Prediction of safe sea-state using finite element method and artificial neural networks

This article proposes a predictive method for identifying the range of sea-states considered safe for the installation of offshore structures. A finite element dynamic analysis of the system for various sea-states characterized by significant wave heights and mean zero-up-crossing wave periods and modeled as a combination of several wave components has been performed. Using this procedure a table of safe and unsafe sea-states is generated. The significant wave height (H_s) and mean zero-up-crossing wave period (T_z) of a future sea-state in a location in the north east Pacific were predicted from the distributions whose parameters were estimated using the artificial neural networks (ANNs) trained for this purpose. The location of US National Oceanographic Data Center (NODC) Buoy 46005 is used in this study.The H_s and T_z of some future sea-states were predicted from their corresponding conditional 7-parameter distribution given some information including a number of previously measured H_s’s and T_z’s. This gives a predicted sea-state for a specific time in future. The parameters of the distributions have been estimated from the outputs of two different 7-network sets of trained ANNs. A pile-driving operation is used as a case study in which the pile configuration, including the non-linear foundation and the gap between the pile and the pile sleeve shims, has been modeled by the finite elements method and the range of sea-states suitable for safe pile-driving operation was identified.     

Wave climate off northern Norway

The wave climate off northern Norway is considered and the investigation is based on wave measurements made at Tromsøflaket by means of a waverider buoy during the years 1977–1981. Data quality of waverider measurements is briefly commented upon; however, more emphasis is given to an evaluation of the long-term representativity of the actual measuring period and to a procedure accounting approximately for a lack of representativity. The wave climate is presented in terms of a smoothed joint probability density function of the significant wave height, H_s, and the spectral peak period, T_p. Based on this distribution a consistent design curve in the H_s, T_p space is established.     

Evaluation of two WAM white capping parameterizations using parallel unstructured SWAN with application to the Northern Gulf of Mexico, USA

The performance of two well accepted formulations for white capping and wind input of third generation wave models, viz., WAM-3 and WAM-4, were investigated using parallel unstructured SWAN (PunSWAN). Several alternative formulations were also considered to evaluate the effects of higher order steepness and wave number terms in white capping formulations. Distinct model configurations were calibrated and validated against available in situ measurements from the Gulf of Mexico. The results showed that some of the in situ calibrated models outperform the saturation level calibrated models in reproducing the idealized wave growth curves. The simulation results also revealed that increasing the power of the steepness term can enhance the accuracy of significant wave height (H_s), at the expense of a higher bias for large waves. It also has negative effects on mean wave period (T_a) and peak wave period (T_p). It is also demonstrated that the use of the quadratic wave number term in the WAM-3 formulation, instead of the existing linear term, ameliorates the T_a underestimation; however, it results in the model being unable to reach any saturation level. In addition, unlike H_s and T_p, it has been shown that T_a is sensitive to the use of the higher order WAM-4 formulation, and the bias is decreased over a wide range of wave periods. However, it also increases the scatter index (SI) of simulated T_a. It is concluded that the use of the WAM-4 wind input formulation in conjunction with the WAM-3 dissipation form, is the most successful case in reproducing idealized wave growth curves while avoiding T_a underestimation of WAM-3 and a potential spurious bimodal spectrum of WAM-4; consequently, this designates another perspective to improve the overall performance of third generation wave models.     

Storm evolution characterization for analysing stone armour damage progression

Storm evolution is fundamental for analysing the damage progression of the different failure modes and establishing suitable protocols for maintaining and optimally sizing structures. However, this aspect has hardly been studied and practically the whole of the studies dealing with the subject adopt the Equivalent triangle storm. As against this approach, two new ones are proposed. The first is the Equivalent Triangle Magnitude Storm model (ETMS), whose base, the triangular storm duration, D, is established such that its magnitude (area describing the storm history above the reference threshold level which sets the storm condition), H_T, equals the real storm magnitude. The other is the Equivalent Triangle Number of Waves Storm (ETNWS), where the base is referred in terms of the real storm's number of waves, N_z. Three approaches are used for estimating the mean period, T_m, associated to each of the sea states defining the storm evolution, which is necessary to determine the full energy flux withstood by the structure in the course of the extreme event. Two are based on the Jonswap spectrum representativity and the other uses the bivariate Gumbel copula (H_s, T_m), resulting from adjusting the storm peaks. The representativity of the approaches proposed and those defined in specialised literature are analysed by comparing the main armour layer's progressive loss of hydraulic stability caused by real storms and that relating to theoretical ones. An empirical maximum energy flux model is used for this purpose. The agreement between the empirical and theoretical results demonstrates that the representativity of the different approaches depends on the storm characteristics and point towards a need to investigate other geometrical shapes to characterise the storm evolution associated with sea states heavily influenced by swell wave components.     

