Incident Wave Forcing Research Articles

Numerical investigations on nonlinear motions of ships sailing in large-amplitude waves based on hybrid HOBEM

This paper presents a nonlinear numerical approach based on hybrid higher-order boundary element method (HOBEM) to investigate the wave-induced motion responses of ships with forward speed. The radiation and diffraction forces in time domain are determined by convolution of the impulsive response functions computed from frequency-domain hydrodynamic data of the hybrid method using a combination of Rankine source and translating-pulsating Green's function. In its numerical implementation, steady flow effects are included in the inner domain encompassing the ship, 9-node bi-quadratic curvilinear elements are employed to discretize the boundaries and analytical quadrature formulas are derived to calculate the influence coefficients related to the Green's function over the control surface so as to improve the accuracy, efficiency and stability. Meanwhile, the nonlinear incident wave force and hydrostatic restoring force are calculated over the instantaneous wetted surface of the ship hull during the motion process to capture the nonlinear properties. Based on the method, a numerical program is developed to predict and analyze the motion response of a modified Wigley hull and a non-wall-sided S175 containership advancing in waves with different amplitudes and heading angles. By comparing the present computed results with experimental data and other numerical solutions, it is found that the nonlinear calculations can produce more accurate motion responses in large-amplitude waves with strong nonlinearity. And the present nonlinear method based on hybrid HOBEM is of higher accuracy and better stability than traditional nonlinear methods based on three-dimensional pulsating source (3DP) and translating-pulsating source (3DTP), especially for S175 with large flare near the waterline.

A Numerical Study on the Responses of Wave-Driven Circulation to Varying Incident Wave Forcing and Reef Morphology in A Reef-Lagoon-Channel System

A Numerical Study on the Responses of Wave-Driven Circulation to Varying Incident Wave Forcing and Reef Morphology in A Reef-Lagoon-Channel System

A numerical method to compute flexible vertical responses of containerships in regular waves

In this paper, a series of simulations of hydroelastic problems of containerships are conducted by a nonlinear 3D panel method which is based on the generalized Taylor Expansion Boundary Element Method (TEBEM). In the structure part, the Transfer Matrix Method is selected to perform a modal analysis which provides key parameters of hydroelastic calculation. In the hydrodynamic part, the nonlinearities arising from the variations of instantaneous wetted surface area are considered in the solutions of hydrostatic restoring forces as well as 1st order incident wave forces. Meanwhile, an extended Modified Logvinovich Model (MLM) is presented to predict the slamming forces due to the large-amplitude incident waves. The numerical predictions of the hydroelastic responses of a 6750-TEU containership and S175 in regular waves are presented. The effects of wave steepness and sailing speed as well as the variation characteristics of load components against with wave direction are studied. The numerical and experimental results are in acceptable agreement which proves the accuracy of the proposed method.

Long‐Distance/Time Surf‐Zone Tracer Evolution Affected by Inner‐Shelf Tracer Retention and Recirculation

AbstractThe evolution of a surf‐zone released tracer ( Liter over 4 hr) was observed for h. Surf‐zone tracer was transported alongshore (y) with relatively steady mean speed vSZ ≈ 0.18 m s−1, consistent with obliquely incident wave forcing. Maximum in situ surf‐zone tracer concentration decayed exponentially with 1.6 km alongshore e‐folding length scale, that is, 2.5 hr advective time scale. Surf‐zone tracer time‐series evolved downstream of the release from a top‐hat structure for y ≤ 1 km to increasingly skewed farther downstream. Within km of the northward propagating tracer front, inner‐shelf tracer was confined to onshore of (surf‐zone width LSZ ≈ 100 m) and was alongshore patchy. A coupled surf‐zone/inner‐shelf tracer advection‐diffusion‐exchange box model reproduces the observed surf‐zone downstream max concentration decay and temporal skewness, with surf‐zone flushing time h. A weaker inner‐shelf unidirectional‐exchange rate kIS ≈ kSZ/2 indicates reduced horizontal mixing outside the surf‐zone. Surf‐zone temporal skewness is linked to inner‐shelf tracer storage, differential surf‐zone/inner‐shelf advection, and recirculation, that is, non‐asymptotic shear dispersion. On the inner‐shelf (), tracer vertical structure differed in the morning versus afternoon suggesting internal tide and solar forced thermal modulation. Model parameters representing surf‐zone processes are well constrained by existing observations and scales. However, the many overlapping inner‐shelf processes make a single process based generalization of inner‐shelf cross‐shore exchange rate (i.e., kIS) and alongshore transport difficult.

