Simulation of the extreme waves generated by typhoon Bolaven (1215) in the East China Sea and Yellow Sea

Record-breaking high waves occurred during the passage of the typhoon Bolaven（1215）（TYB） in the East China Sea（ECS） and Yellow Sea（YS） although its intensity did not reach the level of a super typhoon.Winds and directional wave measurements were made using a range of in-situ instruments mounted on an ocean tower and buoys.In order to understand how such high waves with long duration occurred,analyses have been made through measurement and numerical simulations.TYB winds were generated using the TC96 typhoon wind model with the best track data calibrated with the measurements.And then the wind fields were blended with the reanalyzed synoptic-scale wind fields for a wave model.Wave fields were simulated using WAM4.5 with adjustment of C_d for gust of winds and bottom friction for the study area.Thus the accuracy of simulations is considerably enhanced,and the computed results are also in better agreement with measured data than before.It is found that the extremely high waves evolved as a result of the superposition of distant large swells and high wind seas generated by strong winds from the front/right quadrant of the typhoon track.As the typhoon moved at a speed a little slower than the dominant wave group velocity in a consistent direction for two days,the wave growth was significantly enhanced by strong wind input in an extended fetch and non-linear interaction.

Numerical modelling of nonlinear extreme waves in presence of wind

A numerical wave flume with fully nonlinear free surface boundary conditions is adopted to investigate the temporal characteristics of extreme waves in the presence of wind at various speeds. Incident wave trains are numerically generated by a piston-type wave maker, and the wind-excited pressure is introduced into dynamic boundary conditions using a pressure distribution over steep crests, as defined by Jeffreys＇ sheltering mechanism.A boundary value problem is solved by a higher-order boundary element method（HOBEM） and a mixed Eulerian-Lagrangian time marching scheme. The proposed model is validated through comparison with published experimental data from a focused wave group. The influence of wind on extreme wave properties,including maximum extreme wave crest, focal position shift, and spectrum evolution, is also studied. To consider the effects of the wind-driven currents on a wave evolution, the simulations assume a uniform current over varying water depth. The results show that wind causes weak increases in the extreme wave crest, and makes the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide a comparison to demonstrate the shifts at focal points, considering the combined effects of the winds and the wind-driven currents.

Experimental Investigation on the Extreme Waves Induced by Single Wave Packets in Finite Water Depth

Single Gaussian wave groups with different initial wave steepness εand width N are produced in laboratory in finite depth to study the nonlinear evolution, the extreme events and breaking. The results show that wave groups with larger εwill evolve to be several envelope solitons(short wave groups). By analyzing geometric parameters, a break in the evolution of the wave elevation and asymmetric parameters after extreme wave may be an indicator for the inception of refocus and the maximal wave moving to the middle, namely, wave down-shift occurs. The analysis of the surface elevations with HHT(Hilbert-Huang Transform), which presents the concrete local variation of energy in time and frequency can be exhibited clearly, reveals that the higher frequency components play a major role in forming the extreme event and the contribution to the nonlinearity. Instantaneous energy and frequency in the vicinity of the extreme wave are also examined locally. For spilling breakers, the energy residing in the whole wave front dissipates much more due to breaking, while the energy in the rear of wave crest loses little, and the intra-wave frequency modulation increases as focus. It illustrates that the maximal first order instantaneous frequency fand the largest crest tend to emerge at the same time after extreme wave when significant energy dissipation happens, and vice versa. In addition, it shows that there is no obvious relation of the CDN(combined degree of nonlinearity) to the wave breaking for the single Gaussian wave group in finite water depth.

Harmonic Energy Transfer for Extreme Waves in Current

Ning et al. （2015） developed a 2D fully nonlinear potential model to investigate the interaction between focused waves and uniform currents. The effects of uniform current on focusing wave crest, focal time and focal position were given. As its extension, harmonic energy transfer for focused waves in uniform current is studied using the proposed model by Ning et al. （2015） and Fast Fourier Transformation （FFT） technique in this study. It shows that the strong opposing currents, inducing partial wave blocking and reducing the extreme wave crest, make the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide an explanation to address the shifts of focal points in consideration of the combination effects of wave nonlinearity and current.

