Peak Wave Heights Research Articles

Development and performance of a high-resolution surface wave and storm surge forecast model: application to a large lake

Abstract. A real-time forecast model of surface hydrodynamics in Lake Ontario (Coastlines-LO) was developed to automatically predict storm surges and surface waves. The system uses a dynamically coupled Delft3D–SWAN model with a structured grid to generate 48 h predictions for the lake that are updated every 6 h. The lake surface is forced with meteorological data from the High Resolution Deterministic Prediction System (HRDPS). The forecast model has been running since May 2021, capturing a wide variety of storm conditions. Good agreement between observations and modelled results is achieved, with root mean squared errors (RMSEs) for water levels and waves under 0.02 and 0.26 m, respectively. During storm events, the magnitude and timing of storm surges are accurately predicted at nine monitoring stations (RMSE <0.05 m), with model accuracy either improving or remaining consistent with decreasing forecast length. Forecast significant wave heights agree with observed data (1 %–12 % relative error for peak wave heights) at four wave buoys in the lake. Coastlines-LO forecasts for storm surge prediction for two consecutive storm events were compared to those from the Great Lakes Coastal Forecasting System (GLCFS) to further evaluate model performance. Both systems achieved comparable results with average RMSEs of 0.02 m. Coastlines-LO is an open-source wrapper code driven by open data and has relatively low computational requirements compared to GLCFS, making this approach suitable for forecasting marine conditions in other coastal regions.

Weight Reduction Methodologies for Wave Energy Devices

The OE Buoy is a wave energy converter based on the Backward Bent Duct Buoy oscillating water column model which generates electricity through the fluctuation in wave height. Wave energy conversion devices are often faced with a particularly high levelized cost of energy (LCOE) when compared to other renewable energy devices, and various investigations into bridging this gap have been carried out in recent history. Previous studies on the OE Buoy have suggested that a significant reduction in required construction material is possible as a result of reduced differential pressures acting across the hull walls in operational conditions. Various structural analysis campaigns have been conducted on sections of the hull to assess this theory.
 A Finite Element Analysis (FEA) was performed on a full-scale model of the OE Buoy under maximum design wave loadings in operational conditions at EMEC’s Billia Croo test facility in Orkney, Scotland using Robot Structural Analysis software. A maximum pressure of 145 kPa was calculated for an 18.7 m peak wave height at Billia Croo. The OE Buoy was modelled for both static and dynamic load conditions under various constraint layouts. A modal analysis was conducted on the model which estimates the natural frequency of the OE Buoy to be approximately 6.67 Hz.

Hindcasting and predicting surge heights and waves on the Taiwan coast using a hybrid typhoon wind and tide-surge-wave coupled model

The tide-surge-wave coupled model and hybrid typhoon wind model were developed for the Taiwan coast and employed to predict surge heights and waves under different influential factors during historical typhoon events. The results revealed that the hybrid wind model matched the measured atmospheric pressure and wind speed time series during Typhoon Soudelor (2015) and Typhoon Nesat (2017). Afterward, the measured water level, wave height, and wave period time series at different measuring stations were used to validate the tide-surge-wave coupled model. The coupled model reasonably reproduced the measured data. Subsequently, the validated model was utilized to explore the influence of the radius of maximum wind (RMW), forward speed, atmospheric pressure, wind intensity, and typhoon path on surge height, wave height, and wave setup. The results with model prediction indicate that increasing the RMW causes an increasing negative surge height and wave height and shifts the time of the peak positive surge height and peak wave height. A smaller forward speed results in a larger positive peak surge height and peak wave height at most stations. The maximum ratio changes in negative peak surge height compared with the baseline condition with Typhoon Soudelor (2015) are 105.4% and −116.0% for increasing and decreasing 20 hPa atmospheric pressures at the Linshanbi station, respectively. The differences in maximum peak wave height (ratio change) for an increasing and decreasing 10 m/s wind speed are 6.44 m (47.2%) and −5.80 m (−42.4%), respectively. The predicted results indicate that the difference in the maximum peak positive surge height (maximum ratio change) compared with the baseline condition is 1.1 m (315.2%), thereby shifting the typhoon track to the north by 100 km at the Waipu station.