An Analytical Solution for the Interaction of Waves with Arrays of Circular Cylinders

This paper presents an analytical method to investigate the multiple scattering problem within arrays of vertical bottom-mounted circular cylinders subjected to linear incident waves. Based on the Laplace equation and boundary conditions on the seabed and surface, a formulation of a two-dimensional multiple scattering problem is first obtained by using the variable separation method. Furthermore, the analytical solution of the wave forces on multiple circular cylinders is derived, which consists of the incident wave force due to the linear incident wave and the scattered wave forces considering multiple scattering waves. The presented analytical solution is validated by comparing its results with a numerical method, and the result shows that the analytical solution is in good agreement with the numerical one. Finally, the multiple scattering analysis is conducted on arrays of cylinders with different incident wave numbers, distances between cylinders, and quantities.

An early warning system for wave-driven coastal flooding at Imperial Beach, CA

Waves overtop berms and seawalls along the shoreline of Imperial Beach (IB), CA when energetic winter swell and high tide coincide. These intermittent, few-hour long events flood low-lying areas and pose a growing inundation risk as sea levels rise. To support city flood response and management, an IB flood warning system was developed. Total water level (TWL) forecasts combine predictions of tides and sea-level anomalies with wave runup estimates based on incident wave forecasts and the nonlinear wave model SWASH. In contrast to widely used empirical runup formulas that rely on significant wave height and peak period, and use only a foreshore slope for bathymetry, the SWASH model incorporates spectral incident wave forcing and uses the cross-shore depth profile. TWL forecasts using a SWASH emulator demonstrate skill several days in advance. Observations set TWL thresholds for minor and moderate flooding. The specific wave and water level conditions that lead to flooding, and key contributors to TWL uncertainty, are identified. TWL forecast skill is reduced by errors in the incident wave forecast and the one-dimensional runup model, and lack of information of variable beach morphology (e.g., protective sand berms can erode during storms). Model errors are largest for the most extreme events. Without mitigation, projected sea-level rise will substantially increase the duration and severity of street flooding. Application of the warning system approach to other locations requires incident wave hindcasts and forecasts, numerical simulation of the runup associated with local storms and beach morphology, and model calibration with flood observations.

North Sea Infragravity Wave Observations

Coastal safety assessments with wave-resolving storm impact models require a proper offshore description for the incoming infragravity (IG) waves. This boundary condition is generally obtained by assuming a local equilibrium between the directionally-spread incident sea-swell wave forcing and the bound IG waves. The contribution of the free incident IG waves is thus ignored. Here, in-situ observations of IG waves with wave periods between 100 s and 200 s at three measurement stations in the North Sea in water depths of O(30) m are analyzed to explore the potential contribution of the free and bound IG waves to the total IG wave height for the period from 2010 to 2018. The bound IG wave height is computed with the equilibrium theory of Hasselmann using the measured frequency-directional sea-swell spectra as input. The largest IG waves are observed in the open sea with a maximum significant IG wave height of O(0.3) m at 32 m water depth during storm Xaver (December 2013) with a concurrent significant sea-swell wave height in excess of 9 m. Along the northern part of the Dutch coast, this maximum has reduced to O(0.2) m at a water depth of 28 m with a significant sea-swell wave height of 7 m and to O(0.1) m at the most southern location at a water depth of 34 m with a significant sea-swell wave height of 5 m. These appreciable IG wave heights in O(30) m water depth represent a lower bound for the expected maximum IG wave heights given the fact that in the present analysis only a fraction of the full IG frequency range is considered. Comparisons with the predicted bound IG waves show that these can contribute substantially to the observed total IG wave height during storm conditions. The ratio between the predicted bound- and observed total IG variance ranges from 10% to 100% depending on the location of the observations and the timing during the storm. The ratio is typically high at the peak of the storm and is lower at both the onset and waning of the storm. There is significant spatial variability in this ratio between the stations. It is shown that differences in the directional spreading can play a significant role in this. Furthermore, the observed variability along the Dutch coast, with a substantially decreased contribution of the bound IG waves in the south compared to the northern part of the Dutch coast, are shown to be partly related to changes in the mean sea-swell wave period. For the southern part of the Dutch coast this corresponds to an increased difference with the typically assumed equilibrium boundary condition although it is not clear how much of the free IG-energy is onshore directed barring more sophisticated observations and/or modeling.

