Variations in wave direction estimated using first and second order Fourier coefficients

In most design applications such as alignment of the berthing structure and breakwater alignment, it becomes necessary to determine the direction of design wave. There are two different approaches to determine wave direction. One involves the use of first order Fourier coefficients (mean wave direction) while the other uses second order Fourier coefficients (principal wave direction). Both the average wave direction over the entire frequency range (0.03–0.58 Hz) and the direction corresponding to the peak frequency are used in practice. In the present study, comparison is made on wave directions estimated based on first and second order Fourier coefficients using data collected at four locations in the west and east coasts of India. Study shows that at all locations, the mean and principal wave directions for frequencies ranging from 0.07 to 0.25 Hz (±0.5 times peak frequency) co-vary with a correlation coefficient of 0.99 but at lower and higher frequencies, difference between the parameters is large. Average difference between the mean wave direction at peak frequency and the average over the frequency related to spectral energy more than 20% of maximum value is less, around 13°. Study shows that average difference in the sea and swell directions is around 39°.     

Spectral characteristics of high shallow water waves

The spectral characteristics of shallow water waves with significant wave height more than 2 m based on the data collected along the Indian coast is examined. It was found that the value of Joint North Sea Wave Project (JONSWAP) parameters (α and γ) increases with significant wave height and mean wave period and decreases with spectral peak period. The estimated average value (0.0027 and 1.63) of the JONSWAP parameters, α and γ were less than the generally recommended values of 0.0081 and 3.3, respectively. By carrying out a multi-regression analysis, an empirical equation is arrived relating the JONSWAP parameters with significant wave height, peak wave period and mean wave period. It was found that the Scott spectra underestimate the maximum spectral energy of high waves. The study shows that the measured wave spectra can be represented by JONSWAP spectra with the JONSWAP parameters estimated based on the equation proposed in this paper.     

Wave climate in a groin field

Wave records at seven different locations within a groin field have been analysed by both statistical and spectral approaches to study the general wave climate. The wave heights and periods from the wave records were obtained by both upcross and downcross methods for the statistical approach. The variation of different wave height and wave period parameters with respect to the time of measurement at a particular location and its variation at different locations within the groin field at a particular instant of time are presented and discussed in detail in this paper. It is generally found that the wave heights follow the Weibull distribution.     

Estimation of wind speed and wave height during cyclones

Wave and wind characteristics based on the cyclones, in the vicinity of the Nagapattinam coastline (east coast of India) were estimated. In all, 11 cyclones have crossed near the study region during 1960–1996. For the four severe cyclones, the isobaric charts were collected at three hourly intervals from the India Meteorological Department. The storm variables such as central pressure, radius of maximum wind, speed of forward motion and direction of storm movement were extracted and the method based on standard Hydromet pressure profile, were used for the hindcast of storm wind fields. For all the cyclones the maximum significant wave height within the storm and its associated spectral peak period was estimated using the Young’s model considering the moving wind field and the results are compared with the hurricane wave prediction techniques provided in the shore protection manual published by the US Army Corps of Engineers in 1984. The study shows that the estimated wind speed and the data reported by ships were comparable. Empirical expressions relating wind speed, wave height and wave period to storm parameters were derived. The design wave height for different return periods was obtained by fitting a two-parameter Weibull distribution to the estimated significant wave heights. The design wave height was 9.39 m for 1 in 100 year return period for a direct hit of cyclone.     

Parameterization and simulation of near bed orbital velocities under irregular waves in shallow water

A set of empirical formulations is derived that describe important wave properties in shallow water as functions of commonly used parameters such as wave height, wave period, local water depth and local bed slope. These wave properties include time varying near-bed orbital velocities and statistical properties such as the distribution of wave height and wave period. Empirical expressions of characteristic wave parameters are derived on the basis of extensive analysis of field data using recently developed evolutionary algorithms. The field data covered a wide range of wave conditions, though there were few conditions with wave periods greater than 15 s. Comparison with field measurements showed good agreement both on a time scale of a single wave period as well as time averaged velocity moments.     