A numerical investigation of interactions between extreme waves and a vertical cylinder

In this paper,the interactions between extreme waves and a vertical cylinder are investigated through a 3-D two-phase flow model.The numerical model is verified and validated by experimental data.Then,two factors are considered,the global wave steepness and the frequency bandwidth of the wave groups,in the studies of the in-line wave forces and the wave run-up around a cylinder.It is found that both the in-line wave forces and the wave run-up are remarkably increased with the increase of the global wave steepness,whereas the effect of the frequency bandwidth on the in-line wave forces is relatively weak in comparison with its effect on the wave run-up.The minimum and maximum wave run-ups are located in the directions of 22.5°and 180°with respect to the direction of the incident waves,respectively.Additionally,a new empirical formula is proposed for predicting the in-line wave forces by using only the free surface elevations around the cylinder.The results of the formula agree well with the simulation results.

Impacts of climate change on seasonal extreme waves in the Northwest Atlantic using a Spatial Neural Gas clustering method

Having estimates of wave climate parameters and extreme values play important roles for a variety of different societal activities,such as coastal management,design of inshore and offshore structures,marine transport,coastal recreational activities,fisheries,etc.This study investigates the efficiency of a state-of-the-art spatial neutral gas clustering method in the classification of wind/wave data and the evaluation of extreme values of significant wave heights(Hs),mean wave direction(MWD)and mean wave periods(T0)for two 39-year time periods;from 1979 to 2017 for the present climate,and from 2060 to 2098,for a future climate change scenario in the Northwest Atlantic.These data were constructed by application of a numerical model,WAVEWATCHIII TM(hereafter,WW3),to simulate the wave climate for the study area for both present and future climates.Data from the model was extracted for the wave climate,in terms of the wave parameters,specifically Hs,MWD and T0,which were analyzed and compared for winter and summer seasons,for present and future climates.In order to estimate extreme values in the study area,a Natural Gas(hereafter,NG)clustering method was applied,separate clusters were identified,and corresponding centroid points were determined.To analyze data at each centroid point,time series of wave parameters were extracted,and using standard stochastic models,such as Gumbel,exponential and Weibull distribution functions,the extreme values for 50 and 100-year return periods were estimated.Thus,the impacts of climate change on wave regimes and extreme values can be specified.

Long-Term Extreme Wave Characteristics in the Water Adjacent to China Based on ERA5 Reanalysis Data

Extreme waves have a profound impact on coastal infrastructure;thus,understanding the variation law of risky analysis and disaster prevention in coastal zones is necessary.This paper analyzed the spatiotemporal characteristics of extreme wave heights adjacent to China from 1979 to 2018 based on the ERA5 datasets.Nonstationary extreme value analysis is undertaken in eight repre-sentative points to investigate the trends in the values of 50-and 100-year wave heights.Results show that the mean value of extreme waves is the largest in the eastern part of Taiwan Island and the smallest in the Bohai Sea from 1979 to 2018.Only the extreme wave height in the northeastern part of Taiwan Island shows a significant increase trend in the study area.Nonstationary analysis shows remarkable variations in the values of 50-and 100-year significant wave heights in eight points.Considering the annual mean change,E1,E2,S1,and S2 present an increasing trend,while S3 shows a decreasing trend.Most points for the seasonal mean change demon-strate an increasing trend in spring and winter,while other points show a decreasing trend in summer and autumn.Notably,the E1 point growth rate is large in autumn,which is related to the change in typhoon intensity and the northward movement of the typhoon path.

Resilience of coastal bridges under extreme wave-induced loads

Records of wave-induced damage on coastal bridges during natural hazards have been well documented over the past two decades.It is of utmost importance to decipher the loading mechanism and enhance the resilience of coastal bridges during extreme wave-inducing events.Quantification of vulnerability of these structures is an essential step in designing a resilient bridge system.Recently,considerable efforts have been made to study the force applied and the response of coastal bridge systems during extreme wave loading conditions.Although remarkable progress can be found in the quantification of load and response of coastal superstructures,very few studies assessed coastal bridge resiliency against extreme wave-induced loads.This paper adopts a simplified and practical technique to analyze and assess the resilience of coastal bridges exposed to extreme waves.Component-level and system-level fragility analyses form the basis of the resiliency analysis where the recovery functions are adopted based on the damage levels.It is shown that wave period has the highest contribution to the variation of bridge resiliency.Moreover,this study presents the uncertainty quantification in resiliency variation due to changes in wave load intensity.Results show that the bridge resiliency becomes more uncertain as the intensity of wave parameters increases.Finally,possible restoration strategies based on the desired resilience level and the attitude of decision-makers are also discussed.

