Boussinesq Wave Research Articles

2DH Numerical Study of Solitary Wave Processes around an Idealized Reef-Fringed Island

In order to better understand the role of coral reefs around an isolated island in mitigating tsunami hazards, this study performed a horizontally two-dimensional (2DH) numerical study of tsunami-like solitary wave propagation and run-up around an idealized reef-fringed island. The shock-capturing Boussinesq wave model, the FUNWAVE-TVD is used in the present study and well-validated with existing experimental data for its robustness in predicting 2DH solitary wave processes around an island. Based on the validated model, the typical solitary propagation process around the reef-fringed island and the effects of morphological and hydrodynamic parameters on the maximum run-up heights were systematically investigated. It is found that coral reefs can effectively reduce maximum run-up heights around an isolated island. The reef flat’s water depth, reef flat width, and reef surface roughness are the main factors affecting maximum run-up heights around an island, while the fore-reef slope has little impact. For the idealized reef-fringed island in this study, sea-level rise will cause coral reefs to lose their protective capability on the lee side, and the presence of coral reefs may even enhance tsunami hazards around an island when the reef flat width is very narrow or coral bleaching happens.

A wave-resolving modeling study of rip current variability, rip hazard, and swimmer escape strategies on an embayed beach

Abstract. Drownings due to rip currents are a major threat to beach safety. In this study a high-resolution Boussinesq model with a modified wave-resolving Lagrangian tracking module has been applied to a 2 km long embayed beach, Dadonghai of Sanya, Hainan Island, with the purpose of studying rip current variability, real-time rip hazard identification, and the optimal swimmer escape strategies. The beach stage evolves periodically at the study site and plays an important role in the long-term modulation of the occurrence and strength of rip currents according to the modeling. A series of tests are designed and confirm that rip current strength is closely related to wave properties and tidal levels. Spectral analysis of output time series at specific points shows that the modeled rip currents fluctuate on the orders of 1 and 10 min, which suggests the effects of wave-group-forced infragravity (IG) and very-low-frequency (VLF) motions. Rip hazard levels are defined by combining rip strength and its duration. An attempt to use the GPU-accelerated FUNWAVE-TVD (Total Variation Diminishing version of the Fully Nonlinear Boussinesq Wave Model) embedded with the spectral wave model WAM6-GPU (GPU version of the third-generation spectral wave model WAM Cycle 6) exhibits its capability to evaluate rip hazard levels in real time. One of the differences of the present study from previous works is that the random, wave-resolving tracking of virtual swimmers is performed with 1 m resolution to study beach safety strategies. The results demonstrate that multiple factors contribute to the survival of swimmers caught in the rip currents, including surf-zone bathymetry, rip strength, fine-scale flow patterns, the bather's position, and swimming ability. For weak-to-moderate rip currents and longshore currents, swim onshore consistently seems to be the most successful strategy across all the scenarios in this study. Higher surf-zone exit rates along Dadonghai beach are not favorable for stay afloat action, which puts swimmers at a higher risk of being expelled to deeper water. The effects of wave randomness of incoming wave trains and assignment of wave-following coefficients on Lagrangian tracking are also discussed.

A Beach Profile Evolution Model Driven by the Hybrid Shock-Capturing Boussinesq Wave Solver

An existing Boussinesq wave model, solved in a hybrid format of the finite-difference method (FDM) and finite-volume method (FVM), with good merits of stability and shock-capturing, was used as the wave driver to simulate the beach evolution under nearshore wave action. By coupling the boundary layer model, the sand transport model, and the terrain updating model, the beach evolution model is established. Based on the coupled model, the interaction process between sandbars and waves was simulated, reproducing the process of the original sand bars diminishing, new sandbars creating, and finally disappearing. At the same time, the formation and movement process of sand bars under solitary and regular waves are numerically simulated, in the breaking zone, the water bottom has a larger shear stress, which promotes the sediment activation, transport and erosion formation, and near the breaking point, the decrease of sand-carrying capacity is the main reason for the formation of sandbars, the numerical model can accurately describe the changes in the shoreline profile under wave action.