Statistics of Wind and Waves off Tsuyazaki, Fukuoka, in the Eastern Tsushima Strait

The variability of the sea surface wind and wind waves in the coastal area of the Eastern Tsushima Strait was investigated based on the hourly data from 1990 to 1997 obtained at a station 2 km off Tsuyazaki, Fukuoka. The annual mean wind speed was 4.84 m s⁻¹, with strong northwesterly monsoon in winter and weak southwesterly wind in summer. Significant wave heights and wave periods showed similar sinusoidal seasonal cycles around their annual means of 0.608 m and 4.77 s, respectively. The seasonal variability relative to the annual mean is maximum for wave heights, medium for wind speeds, and minimum for wave periods. Significant wave heights off Tsuyazaki turned out to be bounded by a criterion, which is proportional to the square of the significant wave period corresponding to a constant steepness, irrespective of the season or the wind speed. For terms shorter than a month, the significant wave height and the wave period were found to have the same spectral form as the inshore wind velocity: white for frequencies less than 0.2 day⁻¹ and proportional to the frequency to the −5/3 power for higher frequencies, where the latter corresponds to the inertial subrange of turbulence. The spectral levels of wave heights and wave periods in that inertial range were also correlated with those of the inshore wind velocity, though the scatter was large. This revised version was published online in August 2006 with corrections to the Cover Date.     

SWAN predictions of waves observed in shallow water onshore of complex bathymetry

SWAN model predictions, initialized with directional wave buoy observations in 550-m water depth offshore of a steep, submarine canyon, are compared with wave observations in 5.0-, 2.5-, and 1.0-m water depths. Although the model assumptions include small bottom slopes, the alongshore variations of the nearshore wave field caused by refraction over the steep canyon are predicted well over the 50 days of observations. For example, in 2.5-m water depth, the observed and predicted wave heights vary by up to a factor of 4 over about 1000 m alongshore, and wave directions vary by up to about 10°, sometimes changing from south to north of shore normal. Root-mean-square errors of the predicted wave heights, mean directions, periods, and radiation stresses (less than 0.13 m, 5°, 1 s, and 0.05 m³/s² respectively) are similar near and far from the canyon. Squared correlations between the observed and predicted wave heights usually are greater than 0.8 in all water depths. However, the correlations for mean directions and radiation stresses decrease with decreasing water depth as waves refract and become normally incident. Although mean wave properties observed in shallow water are predicted accurately, nonlinear energy transfers from near-resonant triads are not modeled well, and the observed and predicted wave energy spectra can differ significantly at frequencies greater than the spectral peak, especially for narrow-band swell.     

Extreme waves for Kuwaiti territorial waters

The extreme significant wave heights and the corresponding wave periods were predicted for return periods of 12, 25, 50, 100 and 200 yr for 19 different locations in Kuwaiti territorial waters. Though the total coast length of Kuwait is only about 500 km including all islands and the total area of the Kuwaiti territorial water is about 7611 km², the extreme significant wave height vary from 1.86 to 4.02 m for 100 yr return period, among these 19 locations. In general Weibull distribution is found to fit the data well compared to the Gumbel distribution. The input wave data for the present work is obtained by hind casting waves using a WAM model. Wave data is hindcasted for a total period of 12 yr, starting from 1 January 1993 to 31 December 2004. From the joint probability of wave height and wave period, a simple polynomial relationship is obtained between the significant wave height and mean period for all the 19 locations. It is found that the wave period for wave heights of 100 yr return period cannot exceed 6.5 s. A large number of coastal projects are in progress and many new projects are planned for the near future in the Kuwaiti territorial waters. The results of the present study will be highly useful for optimal design of these projects.     

SWAN模型对实验室小尺度浅水波浪模拟研究

基于浅水斜坡地形的物理模型试验数据,考察SWAN模型对实验室小尺度浅水波浪的模拟效果,进而检验其浅水项的模拟精度。模拟中采用直接输入初始测点的实测海浪谱进行造波,重点考察浅水中三波相互作用和变浅破碎两个源项,对不同工况下,SWAN模式在水深条件变化下的有效波高、谱平均周期、海浪谱演化的模拟能力进行研究。研究表明:模拟的有效波高较符合实测波浪的增长和衰减,但谱平均周期计算值明显偏小;海浪谱的能量转移机制同实测有较大区别,频谱模拟结果出现高频高估、低频低估现象。对两个源项进行对比分析得出三波相互作用对海浪谱的能量转换影响远大于变浅破碎耗散。想要提高近岸区谱平均周期和海浪谱的模拟精度则SWAN模型中三波非线性项的计算精确度仍需更多研究和改进。     

海浪对ASCAT散射计反演风场的影响研究

To improve retrieval accuracy, this paper studies wave effects on retrieved wind field from a scatterometer. First, the advanced scatterometer(ASCAT) data and buoy data of the National Data Buoy Center(NDBC) are collocated. Buoy wind speed is converted into neutral wind at 10 m height. Then, ASCAT data are compared with the buoy data for the wind speed and direction. Subsequently, the errors between the ASCAT and the buoy wind as a function of each wave parameter are used to analyze the wave effects. Wave parameters include dominant wave period(dpd), significant wave height(swh), average wave period(apd) and the angle between the dominant wave direction(dwd) and the wind direction. Collocated data are divided into sub-datasets according to the different intervals of each wave parameter. A root mean square error(RMSE) for the wind speed and a mean absolute error(MAE) for the wind direction are calculated from the sub-datasets, which are considered as the function of wave parameters. Finally, optimal wave conditions on wind retrieved from the ASCAT are determined based on the error analyses. The results show the ocean wave parameters have correlative relationships with the RMSE of the retrieved wind speed and the MAE of the retrieved wind direction. The optimal wave conditions are presented in terms of dpd, swh, apd and angle.     