A simplified model for extreme-wave kinematics in deep sea

Based on the fifth-order Stokes regular wave theory, a simplified model for extreme-wave kinematics in deep sea was developed. In this model, from the wave records the average of two neighboring wave periods for the extreme crest or trough was defined as the period of the Stokes wave by the up and down zero-crossing methods. Then the input wave amplitude was deduced by substituting the wave period and extreme crest or trough into the expression for the fifth-order Stokes wave elevation. Thus the corresponding formula for the wave velocity can be used to describe kinematics beneath the extreme wave. By comparison with the published numerical models and experimental data, the proposed model is validated to be able to calculate the extreme wave velocity rather easily and accurately.

Numerical Modelling of Waves and Surge from Cyclone Mekunu (May 2018) in the Arabian Sea

Cyclone Mekunu developed in the Arabian Sea on 22 May 2018 and made landfall near the Port of Salalah(Oman)on 25 May.Wide spread damages to properties and coastal facilities and human casualties were reported in Yemen and Oman.Less information on numerical modelling of waves and surge is publicly available on this cyclone.Therefore,numerical modelling of Cyclone Mekunu was carried out in the present study to derive waves and storm surge.The MIKE21 Spectral Wave Model and the Flow Model were used in coupled mode to simulate the waves and surge from the cyclone.Model results of waves and surge are presented in this paper for illustration purposes.The methodology of the present study can be used to simulate any cyclone around the world.

Analysis of the pressure at a vertical barrier due to extreme wave run-up over variable bathymetry

The pressure load at a vertical barrier caused by extreme wave run-up is analysed numerically, using the conformal mapping method to solve the two-dimensional free surface Euler equations in a pseudospectral model. Previously this problem has been examined in the case of a flat-bottomed geometry. Here,the model is extended to consider a varying bathymetry. Numerical experiments show that an increasing step-like bottom profile may enhance the extreme run-up of long waves but result in a reduced pressure load.

Estimation of Extreme Coastal Wave Heightsfrom Time Series of Wave Data

A method is presented to extrapolate a time series of wave data to extreme wave heights. The 15-year time series of deepwater wave data collected for 34 min every hour from 1988 to 2002 in the South Pacific Ocean, Australia, is analyzed to generate a set of storm peak wave heights by use of the Peaks-Over-Threshold method. The probability distribution is calculated by grouping the observod storm peak wave heights into a number of wave height classes and assigning a probability to each wave height class. The observed probability distribution is then fitted to eight different probability distribution functions and found to be fitted best by the Weibull distribution （a = 1.17）, nearly best by the FT-Ⅰ, quite well by the exponential, and poorly by the lognormal function based on the criterion of the sum of squares of the errors, SSE （H）. The effect of the threshold wave height on the estimated extreme wave height is also studied and is found insignificant in this study. The 95 % prediction intervals of the best-fit FT-Ⅰ , exponential and Weibull functions are also derived.

A Statistical Linkage between Extreme Cold Wave Events in Southern China and Sea Ice Extent in the Barents-Kara Seas from 1289 to 2017

Arctic sea ice loss and the associated enhanced warming has been related to midlatitude weather and climate changes through modulate meridional temperature gradients linked to circulation. However, contrasting lines of evidence result in low confidence in the influence of Arctic warming on midlatitude climate. This study examines the additional perspectives that palaeoclimate evidence provides on the decadal relationship between autumn sea ice extent (SIE) in the Barents-Kara (B-K) Seas and extreme cold wave events (ECWEs) in southern China. Reconstruction of the winter Cold Index and SIE in the B-K Seas from 1289 to 2017 shows that a significant anti-phase relationship occurred during most periods of decreasing SIE, indicating that cold winters are more likely in low SIE years due to the “bridge” role of the North Atlantic Oscillation and Siberian High. It is confirmed that the recent increase in ECWEs in southern China is closely related to the sea ice decline in the B-K Seas. However, our results show that the linkage is unstable, especially in high SIE periods, and it is probably modulated by atmospheric internal variability.

A Refined Method for Estimating the Annual Extreme Wave Heights at A Project Site

This paper presents a refined method for estimating the annual extreme wave heights at a coastal or offshore project site on the basis of the data acquired at some nearby routine hydrographic stations. This method is based on the orthogonality principle in linear mean square estimation of stochastic processes. The error of the method is analyzed and compared with that of the conventional method. It is found that the method is able to effectively reduce the error so long as some feasible measures are adopted. A simulated test of the method has been conducted in a large scale wind wave flume. The test results are in good agreement with those given by theoretical error analysis. A scheme to implement the method is proposed on the basis of error analysis. The scheme is so designed as to reduce the estimation error as far as possible. This method is also suitable to utilizing satellite wave data for the estimation.