HYDRODYNAMIC AND BOUSSINESQ WAVE MODELING FOR THE N219 AMPHIBIOUS AIRCRAFT SEAPLANE DOCK DEVELOPMENT PLAN IN PANJANG ISLAND

The flight test of N219 Amphibious aircraft will be targeted in 2003/2024. For flight tests, these aircraft need a seaplane dock. One of the potential locations for the seaplane dock is Panjang Island at Seribu Islands. This study aims to know the characteristic of hydrodynamic and wave conditions and to determine whether Panjang Island is suitable for the seaplane dock. This study uses a modeling method with MIKE 21 FM HD-SW module and MIKE 21 Boussinesq Wave (BW) module. The bathymetry data were obtained from the Indonesian Navy Hydrographic and Oceanographic Center (Pushidrosal), tide data is generated from Tide Model Driver (TMD), wave and wind data from ECMWF. The result of surface elevation validation between hydrodynamic modeling and TMD is 92%. During the west monsoon and spring conditions, the difference in the largest and lowest current velocity is quite large (0.018-0.199 m/s), on the other hand, when the tides are in neap conditions (0.008-0.144 m/s). Meanwhile, during the east monsoon and spring conditions, the difference in the largest and lowest current velocities is quite large (0.02-0.193 m/s), on the other hand, when the tides are in neap conditions (0.008-0.146 m/s). The maximum wave height resulting from the 50-year return period waveform modeling between 1.139 - 1.474 m. Meanwhile, the significant wave heights between 0.679 - 0.741 with a significant wave period of 13.45 seconds. In general, the current and wave conditions of the two locations are suitable for the construction of the seaplane dock, except that the dominant wave heights are still above the requirements.

EFFICIENTLY FORECASTING 2-DIMENSIONAL SPECTRA INSIDE SHELTERED PORTS USING SPECTRAL AND PHASE-RESOLVING WAVE MODELS

Ports today are grappling with the impacts of increasing ship sizes and increasingly frequent and more extreme weather events. Under these conditions, being able to predict navigation, handling, and mooring risks accurately, is becoming more crucial to safe and efficient port operations. This is especially important in ports subject to complex wave transformations. Traditionally, in order to capture the various wave transformation processes accurately from offshore to nearshore areas, the coupling of a Spectral wave (SW) and Boussinesq wave (BW) model has been required. Unfortunately, the very high computational costs of BW modelling have inhibited running such models in forecast mode. In response to this highly technical challenge, DHI have developed a transformative method for concatenating outputs from SW and BW models, enabling modelers to forecast 2D Spectra accurately, both inside and outside a sheltered port basin in a computationally efficient manner.

COMPARISON OF NUMERICAL AND EMPIRICAL ESTIMATES OF WAVE CONDITIONS IN THE LEE OF A DETACHED BREAKWATER

This paper presents a comparison of numerical and empirical methods routinely applied by practitioners to examine wave penetration in the lee of a breakwater, using a case study of a breakwater which is planned for Entrance Point, Broome in the northwest of Australia. Wave conditions representative of ambient and extreme conditions were determined from measured data captured directly offshore of the site, and an extreme cyclone metocean study (Baird, 2020). For ambient and extreme tropical cyclone conditions, waves are typically short crested at a peak period of between 4 seconds to 8 seconds. To examine the effectiveness of the offshore breakwater, empirical methods (Goda, 2000), a phase-averaged model (SWAN) and two phase-resolving model systems– the 2D Boussinesq wave model (MIKE21BW) and 3D non-hydrostatic model (MIKE3-Wave FM) - were applied.

