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.     

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.     

Depth inversion in shallow water based on nonlinear properties of shoaling periodic waves

Two depth inversion algorithms (DIA) applicable to coastal waters are developed, calibrated, and validated based on results of computations of periodic waves shoaling over mild slopes, in a two-dimensional numerical wave tank based on fully nonlinear potential flow (FNPF) theory. In actual field situations, these algorithms would be used to predict the cross-shore depth variation h based on sets of values of wave celerity c and length L, and either wave height H or left–right asymmetry s₂/s₁, simultaneously measured at a number of locations in the direction of wave propagation, e.g., using video or radar remote sensing techniques. In these DIAs, an empirical relationship, calibrated for a series of computations in the numerical wave tank, is used to express c as a function of relative depth k_oh and deep water steepness k_oH_o. To carry out depth inversion, wave period is first predicted as the mean of observed L/c values, and H_o is then predicted, either based on observed H or s₂/s₁ values. The celerity relationship is finally inverted to predict depth h. The algorithms are validated by applying them to results of computations for cases with more complex bottom topography and different incident waves than in the original calibration computations. In all cases, root-mean-square (rms)-errors for the depth predictions are found to be less than a few percent, whereas depth predictions based on the linear dispersion relationship—which is still the basis for many state-of-the-art DIAs—have rms-errors 5 to 10 times larger.     

Response based design metocean conditions for a permanently moored FPSO during tropical cyclones: Estimation of greenwater risk

Response based analysis (RBA) is used to establish the design metocean conditions (DMCs) of a generic weather-vaning FPSO off the North West Shelf (NWS) of Australia for determining greenwater severity. A vessel heading prediction tool, an essential component of the RBA analysis for weather-vaning vessels, is developed and evaluated by comparing with full-scale measurements from an operating FPSO. Locations at the bow, amidships and the stern of the vessel are found to be susceptible to greenwater risks and the vessel is often exposed to oblique waves during tropical cyclones. Long-term extrapolation is performed to estimate 1 in. N-year return relative wave-vessel motions represented by both the most probable maximum relative wave-vessel motion within a storm r_mp, and the maximum individual relative wave-vessel motion r_Max. It is observed that r_Max ˜ (1.1–1.2) r_mp. The use of r_Max allows for the variability of the short term maxima per storm and also the fact that the peak in response might not come in the most severe sea-state. Given the focus on greenwater rather than wave severity, the slightly larger value of r_Max at a given return period is used for assessment of greenwater risk. The sea-states that lead to r_Max at a 1 in 100 year level are identified and subsequently used for characterising the wave groups causing maximum relative wave-vessel motion at various locations around the vessel. For a given location, the shapes of the wave time histories which give rise to extreme relative wave-vessel motions in a set of design metocean conditions are similar, indicating that a ‘design wave’, derived within the framework of linear wave theory, may be a useful approach to tackle highly nonlinear and complex greenwater overtopping problems.     

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.     

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。     

Profiles of fully developed (Airy) waves in different water depths

Airy waves have a sinusoidal profile in deep water that can be modeled by a time series at any point x and time t, given by η(x,t) = (H_o/2) cos[2πx/L_o − 2πt/T_w], where H_o is the deepwater height, L_o is the deepwater wavelength, and T_w is the wave period. However, as these waves approach the shore they change in form and dimension so that this equation becomes invalid. A method is presented to reconstruct the wave profile showing the correct wavelength, wave height, wave shape, and displacement of the water surface with respect to the still water level for any water depth.     

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.     

Wave height parameter for damage description of rubble-mound breakwaters

In this paper it will be shown that the wave height parameter H₅₀, defined as the average wave height of the 50 highest waves reaching a rubble-mound breakwater in its useful life, can describe the effect of the wave height on the history of the armor damage caused by the wave climate during the structure's usable life.Using Thompson and Shuttler (Thompson, D.M., Shuttler, R.M., 1975. Riprap design for wind wave attack: A laboratory study on random waves. HRS Wallingford, Report 61, UK) data it will be shown that H₅₀ is the wave parameter that best represents the damage evolution with the number of waves in a sea state. Using this H₅₀ parameter, formulae as van der Meer (van der Meer, J.W., 1988. Rock slopes and gravel beaches under wave attack. PhD Thesis. Technical University of Delft) and Losada and Giménez-Curto (Losada, M.A., Gimenez–Curto, L.A., 1979. The joint effect of the wave height and period on the stability of rubble mound breakwaters using Iribarren's number. Coastal Engineering, 3, 77–96) are transformed into sea-state damage evolution formulae. Using these H₅₀-transformed formulae for regular and irregular sea states it will be shown how damage predictions are independent of the sea state wave height distribution.To check the capability of these H₅₀-formulae to predict damage evolution of succession of sea states with different wave height distributions, some stability tests with regular and irregular waves have been carried out. After analysing the experimental results, it will be shown how H₅₀-formulae can predict the observed damage independently of the sea state wave height distribution or the succession of sea states.     

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.     

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.     