Fault Detection of the Mooring system in Floating Offshore Wind Turbines based on the Wave-excited Linear Model

Floating Offshore Wind Turbines (FOWTs) are more prone to suffer from faults and failures than bottom-fixed counterparts due to the severe wind and wave loads typical of deep water sites. In particular, mooring line faults may lead to unacceptably high operation and maintenance costs due to the limited accessibility of FOWTs. Detecting the mooring line faults is therefore critical, but the application of Fault Detection (FD) techniques has not been investigated yet. In this paper, an FD scheme based on a wave-excited linear model is developed to detect in a reliable way critical mooring line faults occurring at the fairlead and anchor ends. To reach the goal, a linear model of the FOWT is obtained by approximating the wave radiation and incident wave forces. Based on this model, an observer is built to predict the rigid rotor and platform dynamics. The FD scheme is thus implemented by comparing the Mahalanobis Distance of the observer prediction error against a probabilistic detection threshold. Numerical simulations in some selected fault scenarios show that the wave-excited linear model can predict the FOWT dynamics with good accuracy. Based on this, the FD scheme capabilities are demonstrated, showing that it is able to effectively detect two critical mooring line faults.

Numerical Simulation of the Influence of Large-scale Structures on Wave Force of Adjacent Small-scale Bars in Composite Structures

In order to calculate the wave loads on the small and medium scale bars of composite structures accurately, not only the action of incident wave but also the wave diffraction caused by near large-scale structure and the effect of radiation on wave load of small scale bars should be considered. In this paper, based on the VOF method, the three-dimensional wave numerical flume of the wave acting on the composite structure is constructed in Fluent. The incident wave force, diffraction wave force and total force acting on the composite structure are obtained by numerical calculation. Compared with the results obtained by using the Morison formula alone, the effectiveness of the wave loads calculated by the model is verified. The results show that under certain wave conditions, the wave diffraction caused by large-scale structures can not be ignored. In addition, the influence of the incident wave number, the diameter of the pile and the position of the pile on the wave load of the small-scale pile is also studied. The results can provide a scientific reference for the accurate calculation of wave loads on small-scale piles in marine engineering with composite structures.

Rankine source method analysis for nonlinear hydroelastic responses of a container ship in regular oblique waves

Abstract In this study, some numerical solutions for the hydroelastic problems of bodies are studied by means of Rankine source method. Firstly, Rankine source method is generalised to the elastic modes. The difference method is used to obtain the source strength. In order to eliminate the errors in solving process, a damping correction factor is applied. Secondly, the numerical predictions of the nonlinear hydroelastic responses of a 13000-TEU container ship are presented. In the hydrodynamic part, the nonlinear hydrostatic restoring force and nonlinear incident wave force caused by instantaneous wetted surface as well as slamming force are considered. In the structure part, the finite element method is used to solve vertical and horizontal oscillation modes. Finally, the hydroelastic method is extended to the oblique waves by adopting an autopilot model to consider the rudder force/moment. Variation of the different load components with wave direction is studied. The present numerical results show acceptable agreement with previous experimental results.