Very small waves and associated sediment resuspension on an estuarine intertidal flat

Field data from a microtidal estuarine intertidal flat (Tamaki estuary, New Zealand) are used to analyse very small waves (height <10 cm; period 1.0–1.8 s) and associated sediment resuspension under light winds. Mean spectral period at the bed varied over the tidal cycle, driven by changes in surface-wave spectrum and depth-attenuation of orbital motions. Wave-orbital currents exceeded 30 cm/s, disturbing the fine-sand (100–200 μm) matrix of the seabed and resulting in the release of fine silt (particle size <20 μm) at concentrations >120 mg/L. Resuspension was initiated when ∼40% of the maximum zero-downcrossing orbital speeds in a burst exceeded the critical speed for initiation of sediment motion. Sediment concentrations were highest around low tide, when waves were smaller compared to high tide because of a reduced fetch but depth-attenuation of orbital motions was less because the water was shallower. Wave period exerted a control on sediment resuspension through the wave friction factor. There was a hysteresis in the wave Reynolds number such that it was greater on the ebbing tide compared to on the flooding tide: since it did not exceed 3 × 10⁵ the bed was hydraulically smooth, and the wave friction factor therefore is inversely proportional to wave period. Hence, the tidal-cycle hysteresis in wave Reynolds number translated into a smaller wave friction factor on the ebbing tide, and accounting for this caused the ebb and flood sediment concentration data to collapse onto one curve when plotted against wave-induced skin friction. A simple model is presented to evaluate the relative contribution to sediment resuspension of waves associated with weak and strong winds. At the base of the flat (waves competent to resuspend sediment for 5% of the inundation time), waves associated with stronger, infrequent winds dominate resuspension. At the top of the flat (waves competent to resuspend sediment for 30% of the inundation time), waves associated with lighter, frequent winds dominate resuspension. Moderate winds – neither the strongest nor most frequently occurring – dominate resuspension integrated across the profile. The mass of sediment resuspended by waves is greatest towards the top of the flat: shoreward of this, resuspension is smaller because of wave dissipation; seaward of this, resuspension is smaller because of greater depth-attenuation of orbital motions. The location of maximum sediment mass resuspended by waves and the location of maximum duration of resuspension are not necessarily the same.     

Wave attenuation by flexible,idealized salt marsh vegetation

Wave attenuation by vegetation is a highly dynamic process and its quantification is important for understanding shore protection potential and modeling coastal hydrodynamics. Data documenting the interactions of Spartina alterniflora, represented by polyolefin tubing, and single- and double-peaked irregular waves were collected in a large-scale laboratory flume. The laboratory provided a controlled environment to evaluate wave attenuation, including the parameters of stem density, submergence, wave height, and peak period. Wave attenuation appeared to be most dependent on stem density and the ratio of stem length to water depth. Wave attention increased slightly with wave height while no clear trend with respect to wave period was seen. Treating double-peaked spectra as superimposed wave systems revealed a preferential dissipation of the higher-frequency wave system relative to the lower-frequency wave system under emergent conditions. Wave energy loss occurred at all frequencies of both spectral types, with dissipation increasing with frequency above the spectral peak. Parameterizing the spectral equilibrium range as a function of frequency showed a steepening of the spectral tail compared to the − 4 power law under emergent conditions. An empirical relationship defining the bulk drag coefficient for S. alterniflora as a function of the stem Reynolds number is found to serve as a first estimate for engineering applications.     

Comparison of TOPEX/POSEIDON Altimeter Derived Wind Speed and Wave Parameters with Ocean Buoy Data in the North Indian Ocean

Results of comparison exercises carried out between the state-of-the-art TOPEX/POSEIDON altimeter-derived ocean surface wind speed and ocean wave parameters (significant wave height and wave period) and those measured by a set of ocean data buoys in the North Indian Ocean are presented in this article. Altimeter-derived significant wave height values exhibited rms deviation as small as ±0.3 m, and surface wind speed of ±1.6 m/s. These results are found consistent with those found for the Pacific Ocean. For estimation of ocean wave period, the spectral moments-based semiempirical approach, earlier applied on GEOSAT data, was extended to TOPEX/POSEIDON. For this purpose, distributions of first four years of TOPEX/POSEIDON altimeter data and climatology over the North Indian Ocean were analyzed and a new set of coefficients generated for estimation of wave period. It is shown that wave periods thus estimated from TOPEX/POSEIDON data (for the subsequent two years), when compared with independent data set of ocean data buoys deployed in the North Indian Ocean, exhibit improved accuracy (rms ~ ±1.4 nos) over those determined earlier with GEOSAT data.     