Analyzing wave direction scenarios for large waves in deep water and its impact on littoral drift

In this study, four types of wave direction scenarios in large waves greater than 3 m in deep water are examined by analyzing NOAA's wave hindcast data spanning over 40 years. The results reveal that wave direction changes at the starting, peak and ending of large/storm waves, accompanying by changing wave heights with wave direction becoming in perpendicular to the coastal orientation when waves reaching a peak. Within the bulk of NOAA wave data which last 1.65 days, 55.1% of the large/storm waves had wave direction returning to the starting direction on the wane of the waves, while the remaining 44.9% reversed to the opposite side of the starting direction. Based on this finding, littoral drift is calculated for each scenario by the CERC equation, on the basis of deep water wave parameters. The resulting littoral drift is then used in a numerical model to calculate shoreline changes at Jeongdongjin Beach in Korea, where a natural groin block the longshore sediment transport. The result of shoreline change in the vicinity of the groin suggests beach may become stable about one day after the end of a short-term large wave/storm event, or 2 days after the peak wave height.

Application of Delft3D-WAVE in the investigation of the typhoon-induced high wave in Central Vietnam

With a long coastline of around 3260 km, tropical typhoons induce the deadliest disasters in Central Vietnam’s highly populated coastal area. The focus of this paper is two-fold. The first objective is to investigate the feasibility of utilizing Delft3D-WAVE in forecasting typhoon-induced high wave events in Central Vietnam. By running a WRF model simultaneously in multiple domains with different grid resolutions, wind field distribution data during typhoon events were reproduced. Using the generated wind field data, typhoon Kaemi (2000) was employed as the case study to calibrate and validate the wave models. Comparisons between simulated results and observed data showed a good agreement, especially during peak wave height. The combined wind-wave model was applied to estimate the temporal and spatial impacts of high waves caused by the typhoon Ketsana (2009). The second objective is to assess the potetial risk from typhoon-induced wave in Central Vietnam based on the models output. From these results, this study recommends the application of Delft3D-WAVE to investigate high waves induced by typhoon events in Vietnam’s coastal areas.

Coupled modelling of storm surge, circulation and surface waves in a large stratified lake

The wind-driven nature of large lakes suggests that the accuracy of meteorological inputs is essential for hydrodynamic modelling. Moreover, coupling between the meteorological inputs and density stratification may also influence the simulated lake behavior. To investigate wind-driven large lake processes, a high-resolution coupled Delft3D-SWAN model was applied to Lake Ontario to simulate storm surges, surface waves, and circulation during two recent storm events. In both events, the sustained wind speeds approached 20 m s−1; however, variations in wind direction and duration altered the lake's surface wave and storm surge responses. The influence of different atmospheric inputs was investigated by comparing results from two spatially varied atmospheric models: the Rapid Refresh (RAP) and the High-Resolution Deterministic Prediction System (HRDPS). Hydrodynamic simulations using HRDPS were marginally better, with maximum root mean squared errors (RMSE) between modelled and observed water levels of 0.07 m, compared to 0.08 m with RAP. Predictions of the magnitude and timing of the maximum wave heights varied based on wind fields, with differences between predicted peak wave heights of up to 0.4 m. Both events occurred during a stratified period, allowing for a comparative evaluation of the influence of baroclinic and barotropic processes on the simulated surface wave and storm surge results. Simulations including the vertical density gradient gave a better representation of current velocities with depth and resulted in an improved prediction of peak storm surge magnitudes and surface water level behavior following the storms, reducing the RMSE by up to 12%.