A simplified approach for efficiently simulating submarine slump generated tsunamis

A simplified approach was proposed to efficiently simulate the tsunamis generated by a submarine slump. The landslide tsunami generation process was simulated using a long-wave model, simplifying the wave generation problem as a slump traveling down a plane slope with a prescribed trajectory. As a result, the landslide tsunami generation process was parameterized by 11 input parameters. The wave profile at the end of the wave generation process can then be specified as the initial conditions in any numerical tsunami propagation model to study the subsequent tsunami propagation. To demonstrate the capability of this new landslide tsunami generation approach, we used it in combination with an existing Boussinesq wave solver to simulate the 1998 Papua New Guinea landslide tsunami. The results based on the newly calculated physics-based wave profile compare reasonably well with field measurements and the results based on an existing tuning-based wave profile. Sensitivity tests were performed to examine the sensitivity of the runup results to each of the 11 input parameters. Six sets of 100-case Monte Carlo experiments were conducted to investigate the propagation of uncertainty from the input parameters to the runup results. Runup uncertainty was found to be approximately 1.5 times the parameter uncertainty, highlighting the uncertain nature of landslide tsunamis.

Numerical modeling of return period waves based on non-linear Boussinesq wave models to support tidal flood studies in the Kedungsepur area

A number of rapid developments and negative effects of climate change in coastal areas have forced its equilibrium system. As a result, tidal floods, high waves, and storms occur more frequently. The goal of this research is to examine nearshore hydrodynamic conditions by using results from the hindcasting procedure. A non-linear Boussinesq (BW) and Spectral Wave (SW) models are used in this study. The models use the manning coefficient, bathymetry data (BATNAS), significant wave height, and wave period calculated by using the hindcasting method. This research commenced by processing wind data from the European Center for Medium-Range Weather Forecasts (ECMWF) from the years 2009 to 2021 with an interval of 3 hours. Then, wave height for return periods 1-, 50- and 100-years are calculated using Gumbel and Fisher-Tippett type I distribution, respectively. The aforementioned approach produced wave heights of 4.23; 6.16; and 6.49 m for return periods 1, 50, and 100 years, respectively. By using this series of wave data, the models predicted that 1.2 m waves propagate close to the nearshore regions.

Numerical modeling of a potential landslide-generated tsunami in the southern Strait of Georgia

We report results of numerical simulations of a potential subaerial landslide on the coast of Orcas Island and the resultant tsunami waves in the southern Strait of Georgia near the US/Canada border. A likely trigger is strong ground shaking during large earthquakes on the nearby Holocene active Skipjack Island fault zone. For a worst-case scenario, we assume a 0.17 {textrm{km}}^3 rigid subaerial failure on the steep northeast coast of the island, spanning the sim 5 km between previous landslide deposits on the adjacent seafloor. The landslide motion and resulting tsunami generation are modeled using the three-dimensional (3D) non-hydrostatics physics-based NHWAVE model. The simulated failure moves downslope with a peak velocity of 13.64ṁ/s and travels 732 m before coming to rest after 85 s in 75-m water depth. Tsunami propagation is then continued using the 2D fully nonlinear and dispersive Boussinesq wave model FUNWAVE-TVD in a succession of layered and nested grids. The modeling reveals susceptible locations, particularly as waves will arrive with little or no warning. In the near-source region, modeled waves have peak amplitudes of 15–20 m, current speeds of up to 10 m/s, and runup of up to 30 m. Smaller, but significant, wave amplitudes and runup occur throughout the region surrounding Orcas Island. In the tsunami propagation direction, runup reaches 7.5 m at Neptune Beach near Lummi Bay. Both initial and reflected waves cause significant runup (> 1.5 m) along much of the shoreline between Point Roberts and Lummi Bay.

Investigating the Harbour Basin Tranquillity in the Genaveh Port Development Plan

Abstract The Genaveh commercial port was placed on the agenda of the Iranian PMO (ports and maritime organization) to consider economic, commercial and residential development in Bushehr province and specifically in Genaveh city. In order to increase the water capacity of the port, it is necessary to build a new harbour basin for exploitation and commercial purposes at a depth of 5 to 6 meters by extending the existing jetties arms in front of the port. This research aims to investigate the harbour basin’s tranquillity for providing vessels with safe berthing. For this purpose, three modules, namely the flow model (FM), spectral wave (SW) and Boussinesq waves model (BW) from the MIKE 21 software package, were utilized. According to the monitoring data, which is provided by the Iranian PMO, the harbour basin’s tranquillity based on the prevailing wave directions was investigated. Based on the diffraction graph in the harbour basin, the results showed that, according to the percentage of permissible diffraction recommended by different valid regulations, there is a need to modify the geometry of the breakwater arms to increase the harbour basin’s tranquillity at the port in the development plan.