Observation of wave-enhanced turbulence in the near-surface layer of the ocean during TOGA COARE

Dissipation rate statistics in the near-surface layer of the ocean were obtained during the month-long COARE Enhanced Monitoring cruise with a microstructure sensor system mounted on the bow of the research vessel. The vibration contamination was cancelled with the Wiener filter. The experimental technique provides an effective separation between surface waves and turbulence, using the difference in spatial scales of the energy-containing surface waves and small-scale turbulence. The data are interpreted in the coordinate system fixed to the ocean surface. Under moderate and high wind-speed conditions, we observed the average dissipation rate of the turbulent kinetic energy in the upper few meters of the ocean to be 3–20 times larger than the logarithmic layer prediction. The Craig and Banner (J. Phys. Oceanogr. 24 (1994) 2546) model of wave-enhanced turbulence with the surface roughness length from the water side z₀ parameterized according to the Terray et al. (J. Phys. Oceanogr. 26 (1996) 792) formula z₀=cH_s provides a reasonable fit to the experimental dissipation profile, where z is the depth (defined here as the distance to the ocean surface), c≈0.6, and H_s is the significant wave height. In the wave-stirred layer, however, the average dissipation profile deviates from the model (supposedly because of extensive removing of the bubble-disturbed areas close to the ocean surface). Though the scatter of individual experimental dissipation rates (10-min averages) is significant, their statistics are consistent with the Kolmogorov's concept of intermittent turbulence and with previous studies of turbulence in the upper ocean mixed layer.     

Experimental study of unidirectional irregular wave slamming on the three-dimensional structure in the splash zone

The experimental investigation of unidirectional random wave slamming on the three-dimensional structure in the splash zone is presented. The experiment is conducted in the marine environment channel in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology. The test wave is unidirectional irregular wave. The experiments are carried out with perpendicular random waves (β=0°) and oblique random waves (β=15°, 30°, 45°), the significant wave heights H_1/3 ranging from 7.5 to 20 cm with 2.5 cm increment, the peak wave periods T_p ranging from 0.75 to 2.0 s with 0.25 s increment, and the clearance of the model with respect to the significant wave height s/H_1/3 ranging from 0.0 to 0.5 with 0.1 increment. The statistical analysis results of different test cases are presented. The statistical distribution characteristics of the perpendicular irregular wave impact pressures are compared with that of the oblique irregular wave on the underside of the structure. The effect of the wave direction β on the wave impact forces on the underside of the structure is determined. The relation between the impact forces and the parameters such as the significant wave height, the relative structure width and the relative clearance of the structure is also discussed.     

随机波浪中畸形波在三维岛礁地形上的试验研究

在试验水池中，开展了波浪在岛礁地形上演化问题的研究。首先在实验水池中建立了西太平洋某岛礁地形的模型，然后采用改进的JONSWAP谱，由造波机产生不同周期、波高的随机波浪。试验中观察到了不同类型畸形波生成的过程及不同波面形态的畸形波。对偏度、峰度及水深与畸形波要素H_m/H_s（H_m表示波列中的最大波高， H_s为有效波高）的关系进行了详细的分析，同时，对畸形波波高H_fr与偏度的关也进行了分析。通过对试验结果分析，发现峰度与畸形波要素i>H_m/H_s呈正相关， H_fr增大时相应的偏度也会呈现增大的趋势。此外，水深的变化剧烈时（如斜坡、海山位置）有助于畸形波的发生。     

黄渤海海域波浪时空变化特征分析

本文利用欧洲中期预报中心(ECMWF)第五代再分析数据集(ECMWF Reanalysis v5 ERA5,ERA5),对中国黄渤海海域2000-2019年的波浪进行了统计分析。得到如下的结论：1.黄渤海海区波浪具有明显的季节性,渤海区域有效波高呈现出周边小,中间大的特点;黄海海域有效波高Hs呈现由南向北降低的趋势;研究区域冬季有效波高均值大于其他季节。2.平均周期T的季节分布类似于有效波高的季节均值分布。渤海仅秋冬季T的均值存在大于4s的区域;黄海海域T的季节分布也呈现由南向北递减的趋势,其中长江口外海区域秋冬季T的季节均值可达6s。3.有效波高距平场EOF分解结果显示,第一模态表明了波浪变化具有明显的季节性特征;第二模态反映了季风的季节转换对有效波高的影响;第三模态代表的可能是地形的变化对有效波高变化的影响。4．代表点统计结果显示：整个渤海地区的常浪向为 NNE~NE,强浪向以 NE和 NNE 为主;黄海海域的常浪向为SSE-SE向,强浪向以 N和 SSE 为主。     