A Study on the Influence of Sand Median Grain Size on the Short-Term Recovery Process of Shorelines

Recently, the impacts of short-term erosion caused by storm waves on coastal damages are increasingly recognized as social issues, compared to those of long-term erosion from climate change or coastal development. The erosion caused by the storm wave has an episodic characteristic that the shoreline recovers gradually after retreating for a short-term. Furthermore, if shoreline changes caused by longshore sediment transport are not taken into consideration, the shoreline position is determined by following two physical parameters based on the bulk response model. The beach response factor determines converging ultimate erosion on the assumption that incident waves constantly affects a beach, which can be estimated according to the concept of Dean’s profile. On the contrary, the beach recovery factor affects the velocity of the shoreline retreat and recovery. Therefore, the parameter plays an important role to predict the peak erosion due to the storms. However, there are still insufficient researches to utilize it as an engineering design for erosion reduction. In this study, the two methodologies (i.e., approximation formula and statistical analysis) that estimates peak erosion width caused by the storms are compared to extract the beach recovery factor. During the process, it is confirmed that peak wave height has little impact on the beach recovery factor. Instead, it is mainly determined by the median grain size. Also, the beach recovery factor is estimated as a function of median grain size based on the shoreline and sand survey data conducted over ten years. Among the 41 surveyed sites along the east coast, 11 sites of straight-type shorelines that directly react to the incident waves were applied to consider only the short-term recovery process. To prove validity, the estimated applied into the real sea and then the results were compared to the shoreline data extracted from CCTV images. Using these results, the peak erosion width for a target wave event can be predicted with only median grain size. These study results are expected to be used as a concrete and practical means to manage the coast, in preparation for the current and future shoreline erosion threats.

Study on vibration energy harvesting of offshore platform by energy harvester based on nonlinear energy sink

Under the impacts of waves and other marine environment, the jacket offshore platform has an obvious vibration and generates lots of energy. Meanwhile, the platform may suffer fatigue damage. The vibration energy harvesting of a jacket offshore platform under random waves with a nonlinear energy sink (NES) was investigated, and a NES-Energy harvester (NES-EH) was then designed by combining an electromagnetic linear generator with the NES. Moreover, the dynamic model of the NES-EH-offshore platform was built, and the electromagnetic damping and stiffness of the energy harvester were optimized by analyzing the energy capture efficiency and root mean square reduction of the platform displacement. The effects of NES nonlinear stiffness and damping, peak period and effective wave height of irregular waves on the capture power and width of the NES-EH were also analyzed. The results show that nonlinear stiffness and damping of the NES impact the energy capturing efficiency of the NES-EH; the smaller the damping and nonlinear stiffness, the higher the power captured by electromagnetic damping in the NES-EH. Compared with NES, the NES-EH system has a better effect on the vibration control of the platform and can better capture considerable vibration energy.

Impacts of sea level rise and typhoon intensity on storm surges and waves around the coastal area of Qingdao

Climate changes, including sea level rise (SLR) and typhoon intensification (TI), have been widely accepted in coastal communities and significantly affect coastal engineering. In this work, an integrally-coupled tide-surge-wave model was developed to simulate storm tides and waves around the coastal area of Qingdao. The model was validated with observed data under historical typhoon events. The simulated results illustrate that tides change obviously at most representative stations within Jiaozhou Bay. Meanwhile, the effect of SLR on astronomical tide in the flood and the ebb period is more significant than that of the peak tide period. Further investigations reveal that SLR and TI affect storm tides and waves in different ways and the influences are different within Jiaozhou Bay and along the open coast. Besides, the combined effects of SLR and TI on peak storm tides and wave heights are remarkable, which are not a simply linear superposition and present a spatially non-uniform and non-liner pattern. Therefore, it is essential to adopt the coupled model to estimate the possible maximum risk of storm surges and waves around the coastal area of Qingdao. Taking SLR and TI into consideration, the peak of elevation near shore could experience a significant amplification in the future.