Predictions of Ship Extreme Hydroelastic Load Responses in Harsh Irregular Waves and Hull Girder Ultimate Strength Assessment

In this paper, the hydroelastic motion and load responses of a large flexible ship sailing in irregular seaways are predicted and the hull girder ultimate strength is subsequently evaluated. A three-dimensional time-domain nonlinear hydroelasticity theory is developed where the included nonlinearities are those arising from incident wave force, hydrostatic restoring force and slamming loads. The hull girder structure is simplified as a slender Timoshenko beam and fully coupled with the hydrodynamic model in a time domain. Segmented model towing-tank tests are then conducted to validate the proposed hydroelasticity theory. In addition, short-term and long-term predictions of ship responses in irregular seaways are conducted with the help of the developed hydroelastic code in order to determine the extreme design loads. Finally, a simplified strength-check equation is proposed, which will provide significant reference and convenience for ship design and evaluation. The hull girder ultimate strength is assessed by both the improved Rule approach and direct calculation.

Air Gap Prediction for Floating Bodies Using a 3D Numerical Wave Tank Approach

Computations for air gap response of a semisubmersible platform based on a 3D numerical wave tank approach are presented. The developed method is in time domain and can consider nonlinearities associated with incident wave and hydrostatic forces exactly in determining the body response, but the interaction hydrodynamics of radiation and diffraction are based on simplified linearization assumptions. The incident wave can be defined by any suitable wave theory and here defined by a fully nonlinear numerical wave model. After verifying the present computations results in its degenerated linearized version against the usual linear 3D Green function–based frequency-domain results for air gap predictions, systematic comparative studies are undertaken between linear and the approximate nonlinear solutions. It is found that nonlinear computations can yield considerably conservative predictions as compared to fully linear calculations, amounting to a difference of up to 30%–40% in the minimum air gap in steep ambient incident waves at high and moderate frequencies.

Investigation on Ship Hydroelastic Vibrational Responses in Waves

The hydroelastic vibrational responses of a large ship sailing in regular and irregular head waves are investigated numerically and experimentally. A 3D time-domain nonlinear hydroelastic mathematical model is established in which the hydrostatic restoring forces and incident wave forces are calculated on the instantaneous wetted hull surface to consider nonlinear effects of the rigid motion and elastic deformation of the hull in harsh waves. Radiation and diffraction wave forces are computed on the mean wetted surface based on the 3D frequency-domain potential flow theory. The slamming loads are calculated by momentum theory and integrated into the hydrodynamic forces. The 1D Timoshenko beam theory is adopted to model the vibrational structural response and is fully coupled with the presented hydrodynamic theory in time-domain to generate the hydroelastic equation of motion. Moreover, self-propelled segmented model tests were conducted in a laboratory wave tank to experimentally investigate the hydroelastic responses of a target ship in regular and irregular head seas. The numerical and experimental results are systemically compared and analyzed, and the established hydroelastic analysis model turns out to be reliable and effective in the prediction of ship hydroelastic responses in waves.

Pseudo-impulsive solutions of the forward-speed diffraction problem using a high-order finite-difference method

This paper considers pseudo-impulsive numerical solutions to the forward-speed diffraction problem, as derived from classical linearized potential flow theory. Both head- and following-seas cases are treated. Fourth-order finite-difference approximations are applied on overlapping, boundary-fitted grids to obtain solutions using both the Neumann-Kelvin and the double-body flow linearizations of the problem. A method for computing the pseudo-impulsive incident wave forcing in finite water depth using the Fast Fourier Transform (FFT) is presented. The pseudo-impulsive scattering solution is then Fourier transformed into the frequency domain to obtain the wave excitation forces and the body motion response. The calculations are validated against reference solutions for a submerged circular cylinder and a submerged sphere. Calculations are also made for a modern bulk carrier, showing good agreement with experimental measurements.

