the turbulence model and three-dimensional effect on the wave breaking are discussed in this study. The results show that the present two-dimensional multi-phase SPH without a turbulence model can capture the macroscopic characteristics of the flow before the vortices convert to three dimensional flow structures caused by the wave breaking. Then, the processes of shoaling solitary wave breaking with different slopes and relative wave heights are simulated. Compared with the single-phase SPH, the multi-phase SPH is of great help in improving the prediction of wave breaking. A vortex similar to the Rankine Vortex is observed near the wave crest. Its intensity affects the pressure distribution of the gas, and its relative position to the wave crest is relevant to the energy transfer from the water to the gas. During the solitary wave propagating from deep water to shallow water, energy dissipation of gas and water shows four different stages. In the stage of energy dissipation, the gas can absorb the great energy from the water, which effectively dissipates the wave energy.

Numerical Simulation on Reduced Runup Height of Solitary Wave by Fixed Submerged and Floating Rectangular Obstacles

The wave runup height is one of the most important parameters for affecting the design of coastal structures such as dikes, revetments, and breakwaters. In this study, SWASH (Zijlema et al., 2011), a non-hydrostatic pressure numerical model, was used to analyze the effect of reducing The wave runup height of solitary waves by submerged and floating rectangular obstacles. It was confirmed that the SWASH model reproduces the propagation, breaking, and runup of solitary waves quite well. In addition, it was confirmed that the wave deformation of the solitary wave by submerged and floating rectangular obstacles was well reproduced. Finally, we conducted an examination of the effect of reducing the runup height of submerged and floating rectangular obstacles. Reduced runup heights are calculated and the characteristics of runup height reduction according to the dimensions of the obstacle were analyzed. The energy attenuation effect of the floating obstacle is greater than the submerged obstacle, and it is shown to be more effective in reducing the runup height.

Effects of spanwise length and side-wall boundary condition on plunging breaking waves

A systematic study of the effect of the spanwise length and the sidewall boundary condition of a numerical wave flume (NWF) on direct numerical simulation of a plunging breaking wave is performed. To deal with the topological changes of free surfaces, a high-fidelity numerical model is employed to solve the Navier–Stokes equations together with the volume of fluid function. After verification by two-dimensional (2D) simulations of a plunging breaker on a sloping beach, ten NWFs with different spanwise extents and sidewall boundary conditions are studied. Special attention is devoted to the three-dimensionality of the plunging breaker. Compared with three-dimensional (3D) models, the 2D model accurately reproduces the dynamics of a breaking solitary wave in the early stage, but it is inadequate for the study of the post-breaking process. For a 3D NWF with nonslip sidewall boundary condition, the wave domain can be divided into two regions with different physical properties. In the near-wall region, the nonslip boundary condition on the sidewall plays a crucial role in the wave hydrodynamics, while in the central region, the properties of the breaking wave are similar to those for the periodic boundary condition, which provide a closer representation of the real sea environment. The spanwise length of the NWF plays only a minor role in simulations under the periodic boundary condition. Furthermore, lateral boundaries and spanwise length show more influences on a plunging breaker with larger incident wave steepness. This study provides valuable support for the design of numerical simulations of wave breaking.

Large-Amplitude Internal Wave Transformation into Shallow Water

Abstract Large-amplitude internal solitary wave (ISW) shoaling, breaking, and run-up was tracked continuously by a dense and rapidly sampling array spanning depths from 500 m to shore near Dongsha Atoll in the South China Sea. Incident ISW amplitudes ranged between 78 and 146 m with propagation speeds between 1.40 and 2.38 m s−1. The ratio between wave amplitude and a critical amplitude A0 controlled breaking type and was related to wave speed cp and depth. Fissioning ISWs generated larger trailing elevation waves when the thermocline was deep and evolved into onshore propagating bores in depths near 100 m. Collapsing ISWs contained significant mixing and little upslope bore propagation. Bores contained significant onshore near-bottom kinetic and potential energy flux and significant offshore rundown and relaxation phases before and after the bore front passage, respectively. Bores on the shallow forereef drove bottom temperature variation in excess of 10°C and near-bottom cross-shore currents in excess of 0.4 m s−1. Bores decelerated upslope, consistent with upslope two-layer gravity current theory, though run-up extent Xr was offshore of the predicted gravity current location. Background stratification affected the bore run-up, with Xr farther offshore when the Korteweg–de Vries nonlinearity coefficient α was negative. Fronts associated with the shoaling local internal tide, but equal in magnitude to the soliton-generated bores, were observed onshore of 20-m depth.