Vulnerability Analysis of Episodic Beach Erosion by Applying Storm Wave Scenarios to a Shoreline Response Model

Recently, because of the influence of climate change on sea level change, there has been growing concern regarding the erosion of beaches, which play a role in reducing the damage caused by coastal disasters. However, despite these concerns, a comprehensive understanding of the morphodynamic relationship between hazard factors and beach erosion is still lacking. Therefore, in this study, a vulnerability analysis of beach erosion was conducted by applying the shoreline response model (SLRM) of bulk model type, which identifies the physical characteristics of relevant coefficients based on the suspended sediment movement processes. To characterize wave energy incidence, storm wave scenario modeling and extreme wave analysis were conducted using wave data of 40 years on the east coast of Korea provided by the National Oceanic and Atmospheric Administration. A dimensionless mathematical function representing the storm wave scenario was proposed as a function of the peak wave height. In addition, to examine whether the beach vulnerability curve (BVC) obtained from the SLRM is valid, it was compared with the long-term shoreline observation data conducted at Maengbang Beach. For the past 9 years, sand sampling and shoreline observations were performed at Maengbang Beach about 5 times a year. However, since observations were performed in time intervals of several months, the direct comparison with model results was impossible, so a comparative analysis through statistical analysis of shoreline variability was performed. The variability of the shoreline for each reference point followed a normal distribution with a standard deviation of approximately 7.1 m. As a result of comparing the BVC results obtained from these statistical characteristics with those obtained from the model, significant similarity was shown in the high wave condition. Finally, the model was performed on two factors (mean wave height and peak wave height) which appear in SWSF and three factors (wave energy at breaking point, beach response factor and beach recovery factor) which appear in SLRM, and by analyzing the results, an approximate formula for the BVC is derived. This novel BVC approximation equation provides an intuitive understanding of the factors that affect beach vulnerability as well as their importance, and estimates the beach buffer section required to prevent coastal facilities from being damaged by erosion during a specific period. The results of this study can help limit reckless coastal development and mitigate erosion damage.

Shoreline Variation Analysis by Cross-Shore Sediment Transport Resulting from Effects of Storm Waves

Kim, T.K.; Jeong, J.H., and Lee, J.L., 2021. Shoreline variation analysis by cross-shore sediment transport resulting from effects of storm waves. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 539–543. Coconut Creek (Florida), ISSN 0749-0208. Coastal beach erosion is affected by not only the wave energy of a storm wave, but also its duration. Therefore, this study analyzes the duration characteristics for different storm wave scenarios using wave data obtained over 40 years; these data were provided by the National Oceanic and Atmospheric Administration (NOAA). Further, the vulnerability of shoreline erosion deduced from the correlation between the cumulative breaking wave energy and observed shoreline variability was discussed. To analyze the duration of storm wave scenarios, we propose dimensionless characteristics for peak wave height per storm wave scenario and a representative mathematical function for storm wave scenarios. Shoreline variability is calculated using the shoreline survey data for Bongpo Beach, located on the eastern coast of South Korea, measured quarterly for nine years. The cumulative breaking wave energy flowing into the beach generally exhibited a linear relationship with the shoreline variability. Therefore, this study suggests a simple method to determine the extent to which the shoreline retreats given the peak wave height of the incoming wave scenario.

Observation of nearshore crescentic sandbar formation during storm wave conditions using satellite images and video monitoring data