Analytical and numerical investigation of edge waves near a vertical breakwater over a convex bottom

Vertical breakwaters are commonly built on the shore, and their existence must influence the character of nearshore dynamics. Analytical solutions based on linear-shallow water equation are derived for edge waves on a convex exponential profile which may be used to idealize the actual bottom profile with a vertical breakwater at the shoreline. The free surface elevation of the edge waves is described using the first kind of the Bessel functions of order ν. The amplitude profiles are similar to those of edge waves on a sloping beach but confined to a narrower offshore domain near the vertical breakwater. The dispersion relationship is derived from the no-flux boundary condition at the vertical breakwater. The wave number is not only related to the frequency but also the water depth at the vertical breakwater and the profile parameter. The group velocity increases rapidly to the maximum value with the increase of frequency, then decreases slowly and finally approaches the classic shallow water wave celerity of the depth at the vertical breakwater. The possible reason for this distinct behavior may be because dynamic characteristics of edge waves are highly dependent on the profile. Moreover, an extensively validated Boussinesq wave model is used to conduct numerical experiments for edge waves induced by surface bumps. The numerical results are consistent with the proposed solutions, confirming the validity of the new analytical solutions.

An Efficient Technique for Time-Fractional Water Dynamics Arising in Physical Systems Pertaining to Generalized Fractional Derivative Operators

This study proposed the q ˜ -homotopy analysis transform method ( q ˜ -HATM) as a revolutionary mathematical method for addressing nonlinear time-fractional Boussinesq and approximate long wave dynamics models with the Caputo and Atangana–Baleanu fractional derivatives in the Caputo sense. Through a specific velocity distribution, these models play an essential role in explaining the physics of wave propagation. The q ˜ -HATM is a new improvement to the Elzaki transform (ET) that simplifies the computations. The presented scheme addresses computational complexity by avoiding the use of Adomian and He’s polynomials, which is a distinguishing feature of this innovative methodology over decomposition and the homotopy perturbation transform method. The convergence analysis and error analyses are carried out in the current investigation for the upcoming strategy. We provide illustrations to exemplify the suggested system’s strength and efficacy, and the error estimates are described to ensure reliability. The analytical and graphic illustrations show that the projected methodology is numerically very precise and pragmatic to analyze the solution of fractional associated dynamics that arise in physics and engineering.

Hydrodynamic response of moored ships to seismic-induced harbor oscillations

Free-surface oscillations induced by seismic waves were observed in many harbors. These free-surface fluctuations could lead to damage in a wide range of forms, such as breakage of mooring systems due to excessive ship motions. The damage to moored ships and mooring systems will remarkably reduce their emergency capability to incoming tsunamis, probably further leading to property losses and casualties. However, investigation of floating bodies under seismic-induced free-surface oscillations is rare. Particularly, the hydrodynamic response of moored ships to seismic-induced harbor oscillations has not yet been studied. In this article, the transient hydrodynamic characteristics of moored ships under seismic-induced harbor oscillations are investigated by a hybrid Boussinesq-panel model where the free-surface oscillations are modeled by a fully nonlinear Boussinesq wave model and are further used to drive the ship motions. Results reveal that seismic-induced harbor oscillations can trigger long-period movements of moored ships, consistent with the existing observations. The long-period ship motions consist of the natural modes of the mooring system and the forced modes relating to long-period harbor oscillations. Notably, the ship's maximum displacement can be amplified remarkably when the periods of natural modes coincide with those of the forced modes. The effects of modal shapes of seismic-induced multi-mode harbor oscillations on the ship motions are analyzed. Finally, a brief discussion on studying the countermeasures against ship motions triggered by seismic-induced harbor oscillations is presented. • The hydrodynamic response of moored ships to seismic-induced harbor oscillations is first investigated using a hybrid Boussinesq-panel model. • The capacity of seismic-induced harbor oscillations to trigger long-period movements of moored ships is revealed, especially reproducing a typical process of this phenomenon. • The transient hydrodynamic characteristics of moored ships under seismic-induced harbor oscillations are analyzed, especially considering the resonant case when the natural periods of the ship motions are close to that of harbor oscillations. • The effects of modal shapes of seismic-induced multi-mode harbor oscillations on the ship motions are examined.