Numerical Simulation of Solitary Waves Propagating on Stepped Slopes Beaches

The objective of the current paper is to study the propagating and breaking of solitary waves on stepped slopes beaches, to simulate the shoaling and breaking, specifically the location of breaking point Xb, and solitary wave height at breaking Hb of solitary waves on the different stepped slopes. Ansys Fluent is used to implement the simulation, a two-dimensional volume of fluid (VOF) which is based on the Reynolds-Averaged Navier–Stokes (RANS) equations and the k–ε turbulence closure solver. The obtained results were firstly validated with existing empirical formulas for solitary wave run-up on the slope without stepped structure and are compared with the experimental and numerical results. The numerical computation has been carried out for several, configurations of beach slopes with tan ß= 1:15, 1:20, 1:25, wave height H0= 0.04, 0.06, 0.08m, water depth h0= 0.15, 0.2, 0.25m, and step height Sh= 0.025, 0.05, 0.075m. A set of numerical simulations were implemented to analyze shoaling and breaking of solitary waves, wave reflection, wave transmission, and wave run-up with various parameters wave heights, water depth, beach slopes, and Sh step height.

Breaking Solitary Waves Run-Up on the Inclined Beach

Breaking Solitary Waves Run-Up on the Inclined Beach

WITHDRAWN: A two-phase flow numerical modeling of plunging breaking solitary waves using artificial slope variation

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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.

On the evolution and runup of a train of solitary waves on a uniform beach

In this paper the runup of a train of successive solitary waves is studied. Using a wavemaker with 5-m stroke, a series of evenly-spaced solitary waves, up to nine, is generated in a wave flume. These solitary waves shoal and run up on a 1 on 10 slope. The nonlinearity parameter, i.e., the wave height to water depth ratio, ranges between 0.11 and 0.39. The experimental data show that the runup heights of successive solitary waves reach an asymptotic value after the fourth wave in all cases studied. Depending on the nonlinearity, the runup characteristics can be categorized as either weakly or strongly interacting cases. For the former the runup heights of the successive waves are almost identical to that of a single solitary wave. For the latter, the asymptotic runup value is always lower than that of the first wave. Using the experimental data, two- and three-dimensional Reynolds-Averaged Navier-Stokes equations models are first validated with a high degree of accordance. Additional numerical simulations are performed to extend the experimental database and investigate effects of beach slopes and higher wave nonlinearity values. Finally, using both numerical results and the laboratory data, the unified empirical runup formula for single breaking solitary waves and breaking periodic waves is found applicable to obtain the maximum runup height of successive solitary waves.

Laboratory investigation of turbulent dissipation in an internal solitary wave breaking over a submerged Gaussian ridge

Laboratory experiments were conducted to investigate an internal solitary wave breaking over a submerged Gaussian ridge. Particle image velocimetry (PIV) was performed with a high-speed camera to analyze the macro- and microstructures of wave-breaking evolution and subsequent induced turbulence and mixing. Four types of wave breaking, namely, plunging breaking, collapsing breaking, plunging-collapsing breaking, and surging breaking, were identified, along with their different evolutionary processes and breaking mechanisms. The turbulent dissipation rates estimated from the PIV results were on the order of 10−6 to 10−4 m2/s3 during the breaking, with the smallest values in the plunging breaking and the largest in surging breaking. Generally, the intensity of turbulence in plunging breakers seems to be insensitive to the changing wave slope; however, the surging breaker shows an opposite trend.

Sliding-wave acceleration of ions in high-density gas jet targets.

A hybrid mechanism of ion acceleration is investigated which demonstrates the higher spectral density of protons at high energies. The interaction of few-cycle terrawatt laser pulses with near-critical density gas target is studied with the help of two-dimensional particle-in-cell simulation. The generation of few MeV protons with high spectral concentration near cutoff is attributed to the propagation of solitary waves in the decaying density profile of the gas jet. Plasma dynamics at longer time scale is explained by semianalytical modeling and conditions for solitary wave breaking are presented.