Crescentic nearshore sandbars (CNSBs) that are observed in the shallow waters (< 10 m) of sandy beaches are important for understanding coastal dynamics because of their strong interaction with nearshore circulation. However, their formation, originating from shore-parallel straight nearshore sandbars (SNSBs), has rarely been observed in the field because their occurrence is typically short (less than a week). In this study, a process in which a nearly SNSB changed into a fully developed CNSB was observed using satellite images, field surveys, and video monitoring data at a sandy beach in South Korea. Freely available Sentinel-2 satellite images and the bathymetry data measured by echosounders were used to find out formation of an SNSB system after attack of Typhoon Tapah in September 2019 and that the SNSB changed to a CNSB in February 2020. The process was narrowed down using video monitoring data and hydrodynamic measurements, observing that two storm waves with maximum wave heights of >3 m developed in the site over a one-month period in January 2020 when the CNSB formed. The first storm wave had a sharp peak wave height that reached ~5 m and lasted ~2 days. The second storm wave had lower wave energy but several peak waves of ~4 m height and a total storm period of ~6 days. During both storm periods, the infragravity wave energy increased and strong (>0.5 m/s) offshore and longshore (northwest) currents developed for ~1 day and ~ 3 days for the first and second storm respectively. The results from video monitoring data show that a nearly developed SNSB system transformed into a weakly developed CNSB system after the first storm when alongshore variability on the nearly SNSB was intensified to become horns and bays of the weak CNSB. During the second storm, the CNSB system fully developed as the horns moved further onshore and the bays further offshore shaping the clear horn and bay pattern. This indicates that positive feedback between the flows and sediments played a key role for the formation of the CNSB and, therefore, the self-organization mechanism might be appropriate to describe the process during the two storm periods. Specifically, the high infragravity wave energy and strong quasi-steady currents were important because they could trigger the development of rip channels during the first storm whereas the channels were further strengthened by the long consistency of currents during the second storm.

Sensitivity of Tsunami Scenarios to Complex Fault Geometry and Heterogeneous Slip Distribution: Case‐Studies for SW Iberia and NW Morocco

AbstractThe SW Iberian margin is one of the most seismogenic and tsunamigenic areas in W‐Europe, where large historical and instrumental destructive events occurred. To evaluate the sensitivity of the tsunami impact on the coast of SW Iberia and NW Morocco to the fault geometry and slip distribution for local earthquakes, we carried out a set of tsunami simulations considering some of the main known active crustal faults in the region: the Gorringe Bank (GBF), Marquês de Pombal (MPF), Horseshoe (HF), North Coral Patch (NCPF) and South Coral Patch (SCPF) thrust faults, and the Lineament South strike‐slip fault. We started by considering for all of them relatively simple planar faults featuring with uniform slip distribution; we then used a more complex 3D fault geometry for the faults constrained with a large 2D multichannel seismic dataset (MPF, HF, NCPF, and SCPF); and finally, we used various heterogeneous slip distributions for the HF. Our results show that using more complex 3D fault geometries and slip distributions, the peak wave height at the coastline can double compared to simpler tsunami source scenarios from planar fault geometries. Existing tsunami hazard models in the region use homogeneous slip distributions on planar faults as initial conditions for tsunami simulations and therefore underestimate tsunami hazard. Complex 3D fault geometries and non‐uniform slip distribution should be considered in future tsunami hazard updates. The tsunami simulations also support the finding that submarine canyons attenuate the wave height reaching the coastline, while submarine ridges and shallow shelves have the opposite effect.

Combined Oscillating Water Column & hydrogen electrolysis for wave energy extraction and management. A case study: The Port of Motril (Spain)

This paper presents a theoretical novel approach to a marine infrastructure, which jointly uses an OWC (Oscillating Water Column) and hydrogen electrolysis as a clean source of primary conversion for energy management, capable to satisfy a continuous designed demand. A case study in the Port of Motril (Southern Spain) is proposed in order to analyze the performance of the power plant. The assessment covers the sale and management profits from the harvested energy from waves in the electricity market, and from the electrolysis of the oceanic water H2O plus dissolved salts μ into hydrogen H2, oxygen O2 and salts μ components, also known as green hydrogen.The investment analysis of the project is conducted through the dynamic financial index Net Present Value (NPV), using Monte Carlo techniques to determine the repayment period. The results are consistent, showing that the plant could supply the annual electricity demand of 356 people with a short repayment period. The amount of energy depends on peak periods Tp and wave heights Hs, which means that other locations could be found so as to improve the performance of the plant in terms of productions of energy and demand supply.