Partially nonlinear time domain analysis on ship motions in waves with translating-pulsating source Green function

The motion responses of ship in waves were investigated in time domain with both linear and partially nonlinear numerical method. The retardation functions that accounted for the memory effect were computed from transforms of frequency hydrodynamic data evaluated based on the Three Dimensional Translating-pulsating Source Green function (3DTP). Numerical simulations were carried out to validate the present linear method. It was found that the motion responses obtained from equations referenced to the equilibrium axis system indicate shifts when compared with the frequency domain results, especially for the pitch motion, while motion responses obtained from equations referenced to the body fixed axis system indicate satisfactory agreement with both the frequency domain results and experimental results. Then nonlinear incident wave forces and hydrostatic restoring forces were calculated on the instantaneous wet surface of hull. The contributions of the incident wave and the restoring forces on nonlinearity with increasing wave amplitude were analyzed for three vehicles with different hull forms. The results illustrates that the motion transfer functions of Wigley III hull see an upward trend at the resonant zone with the increasing wave amplitude, while those of S60 hull depict a downward trend and those of SWATH 6A remain almost constant.

Beach recovery capabilities after El Niño 2015–2016 at Ensenada Beach, Northern Baja California

This study investigates the recovery capabilities of a single-barred beach in the Pacific Mexican coast before and after the 2015–2016 El Nino winter. Concurrent hydrodynamic and morphological data collected over a 3-year period (August 2014–2017) were analysed to determine the subaerial-subtidal volumetric exchange and cross-shore subtidal sandbar migrations, in relation to the incident wave forcing. The beach presented a seasonal seaward and landward sandbar migration cycle. The sandbar migrated offshore during the energetic waves between November and February, and onshore during the milder wave period in spring, until welding to the subaerial beach around May. The transfer of sediment towards the subaerial section continued over the summer, reaching a complete recovery by September/October. Prior to El Nino, the subaerial beach successfully recovered by the end of summer 2015 through the landward sandbar migration process. The 2015–2016 energetic winter waves caused a subaerial volume loss of ~ 140 m3 m−1 (from October 2015 to March 2016), more than twice the amount eroded in the other winters, and the sandbar moved further offshore and to deeper depths (3–4 m) than the winter before. In addition, the energetic 2015–2016 winter waves lasted for 2 months longer than in other years, making the 2016 spring shorter. Consequently, during the onshore migration, the sandbar was unable of reaching shallow depths, and a large portion of sand remained in the subtidal beach. The subaerial beach recovered 60 and 65% of the loss in the 2016 and 2017 summers, respectively. It is concluded that the landward migration process of the sandbar during the spring is critical to ensure a full subaerial beach recovery over the mild wave period in summer. The recovery capabilities of the subaerial beach will depend on the cross-shore distance and depth where the sandbar is located, and on the duration of mild wave conditions required for the sandbar to migrate onshore.

Climate forcing of regionally-coherent extreme storm impact and recovery on embayed beaches

The effective management of sedimentary coastlines demands a good understanding of the seasonal and inter-annual cycles in beach volumes, as well as the potential impact of extreme events. This paper uses a 10-year time series (2007–2017) of supra- and intertidal beach volume from exposed and cross-shore transport-dominated sites to examine the extent to which beach behaviour is coherent over a relatively large region (100-km stretch of coast) and predictably coupled to incident wave forcing. Over the study period, 10 beaches, exposed to similar wave/tide conditions, but having different sediment characteristics, beach lengths and degrees of embaymentisation, showed coherent and synchronous variations in sediment volumes, albeit at different magnitudes. The sequence of extreme storms of the 2013/14 winter, which represents the most erosive event over at least a decade along most of the Atlantic coast of Europe, is included in the data set, and three years after this winter, beach recovery is still on-going for some of the 10 beaches. Post-storm beach recovery was shown to be mainly controlled by post-storm winter wave conditions, while summer conditions consistently contributed to modest beach recovery. Skilful hindcasts of regional changes in beach volume were obtained using an equilibrium-type shoreline model (ShoreFor; Davidson et al., 2013), demonstrating that beach changes are coherently linked to changes in the offshore wave climate and are sensitive to the antecedent conditions. The ShoreFor model can successfully be applied to exposed coastal areas dominated by cross-shore sediment transport, and can also be used as a relatively simple and regional tool for the future management of beaches where coherence in coastal response is observed. Furthermore, a good correlation was found between the beach volume changes and the new climate index WEPA (West Europe Pressure Anomaly; Castelle et al., 2017b), which offers new perspectives for the role and the use of climatic variations proxies to forecast coastline evolution.