Nonlinear numerical simulation on extreme-wave kine-matics

A fully nonlinear numerical model based on a time-domain higher-order boundary element method （HOBEM） is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary conditions are satisfied and a semi-mixed Euler-Lagrange method is used to track free surface; a fourth-order Runga-Kutta technique is adopted to refresh the wave elevation and velocity potential on the free surface at each time step; an image Green function is used in the numerical wave tank so that the integrations on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the measured point, numerical solutions agree well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.

Modeling nonstationary extreme wave heights in present and future climates of Greek Seas

In this study the generalized extreme value （GEV） distribution function was used to assess nonstationarity in annual maximum wave heights for selected locations in the Greek Seas, both in the present and future climates. The available significant wave height data were divided into groups corresponding to the present period （1951-2000）, a first future period （2001-2050）, and a second future period （2051-2100）. For each time period, the parameters of the GEV distribution were specified as functions of time-varying covariates and estimated using the conditional density network （CDN）. For each location and selected time period, a total number of 29 linear and nonlinear models were fitted to the wave data, for a given combination of covariates. The covariates used in the GEV-CDN models consisted of wind fields resulting from the Regional Climate Model version 3 （RegCM3） developed by the International Center for Theoretical Physics （ICTP） with a spatial resolution of 10 km ×10 km, after being processed using principal component analysis （PCA）. The results obtained from the best fitted models in the present and future periods for each location were compared, revealing different patterns of relationships between wind components and extreme wave height quantiles in different parts of the Greek Seas and different periods. The analysis demonstrates an increase of extreme wave heights in the first future period as compared with the present period, causing a significant threat to Greek coastal areas in the North Aegean Sea and the Ionian Sea.

Response Spectrum Method for Extreme Wave Loading With Higher Order Components of Drag Force

Response spectra of fixed offshore structures impacted by extreme waves are investigated based on the higher order components of the nonlinear drag force. In this way, steel jacket platforms are simplified as a mass attached to a light cantilever cylinder and their corresponding deformation response spectra are estimated by utilizing a generalized single degree of freedom system. Based on the wave data recorded in the Persian Gulf region, extreme wave loading conditions corresponding to different return periods are exerted on the offshore structures. Accordingly, the effect of the higher order components of the drag force is considered and compared to the linearized state for different sea surface levels. When the fundamental period of the offshore structure is about one third of the main period of wave loading, the results indicate the linearized drag term is not capable of achieving a reliable deformation response spectrum.

Extreme Wave Simulation with Iterative Adaptive Approach in Numerical Wave Flume

Extreme wave is highly nonlinear and may occur due to diverse reasons unexpectedly.The simulated results of extreme wave based on wave focusing,which were generated using high order spectrum method,are presented.The influences of the steepness,frequency bandwidth as well as frequency spectrum on focusing position shift were examined,showing that they can affect the wave focusing significantly.Hence,controlled accurate generation of extreme wave at a predefined position in wave flume is a difficult but important task.In this paper,an iterative adaptive approach is applied using linear dispersion theory to optimize the control signal of the wavemaker.The performance of the proposed approach is numerically investigated for a wide variety of scenarios.The results demonstrate that this approach can reproduce accurate wave focusing effectively.

A METHOD FOR DETERMINING EXTREME WAVE HEIGHT

A method to determine the design value of the extreme wave height is introduced in this paper. The method is, based on the theoretical distribution of wave heights or the experiential probability distribution of wave heights, to calculate the mode of the extreme wave height and the design value with good assuredness. In fitting the experiential distribution of the observed wave heights, the paper adopts the simulating function of F(x) = 1 - exp[ ?axb exp( -cxd )] and the non-linear parameter in the function is determined by the Non-Linear Least Square Method. The practical application of the method has proved that it is not only simple and convenient, but also very effective in engineering design practice.

Cyclone and Tsunami Hazards in the Arabian Sea-A Numerical Modelling Case Study by Royal HaskoningDHV

Significant loss of life and damage to properties, ecosystems and marine facilities occur due to various natural hazards such as cyclones and tsunamis. Royal HaskoningDHV has developed regional hydrodynamic and wave models covering the Northern Arabian Sea to address these issues. Cyclone modelling was carried out on 11 major cyclones since 1945 and the tsunami modelling on an earthquake along the Makran Fault Line in 1945. Sample results from these modelling studies are presented in this paper. The methodology described in this article for modelling cyclones and tsunamis in the Arabian Sea could be applied to simulate these natural hazards at other sites around the world.