Constructal Design Applied to Geometric Shapes Analysis of Wave Energy Converters

This paper deals with numerical simulation and the geometrical analysis of an ocean Wave Energy Converter (WEC), which has as the operating principle the Oscillating Water Column (OWC). The goal was to evaluate the geometric shape influence of the OWC chamber in the hydropneumatic power available. Therefore, four geometric shapes were analyzed: i) Rectangle (RT), ii) Trapezium (TP), iii) Inverted Trapezium (TI) and iv) Double Trapezium (DT). For this, the OWC device was subject to a JONSWAP wave spectrum with peak period (TS) equal to 7.5 s and peak wave height (HS) equal to 1.5 m. To do so, Constructal Design was employed varying the Degree Of Freedom (DOF) H1/L (ratio between the height and length of the OWC chamber entrance). The problem constraints were the entrance area and the total area of the OWC chamber that were kept constant. For the numerical solution a Computational Fluid Dynamics (CFD) code, based on the Finite Volume Method (FVM),de0 was used. The multiphase Volume of Fluid (VOF) model was applied to tackle with the water-air interaction. The results indicated that when the Rectangle (RT) geometrical shape was employed an improvement of nearly 99% was achieved.

On the Sensitivity of Typhoon Wave Simulations to Tidal Elevation and Current

The sensitivity of storm wave simulations to storm tides and tidal currents was investigated using a high-resolution, unstructured-grid, coupled circulation-wave model (Semi-implicit Cross-scale Hydroscience Integrated System Model Wind Wave Model version III (SCHISM-WWM-III)) driven by two typhoon events (Typhoons Soudelor and Megi) impacting the northeastern coast of Taiwan. Hourly wind fields were acquired from a fifth-generation global atmospheric reanalysis (ERA5) and were used as meteorological conditions for the circulation-wave model after direct modification (MERA5). The large typhoon-induced waves derived from SCHISM-WWM-III were significantly improved with the MERA5 winds, and the peak wave height was increased by 1.0–2.0 m. A series of numerical experiments were conducted with SCHISM-WWM-II and MERA5 to explore the responses of typhoon wave simulations to tidal elevation and current. The results demonstrate that the simulated significant wave height, mean wave period and wave direction for a wave buoy in the outer region of the typhoon are more sensitive to the tidal current but less sensitive to the tidal elevation than those for a wave buoy moored in the inner region of the typhoon. This study suggests that the inclusion of the tidal current and elevation could be more important for typhoon wave modeling in sea areas with larger tidal ranges and higher tidal currents. Additionally, the suitable modification of the typhoon winds from a global atmospheric reanalysis is necessary for the accurate simulation of storm waves over the entire region of a typhoon.

Frequency domain prediction of peak nonlinear wave heights of structure-TLD systems

Prediction of peak wave heights early in the TLD design process is critical to ensure proper tank freeboard is allocated. If insufficient freeboard is allocated, the performance of the TLD may be adversely affected by the waves impacting with the tank ceiling. A frequency domain model is developed to predict the spectral response of the first two TLD sloshing modes. A probability density function of the wave height envelop for the first two sloshing modes is derived and employed to predict the peak wave height expected during a specified duration of time.Scale-model structure-TLD tests and nonlinear simulations are employed to evaluate the proposed frequency domain model. The model predicts the RMS response of the second order sloshing mode within a relative error of 15% when compared to simulations. The error increases when the water depth ratio is small. The predicted peak structural responses are in excellent agreement with those that are simulated or measured. The predicted peak TLD wave heights show a maximum error of 20% for all the cases considered. The peak factor relating the peak wave height to the RMS response of the fundamental sloshing mode increases with a decreasing liquid depth and increasing RMS response amplitude. The proposed model enables a rapid estimation of the peak wave response without resorting to computationally expensive nonlinear time domain simulations.