Infragravity Seiches in a Small Harbor

A method is developed to estimate harbor seiche at Marina di Carrara, Italy, from the properties of wind-generated incident waves outside the harbor. A linear model of the spatial structure of amplified seiche modes is combined with empirical estimates of the response of each mode to variable incident wave forcing. These empirical coefficients parameterize the complex nonlinear transfer of energy from wind waves to lower frequency seiche. As at other small harbors (<1 km2 surface area) on ocean coasts, and consistent with previous analyses at Carrara, the observed seiche is relatively energetic at several periods between about 1 and 15 min that are highly amplified theoretically, and the spatial structure of modeled and observed seiches agree as well. The longest seiche (≈15 min) mode is almost spatially uniform within the harbor and dominates with low-energy, short-period incident wind waves (measured 1 km offshore of the harbor). Increased wave energy and longer periods excite shorter period (1–3 min) seiche modes with more complex spatial structure, including small areas of high amplification, which have led to operational issues. The energy in each of the six most energetic seiche modes is related in this paper empirically to offshore incident wind wave height and peak period, allowing detailed predictions of harbor seiche from routine wind wave forecasts. The approach appears applicable to relatively small, shallow harbors with reflective quay walls, in which the exterior harbor mouth is exposed, and the interior sheltered from energetic wind-generated waves.

Initial spreading of a mega feeder nourishment: Observations of the Sand Engine pilot project

Sand nourishments are a widely applied technique to increase beach width for recreation or coastal safety. As the size of these nourishments increases, new questions arise on the adaptation of the coastal system after such large unnatural shapes have been implemented. This paper presents the initial morphological evolution after implementation of a mega-nourishment project at the Dutch coast intended to feed the surrounding beaches. In total 21.5millionm3 dredged material was used for two shoreface nourishments and a large sandy peninsula. The Sand Engine peninsula, a highly concentrated nourishment of 17millionm3 of sand in the shape of a sandy hook and protruding 1km from shore, was measured intensively on a monthly scale in the first 18months after completion. We examine the rapid bathymetric evolution with concurrent offshore wave forcing to investigate the feeding behaviour of the nourishment to the adjacent coast. Our observations show a large shoreline retreat of O (150m) along the outer perimeter of the peninsula, with locally up to 300m retreat. The majority (72%) of the volumetric losses in sediment on the peninsula (1.8millionm3) were compensated by accretion on adjacent coastal sections and dunes, confirming the feeding property of the mega nourishment. Further analyses show that the morphological changes were most pronounced in the first 6months while the planform curvature reduced and the surf zone slope flattened to pre-nourishment values. In the following 12months the changes were more moderate. Overall, the feeding property was strongly correlated to incident wave forcing, such that months with high incoming waves resulted in more alongshore spreading. Months with small wave heights resulted in minimal change in sediment distribution alongshore and mostly cross-shore movement of sediment.

Observations of runup and energy flux on a low‐slope beach with high‐energy, long‐period ocean swell

AbstractThe transformation of surface gravity waves from 11 m depth to runup was observed on the low‐sloped (1/80) Agate Beach, Oregon, with a cross‐shore transect of current meters, pressure sensors, and a scanning lidar. Offshore wave heights H0 ranged from calm (0.5 m) to energetic (&gt;7 m). Runup, measured with pressure sensors and a scanning lidar, increases linearly with (H0L0)1/2, with L0 the deep‐water wavelength of the spectral peak. Runup saturation, in which runup oscillations plateau despite further increases in (H0L0)1/2, is not observed. Infragravity wave shoaling and nonlinear energy exchanges with short waves are included in an infragravity wave energy balance. This balance closes for high‐infragravity frequencies (0.025–0.04 Hz) but not lower frequencies (0.003–0.025 Hz), possibly owing to unmodeled infragravity energy losses of wave breaking and/or bottom friction. Dissipative processes limit, but do not entirely damp, increases in runup excursions in response to increased incident wave forcing.