Analysis of parametric effects in the wave profile of the variant Boussinesq equation through two analytical approaches

Abstract The variant Boussinesq equation has significant application in propagating long waves on the surface of the liquid layer under gravity action. In this article, the improved Bernoulli subequation function (IBSEF) method and the new auxiliary equation (NAE) technique are introduced to establish general solutions, some fundamental soliton solutions accessible in the literature, and some archetypal solitary wave solutions that are extracted from the broad-ranging solution to the variant Boussinesq wave equation. The established soliton solutions are knowledgeable and obtained as a combination of hyperbolic, exponential, rational, and trigonometric functions, and the physical significance of the attained solutions is speculated for the definite values of the included parameters by depicting the 3D profiles and interpreting the physical incidents. The wave profile represents different types of waves associated with the free parameters that are related to the wave number and velocity of the solutions. The obtained solutions and graphical representations visualize the dynamics of the phenomena and build up the mathematical foundation of the wave process in dissipative and dispersive media. It turns out that the IBSEF method and the NAE are powerful and might be used in further works to find novel solutions for other types of nonlinear evolution equations ascending in physical sciences and engineering.

Fully nonlinear interfacial periodic waves in a two-layer fluid with a rigid upper boundary and their loads on a cylindrical pile

Based on the fully nonlinear potential flow theory, interfacial periodic gravity waves in a two-layer fluid with a rigid upper boundary are investigated quasi-analytically using the homotopy analysis method (HAM), and the corresponding wave loads on a cylindrical pile are estimated by Morison’s empirical formula. Because of the great freedom in the choices of auxiliary linear operators, initial guesses, and convergence-control parameter, convergent series solutions are obtained in the framework of the HAM. For Boussinesq wave loads on the cylinder in one wave period, there exists a phenomenon of peak–valley mismatch between the upper and lower layer inertial loads; the total drag, total inertial and global loads reach their own peaks almost at the same time when the upper layer load equals the lower layer load. As the wave height increases, the dominant load changes from inertial load to drag load. Previous theoretical studies about internal or interfacial periodic wave loads on a cylinder were mainly based on linear or weakly nonlinear wave models, which causes the lack of corresponding theoretical research in the frame of fully nonlinear wave theory. Compared with linear and weakly nonlinear wave models, the fully nonlinear wave model considered in this paper provides more accurate results for the maximal loads on a slender cylindrical pile exerted by Boussinesq interfacial periodic waves, especially for strongly nonlinear cases. All of these should enhance our understanding of internal periodic waves and their loads on a marine riser.

Block-structured, equal-workload, multi-grid-nesting interface for the Boussinesq wave model FUNWAVE-TVD (Total Variation Diminishing)

Abstract. We describe the development of a block-structured, equal-CPU-load (central processing unit), multi-grid-nesting interface for the Boussinesq wave model FUNWAVE-TVD (Fully Nonlinear Boussinesq Wave Model with Total Variation Diminishing Solver). The new model framework does not interfere with the core solver, and thus the core program, FUNWAVE-TVD, is still a standalone model used for a single grid. The nesting interface manages the time sequencing and two-way nesting processes between the parent grid and child grid with grid refinement in a hierarchical manner. Workload balance in the MPI-based (message passing interface) parallelization is handled by an equal-load scheme. A strategy of shared array allocation is applied for data management that allows for a large number of nested grids without creating additional memory allocations. Four model tests are conducted to verify the nesting algorithm with assessments of model accuracy and the robustness in the application in modeling transoceanic tsunamis and coastal effects.