Study of an Electromagnetic Ocean Wave Energy Harvester Driven by an Efficient Swing Body Toward the Self-Powered Ocean Buoy Application

Ocean wave is one of the promising renewable energy sources all around the world. In this paper, an electromagnetic ocean wave energy harvester (OWEH) based on efficient swing body mechanism is presented. A swing body senses the ultra-low frequency wave motion and drive the rotor of an electromagnetic power module (EPM) rotating at high speed through transmission gears. A series of electromagnetic and dynamic simulations were carried out to optimize the power generation capability of the OWEH. Additionally, the power management circuit is specially designed such that the generated power is able to charge a lithium battery and discharge an external load automatically. The OWEH is installed inside an ocean buoy and tested in the Yellow China Sea. When the peak wave height is greater than 0.6 m, the maximum peak-to-peak output voltage is 15.9 V. The corresponding output power is as high as 0.13 W and the maximum power density is 0.21 mW/cm 3 , where the internal resistance of the OWEH is 122 Ω. Due to the high performance and adaptability, the OWEH can potentially power many low power components, which opens a promising way for improving the life of ocean buoys. Considering the small dimension of 10 × 10 × 6.3 cm 3 , this OWEH can be mounted inside most buoys easily and realize the self-powered ocean buoys in the near future.

Assessment of the peak tsunami amplitude associated with a large earthquake occurring along the southernmost Ryukyu subduction zone in the region of Taiwan

Abstract. The southernmost portion of the Ryukyu Trench near the island of Taiwan potentially generates tsunamigenic earthquakes with magnitudes from 7.5 to 8.7 through shallow rupture. The fault model for this potential region dips 10∘ northward with a rupture length of 120 km and a width of 70 km. An earthquake magnitude of Mw 8.15 is estimated by the fault geometry with an average slip of 8.25 m as a constraint on the earthquake scenario. Heterogeneous slip distributions over the rupture surface are generated by a stochastic slip model, which represents the decaying slip spectrum according to k−2 in the wave number domain. These synthetic slip distributions are consistent with the abovementioned identical seismic conditions. The results from tsunami simulations illustrate that the propagation of tsunami waves and the peak wave heights largely vary in response to the slip distribution. Changes in the wave phase are possible as the waves propagate, even under the same seismic conditions. The tsunami energy path not only follows the bathymetry but also depends on the slip distribution. The probabilistic distributions of the peak tsunami amplitude calculated by 100 different slip patterns from 30 recording stations reveal that the uncertainty decreases with increasing distance from the tsunami source. The highest wave amplitude for 30 recording points is 7.32 m at Hualien for 100 different slips. Compared with the stochastic-slip distributions, the uniform slip distribution will be highly underestimated, especially in the near field. In general, the uniform slip assumption only represents the average phenomenon and will consequently ignore the possibility of tsunami waves. These results indicate that considering the effects of heterogeneous slip distributions is necessary for assessing tsunami hazards to provide additional information about tsunami uncertainties and facilitate a more comprehensive estimation.

Nonlinear modelling of tuned sloshing dampers with large internal obstructions: Damping and frequency effects

Internal obstructions are commonly employed in tuned sloshing damper (TSD) tanks to increase the inherent damping of the sloshing liquid closer to its optimal value for the targeted excitation amplitude. However, these obstructions also produce added mass, which acts to decrease the natural sloshing frequency of the tank. Using potential flow theory, this study develops both a linearized equivalent mechanical model and a fourth-order nonlinear multimodal model that are capable of accommodating the fluid drag and added mass that are generated by the paddles. The linearized equivalent mechanical model represents the sloshing liquid as an equivalent spring–mass–dashpot system with amplitude-dependent damping. The fourth-order nonlinear multimodal model captures the nonlinear coupling that occurs among the first four sloshing modes. Shake table tests are then conducted on a scale model TSD tank equipped with vertical paddles of cruciform plan section. The sloshing forces predicted by the linearized and nonlinear models are in reasonable agreement with the experimental results. The nonlinear model is generally in good agreement with the experimental wave heights, whereas the linearized model often underestimates the peak wave heights considerably. A plot is created which shows the frequency shift produced by the paddles as a function of the width of the paddles. If the paddles’ widths are greater than approximately 5% of the tank width, the effect on the natural sloshing frequency is noticeable.