Joint modelling of wave spectral parameters for extreme sea states

Characterising the dependence between extremes of wave spectral parameters such as significant wave height (H_S) and spectral peak period (T_P) is important in understanding extreme ocean environments and in the design and assessment of marine structures. For example, it is known that mean values of wave periods tend to increase with increasing storm intensity. Here we seek to characterise joint dependence in a straightforward manner, accessible to the ocean engineering community, using a statistically sound approach.Many methods of multivariate extreme value analyses are based on models which assume implicitly that in some joint tail region each parameter is either independent of or asymptotically dependent on other parameters; yet in reality the dependence structure in general is neither of these. The underpinning assumption of multivariate regular variation restricts these methods to estimation of joint regions in which all parameters are extreme; but regions where only a subset of parameters are extreme can be equally important for design. The conditional approach of Heffernan and Tawn (2004), similar in spirit to that of Haver (1985) but with better theoretical foundation, overcomes these difficulties.We use the conditional approach to characterise the dependence structure of H_S and T_P. The key elements of the procedure are: (1) marginal modelling for all parameters, (2) transformation of data to a common standard Gumbel marginal form, (3) modelling dependence between data for extremes of pairs of parameters using a form of regression, (4) simulation of long return periods to estimate joint extremes. We demonstrate the approach in application to measured and hindcast data from the Northern North Sea, the Gulf of Mexico and the North West Shelf of Australia. We also illustrate the use of data re-sampling techniques such as bootstrapping to estimate the uncertainty in marginal and dependence models and accommodate this uncertainty in extreme quantile estimation.We discuss the current approach in the context of other approaches to multivariate extreme value estimation popular in the ocean engineering community.     

Variation of the tidal properties around Gran Canaria

Analysis of water level and current meter series from different locations on the island shelf of Gran Canaria reveals strong variations in tidal properties. Semidiurnal sea level amplitudes agree with the results obtained from global tidal models for this region only on the northern coast of the island, while they decrease towards the southwest (10 cm difference for the M₂ constituent). Semidiurnal currents present maxima at the southeastern and northwestern extremities of the island (30–40 cm s⁻¹ for M₂) and minima in the north-northeast and southwest (3–6 cm s⁻¹ for M₂), showing simultaneous strong changes in the phase. Diurnal levels and currents display smaller variations than the semidiurnal band. The behaviour of semidiurnal constituents is studied with the help of analytical and numerical solutions, in which the incident wave is modelled by a barotropic M₂ Kelvin wave. The results show that the insular shelf could be a source of differences in level amplitudes around the island and could be also responsible for the enhancement of currents in the southeast and northwest. They also show that the variation of the current phases is due to the amplification of the standing character of the wave at the northeastern and southwestern parts of the shelf.     

On the long-term joint distribution of characteristic wave height and period and its application

By analysing the scatter diagrams of characteristic the wave height H and the period T on the basis of instrumental data from various ocean wave stations, we found that the conditional expectation and standard deviation of wave period for a given wave height can be better predicted by using the equations of normal linear regression rather than by those based on the log- normal law. The latter was implied in Ochi' s bivariate log-normal model(Ochi. 1978) for the long-term joint distribution of H and T. With the expectation and standard deviation predicted by the normal linear regression equations and applying proper types of distribution, we have obtained the conditional distribution of T for given H. Then combining this conditional P(T / H) with long-term marginal distribution of the wave height P(H) we establish a new parameterized model for the long-term joint distribution P(H,T). As an example of the application of the new model we give a method for estimating wave period associated with an extreme w     

Tsunamis in the central part of the Caspian Sea

This paper describes the geotectonics of the Caspian Sea basin and the seismicity of its central part. The seismicity analysis enables us to identify the most probable zones of tsunami generation. We also present a brief review of the historical records of tsunamis in the Caspian Sea. In order to estimate the tsunami risk, we used the method of numerical hydrodynamic simulation while taking into account the real topography of the Caspian Sea. The computation of the wave field for the possible tsunamis occurring in the central part of the Caspian Sea allowed us to estimate the maximum expected heights of the waves along the coast of the CIS countries (Russia, Azerbaijan, Kazakhstan, and Turkmenistan). On the basis of the earthquake statistics in the region and the results of numerical experiments, we show that the extreme wave heights can reach 10 m at certain parts of the coast. Such extreme events correspond to extended (up to 200 km) seismic sources with M _S ～ 8 and a recurrence period of T ≈ 1600 years. The tsunami wave heights are expected to be as high as 3 m for sources of lesser extent (<50 km) with earthquake magnitudes of M _S ～ 7 and a recurrence period of 200 years.     