Geological control of beach morphodynamic state

The concept of beach morphodynamic states has achieved widespread acceptance in the coastal geological literature since its inception in the mid-1980s and expansion in the 1990s. Much of the pioneering work was undertaken in Australia under a range of environmental conditions in microtidal environments and a close empirical relationship between beach 3-dimensional morphology and the Dean's parameter (H_b/W_sT) was established. Subsequently, the Relative Tidal Range parameter (H_b/TR) was extended to beaches of all tidal ranges.In this paper, observations are presented from 25 beaches around the north coast of Ireland. These beaches exist on an environmental gradient that encompasses marked tidal and wave energy variability (micro to macrotidal and low to high wave energy). Each beach was visually categorised into one of several established beach states described in the literature, on the basis of field observations. For each beach, the RTR and Dean's parameter were calculated for the immediately antecedent period and used to predict the beach state using published relationships. Observed and predicted beach states were then compared.Comparison of observed and predicted beach states showed that while beaches with observed dissipative morphology typically matched the expected criteria, most other beach states did not. Lack of agreement between predicted and observed beach states has been reported elsewhere and attributed to failings in the RTR and Dean's parameter. In addition, this study identifies geological factors as important constraints on actual beach state. In the majority of beaches studied, inherited geological factors appear to be more important determinants of beach morphology than contemporary dynamics.     

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.     

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.     

X-波段雷达近海海浪频谱反演的神经网络模型

X-波段雷达作为国内海浪观测的一种新工具,在海浪频谱获取和有效波高反演方面仍存在较多问题.本文利用非线性回归方法,将现场实测浮标数据频谱和雷达一维图像谱分别与标准频谱模型进行拟合,发现浮标频谱和一维图像谱具有标准频谱的特征,能够较准确地获取相应的谱参数.提出了建立由雷达一维图像谱参数反演海浪频谱参数的神经网络模型,同时在模型中加入影像序列信噪比,进而反演有效波高,并将反演结果与现场实测数据和传统算法(建立影像序列信噪比与有效波高之间的线性回归方程)进行了对比,结果表明,获取谱参数的误差和反演有效波高的平均误差在20％以内,而传统算法计算有效波高平均误差在20％以上.     

Sediment transport and beach morphodynamics induced by free long waves,bound long waves and wave groups

New laboratory data are presented on the influence of free long waves, bound long waves and wave groups on sediment transport in the surf and swash zones. As a result of the very significant difficulties in isolating and identifying the morphodynamic influences of long waves and wave groups in field conditions, a laboratory study was designed specifically to enable measurements of sediment transport that resolve these influences. The evolution of model sand beaches, each with the same initial plane slope, was measured for a range of wave conditions, firstly using monochromatic short waves. Subsequently, the monochromatic conditions were perturbed with free long waves and then substituted with bichromatic wave groups with the same mean energy flux. The beach profile changes and net cross-shore transport rates were extracted and compared for the different wave conditions, with and without long waves and wave groups. The experiments include a range of wave conditions, e.g. high-energy, moderate-energy, low-energy waves, which induce both spilling and plunging breakers and different turbulent intensities, and the beaches evolve to form classical accretive, erosive, and intermediate beach states. The data clearly demonstrate that free long waves influence surf zone morphodynamics and promote increased onshore sediment transport during accretive conditions and decreased offshore transport under erosive conditions. In contrast, wave groups, which can generate both forced and free long waves, generally reduce onshore transport during accretive conditions and increase offshore transport under erosive conditions. The influence of the free long waves and wave groups is consistent with the concept of the relative fall velocity, H/w_sT, as a dominant parameter controlling net beach erosion or accretion. Free long waves tend to reduce H/w_sT, promoting accretion, while wave groups tend to increase the effective H/w_sT, promoting erosion.     

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.     

Sub aerial random wave pressure and layer thickness on impermeable sea walls

Investigations on sub aerial wave pressures and layer thickness on plane impermeable and non-overtopping seawallns were carried out by using physical model studies. Seawalls with slopes of 1:3, 1:4 and 1:6 were used. JONSWAP spectrum with significant wave height, H_s from 0.08 to 0.2 m and peak periods, T_p from 1.5 to 6.0 s and a constant water depth of 0.7 m is used. Based on extensive measurements, empirical formulas for practical applications are proposed to predict the maximum, significant and mean sub aerial random wave pressure and layer thickness (thickness of water layer perpendicular to the still water level on the run-up zone) by using the surf similarity parameter, significant wave height and elevation on the sub aerial region as inputs. It is found that the maximum layer thickness is 1.11 times the significant layer thickness and maximum sub Arial wave pressure is 1.06 times the significant wave pressures. The predictive equations based on extensive measurements can be used for the design of non-overtopping seawalls.     

Stochastic bivariate time series models of waves in the North Sea and their application in simulation-based design

In this paper, we present and evaluate three long-term wave models for application in simulation-based design of ships and marine structures. Designers and researchers often rely on historical weather data as a source for ocean area characteristics based on hindcast datasets or in-situ measurements. The limited access and size of historical datasets reduces repeatability of simulations and analyses, making it difficult to assess the sampling variability of performance and loads on marine vessels and structures. Markov, VAR and VARMA wave models, producing independent long-term time series of significant wave height (H_s) and spectral peak period (T_p), is presented as possible solutions to this problem. The models are tested and compared by addressing how the models affect interpretation of design concepts and the ability to replicate statistical and physical characteristics of the wave process. Our results show that the VAR and VARMA models perform sufficiently in describing design performance, but does not capture the physical process fully. The Markov model is found to perform worst of the tested models in the applied tests, especially for measures covering several consecutive sea states.