A coupled model for sediment transport dynamics and prediction of seabed morphology with application to 1DH/2DH coastal engineering problems

Coastline retreat poses a threat to nearshore environment and the assessment of erosion phenomena is required to plan the coastal engineering works. The hydro-morphodynamic response of a beach to natural and artificial forcing factors differ considerably, as the nearshore processes are especially complex and depended on a multitude of parameters, including prevailing wave and hydrodynamic conditions, beach topography, sediment characteristics and the presence of coastal protection works. The present study serves the purpose of numerically evaluating nearshore morphological processes and ultimately assessing the capacity of coastal defence structures to control beach erosion. For this reason, a new sediment transport model including unsteady effects and swash zone morphodynamics, was coupled to the highly nonlinear Boussinesq wave model FUNWAVE-TVD, providing integrated predictions of bed level evolution, across various timescales of interest. The compound model was validated thoroughly against laboratory data and other numerical investigations. Overall, a good agreement between experimental and numerical results was achieved for a number of test cases, investigating the effects of different types of shore protection structures. The proposed integrated model can be a valuable tool for engineers and scientists desiring to obtain accurate bed level predictions, over complex mildly and steeply sloping sea bottoms composed of non-cohesive sediment particles.

Influences of beach berm height on beach response to storms: A numerical study

The field observation at two neighboring beaches showed significant effects of berm height on beach profile changes during a major storm. The fully nonlinear Boussinesq wave model, FUNWAVE-TVD, with a sediment transport module was used to simulate the beach erosion processes of the two beaches. The model reproduced the beach profile changes in good agreement with the measured data. The model results revealed that, for the beach with a higher berm, the wave force, wave-induced undertow flow, along with the higher sediment concentration on the berm induce more offshore sediment transport and cause significant beach profile changes compared to the beach with a lower berm. The erosion trend with different berm heights was predicted by using a series of numerical tests with different berm heights and offshore forcing conditions. The test results suggested that beach erosion increases with the berm height until the berm height reaches a certain level.

On the solution of fractional modified Boussinesq and approximate long wave equations with non-singular kernel operators

<abstract><p>In this paper, we used the Natural decomposition approach with nonsingular kernel derivatives to explore the modified Boussinesq and approximate long wave equations. These equations are crucial in defining the features of shallow water waves using a specific dispersion relationship. In this research, the convergence analysis and error analysis have been provided. The fractional derivatives Atangana-Baleanu and Caputo-Fabrizio are utilised throughout the paper. To obtain the equations results, we used Natural transform on fractional-order modified Boussinesq and approximate long wave equations, followed by inverse Natural transform. To verify the approach, we focused on two systems and compared them to the exact solutions. We compare exact and analytical results with the use of graphs and tables, which are in strong agreement with each other, to demonstrate the effectiveness of the suggested approaches. Also compared are the results achieved by implementing the suggested approaches at various fractional orders, confirming that the result comes closer to the exact solution as the value moves from fractional to integer order. The numerical and graphical results show that the suggested scheme is computationally very accurate and simple to investigate and solve fractional coupled nonlinear complicated phenomena that exist in science and technology.</p></abstract>

Simulation of wave incident boundary for spatially inhomogeneous multidirectional irregular waves

Accurately simulating the incidence of the spatially inhomogeneous multidirectional irregular waves in numerical modeling of wave propagation on coastal areas is vitally important for engineering design. In this paper, the Inhomog-Bound-EEED, Inhomog-Bound-PTPD and Inhomog-Bound-DSFD approaches are established and their capabilities for simulating the inhomogeneous incident wave boundary are verified by the coupling of Boussinesq wave model with theoretical diffraction wave model and with SWAN wave model. The incident wave information of the Boussinesq wave model is simulated by the proposed methods based on the wave information provided by the wave diffraction or SWAN model. The simulated time series and significant wave heights by the Boussinesq wave model show good agreement with the results of the theoretical diffraction wave model, which verifies the validities of the proposed Inhomog-Bound-PTPD and Inhomog-Bound-DSFD approaches. The obvious consistency of the simulated results for the analyzed significant wave heights and directional distributions between the Boussinesq wave model and the theoretical diffraction wave model verifies the effectiveness of the Inhomog-Bound-DSFD method, and the method is further applied to the numerical coupling of the Boussinesq wave model and SWAN model. The proposed three methods have good applicability to simulate the spatially inhomogeneous multidirectional irregular wave incident boundary.