Statistical studies on the wave-form and maximum height of large Tsunamis

The tide-gauge records of large tsunamis are classified into three types, A, B and C. The “A” type record is made up of one or a few large waves near the wave front. The “B” type record consists of one or a few wave groups. The “C” type is the combination of the “A” and “B” types. The data used are; the Kamchatka Tsunami of Nov. 4, 1952, the Aleutian Tsunami of March 9, 1957, the Chilean Tsunami of May 22, 1960 and the Alaska Tsunami of March 28, 1964. The A type occurs mostly at isolated islands in the Pacific Ocean and occasionally at continental coasts. The B type is mostly distributed on the continental coast and along the island-arc. The distribution of the C type differs from tsunami to tsunami. The relation between the delay time of the maximum wave and the the travel time of the wave front is as follows:

1. For the wave of the A type and the head wave of C type, the delay time (t _D ) is constant for all travel times.
2. For the first wave group of B and C types, the delay time (T ₁) is constant or slow decreases with travel time. For the second and third wave groups of B and C types, the definite decrease of delay times (T ₂ andT ₃) with travel time is observed.

The height (h) of the maximum wave of A and C types decreases generally with travel time. The maximum wave height along the path between Kamchatka and Chile, however, shows the increase. For all wave groups the wave heights (H ₁,H ₂ andH ₃) of B and C types increases with travel time. Some speculations on the causes of these features are also presented.     

Wave groupiness and spectral bandwidth as relevant parameters for the performance assessment of wave energy converters

To date the estimation of long-term wave energy production at a given deployment site has commonly been limited to a consideration of the significant wave height H_s and mean energy period T_e. This paper addresses the sensitivity of power production from wave energy converters to the wave groupiness and spectral bandwidth of sea states. Linear and non-linear systems are implemented to simulate the response of converters equipped with realistic power take-off devices in real sea states. It is shown in particular that, when the converters are not much sensitive to wave directionality, the bandwidth characteristic is appropriate to complete the set of overall wave parameters describing the sea state for the purpose of estimating wave energy production.     

A note on the joint distribution of wave height and period during the growth phase of a storm

In this note the effect of changes in sea-state, as measured by the significant wave heigh H_s, on the joint distribution of individual wave height and period are considered. Wave data, obtained from a Waverider buoy during the growth phase of a storm, are used in the analysis. It is found that, by correctly scaling the individual heights and periods, the form of the joint distribution does not depend on H_s, but is dependent on the bandwidth of the spectrum. The results obtained also give some indication of the period of individual, high zero-upcrossing waves.     

Joint modelling of extreme ocean environments incorporating covariate effects

Characterising the joint distribution of extremes of ocean environmental variables such as significant wave height (H_S) and spectral peak period (T_P) is important for understanding extreme ocean environments and in the design and assessment of marine and coastal structures. Many applications of multivariate extreme value analysis adopt models that assume a particular form of extremal dependence between variables without justification. Models are also typically restricted to joint regions in which all variables are extreme, but regions where only a subset of variables is extreme can be equally important for design. The conditional extremes model of Heffernan and Tawn (2004) provides one approach to overcoming these difficulties.Here, we extend the conditional extremes model to incorporate covariate effects in all of threshold selection, marginal and dependence modelling. Quantile regression is used to select appropriate covariate-dependent extreme value thresholds. Marginal and dependence modelling of extremes is performed within a penalised likelihood framework, using a Fourier parameterisation of marginal and dependence model parameters, with cross-validation to estimate suitable model parameter roughness, and bootstrapping to estimate parameter uncertainty with respect to covariate.We illustrate the approach in application to joint modelling of storm peak H_S and T_P at a Northern North Sea location with storm direction as covariate. We evaluate the impact of incorporating directional effects on estimates for return values, including those of a structure variable, similar to the structural response of a floating structure. We believe the approach offers the ocean engineer a straightforward procedure, based on sound statistics, to incorporate covariate effects in estimation of joint extreme environmental conditions.     

Tropospheric lapse rate and its relation to surface temperature from reanalysis data

Estimates of the tropospheric lapse rate γ and analysis of its relation to the surface temperature T _s in the annual cycle and interannual variability have been made using the global monthly mean data of the NCEP/NCAR reanalysis (1948–2001). The tropospheric lapse rate γ is about 6.1 K/km in the Northern Hemisphere (NH) as a whole and over the ocean and about 6.2 K/km over the continents. The value of γ decreases from 6.5 K/km at low latitudes to 4.5 K/km at polar latitudes. The values of dγ/dT _s, the parameter of sensitivity of γ to the variation of T _s for the NH in the interannual variability, are found to be about 0.04 km^?1 (0.041 km^?1 for the NH as a whole, 0.042 km^?1 over the ocean, and 0.038 km^?1 over the continents). This corresponds to an increase in γ of approximately 0.7% when the surface temperature of the NH is increased by 1 K. Estimates of dγ/dT _s vary from about 0.05 km^?1 in the subtropics to 0.10 km^?1 at polar latitudes. When dγ/dT _s is positive, the surface and tropospheric warming means a temperature decrease above a certain critical level H _cr. The height of the level H _cr with constant temperature, which is defined by the inverse value (dγ/dT _s)^?1, is about 25 km for the NH as a whole, i.e., above the tropopause. In the subtropics, H _cr is about 20 km. At polar latitudes, H _cr decreases to about 10 km. Positive values of dγ/dT _s characterize a positive climatic feedback through the lapse rate and indicate a general decrease in the static stability of the troposphere during global warming. Along with a general tendency of γ to increase with rising T _s, there are regional regimes with the opposite tendency, mainly over the ocean. The negative correlation of γ with T _s is found over the oceanic tropics and midlatitudes, in particular, over the oceanic belt around Antarctica.     

Analysis of temporal and spatial characteristics of waves in the Indian Ocean based on ERA-40 wave reanalysis

Based on the 45-year (09/1957-08/2008) European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA-40) wave reanalysis dataset, this study analyzes interannual and interdecadal variabilities and intraseasonal oscillations of sea surface wind speed (WS), wind sea wave height (H^w), swell wave height (H^s) and significant wave height (H_s) in the Roaring Forties and tropical waters of the Indian Ocean, to determine swell propagation characteristics. The results show: (1) monthly variabilities of H^s in the Roaring Forties are in good agreement with those in tropical waters of the Indian Ocean; swell plays a dominant role in mixed waves throughout most of the Indian Ocean; and WS, H^w, H^s, and H_s exhibit a significant increasing trend over the 45-year study period. (2) H^s in the Roaring Forties and tropical waters of the Indian Ocean share a common period of 9.8–10.4 years on an interdecadal scale; and WS and H^s in the Roaring Forties and H^s in the tropical waters of the Indian Ocean share a common period of approximately 8 days (weekly oscillation) on an intraseasonal scale. (3) Swell of the Roaring Forties needs approximately 30 h to fully respond to the wind in this region. Approximately 84 h are required for H^s to propagate from the Roaring Forties to the tropical waters of the south Indian Ocean, while it takes approximately 132–138 h for H^s to propagate from the Roaring Forties to the tropical waters of the north Indian Ocean.     

Triangular Configuration Tension Leg Platform behaviour under random sea wave loads

This study investigates the dynamic response of a Triangular Configuration Tension Leg Platform (TLP) under random sea wave loads. The random wave has been generated synthetically using the Monte-Carlo simulation with the Peirson–Moskowitz (P–M) spectrum. Diffraction effects and second-order wave forces have not been considered. The evaluation of hydrodynamic forces is carried out using the modified Morison equation with water particle kinematics evaluated using Airy's linear wave theory. Wave forces are taken to be acting in the surge degree-of-freedom. The effect of coupling of various structural degrees-of-freedom (surge, sway, heave, roll, pitch and yaw) on the dynamic response of the TLP under random wave loads is studied. Parametric studies for random waves with different H_s and T_z under the presence of current have also been carried out. For the orientation of the TLP, surge, heave and pitch degrees-of-freedom responses are influenced significantly. The surge power spectral density function (PSDF) indicates that the mean square response is affected by the amplification at the natural frequency of the surge degree-of-freedom and also at the peak frequency of the wave loading. The PSDF of the heave response shows higher peak values near the surge frequency and near the peak frequency of the wave loading. Surge response, therefore, influences heave response to the maximum. Variable submergence seems to be a major source of nonlinearity and significantly enhances the responses in surge, heave and pitch degrees-of-freedom. In the presence of current, the response behaviour of the TLP is altered significantly introducing a non-zero mean response in all degrees-of-freedom.