响水近岸海域波浪特性研究

基于响水波浪站累计一整年的现场观测资料,分析了波高和波周期的年内变化特性,研究了波浪的统计特性和波谱特性,并总结归纳了该海域各特征波要素之间以及各波谱参数之间的转换关系。结果显示:响水海域全年有效波高的变化幅度在0.10~2.80 m之间,年平均值为0.56 m;最大波高的变化幅度在0.15~5.58 m之间,年平均值为0.93 m;平均波周期的变化范围为1.91~9.02 s,年平均值为3.90 s。夏季大波高发生频率明显要小于冬、春季节,波浪季节性变化较为显著。就波高和波周期分布而言,通过拟合得出的Weibull分布较为适合本海域实测波高分布和波周期分布。波谱特性方面,本海域双峰谱占到总数的62.5%,且低频谱峰值普遍高于高频谱峰值,其中低频谱峰出现在0.04 Hz左右,高频谱峰则出现在0.15~0.20 Hz之间,分别为本海域涌浪和风浪所集中的频率区间。采用回归分析方法进一步分析了各特征波要素之间以及各波谱参数之间的关系,发现多数波参数之间存在显著的相关性,但受波浪浅水变形影响,各参数之间的比值与理论深水关系有所区别。本文的研究成果可为沿海建筑物的设计以及防灾减灾提供参考和依据。     

CODAR wave measurements from a North Sea semisubmersible

CODAR, a high-frequency (HF) compact radar system, was operated continuously over several weeks aboard the semisubmersible oil platform Treasure Saga for the purpose of wave-height directional measurement and comparison. During North Sea winter storm conditions, the system operated at two different frequencies, depending on the sea state. Wave data are extracted from the second-order backscatter Doppler spectrum produced by nonlinearities in the hydrodynamic wave/wave and electromagnetic wave/scatter interactions. Because the floating oil rig itself moves in response to long waves, a technique has been developed and successfully demonstrated to eliminate to second order the resulting phase-modulation contamination of the echo, using separate accelerometer measurement of the platform's lateral motions. CODAR wave height, mean direction, and period are compared with data from a Norwegian directional wave buoy; in storm seas with wave heights that exceeded 9 m, the two height measurements agreed to within 20 cm RMS, and the mean direction to better than 15° RMS     

Data assimilation of partitioned HF radar wave data into Wavewatch III

In this study the assimilation of HF radar data into a high resolution, coastal Wavewatch III model is investigated. An optimal interpolation scheme is used to assimilate the data and the design of a background error covariance matrix which reflects the local conditions and difficulties associated with a coastal domain is discussed. Two assimilation schemes are trialled; a scheme which assimilates mean parameters from the HF radar data and a scheme which assimilates partitioned spectral HF radar data. This study demonstrates the feasibility of assimilating partitioned wave data into a coastal domain. The results show that the assimilation schemes provide satisfactory improvements to significant wave heights but more mixed results for mean periods. The best improvements are seen during a stormy period with turning winds. During this period the model is deficient at capturing the change in wave directions and the peak in the waveheights, while the high sea state ensures good quality HF radar data for assimilation. The study also suggests that there are both physical and practical advantages to assimilating partitioned wave data compared to assimilating mean parameters for the whole spectrum.     

A note on nearshore wave features: Implications for wave generation

This paper analyses 10 years of wave data from the Mediterranean Spanish (Catalan) coast considering the mean wave climate and storm events from the standpoint of wind-wave momentum transfer and wave prediction. The data, registered by a buoy at about 12 km from the coastline, revealed two main groups of wave storms, with NW and E directions. NW storms correspond to a fetch-limited situation since the intense wind blows from land. Low-pressure centres located over the Mediterranean Sea produce easterly storms. Near the coast the eastern winds from the sea are replaced by NW winds coming from meteorological patterns over northern Spain and south-western France. Wave storms are classified and studied to obtain their main features (including spectral width, wave length, wave age and bimodality) and discussed in terms of wind-wave momentum transfer for operational wave predictions. Observations show a complex coastal wave climate. Fetch-limited storms presented smaller spectral widths while varying wind situations presented larger widths due to the presence of bimodal spectra. These wave features are highly relevant for wind–ocean momentum transfer and, thus, for current and wave predictions. The spectral width proved to be a good indicator of sea complexity and is thus applicable for improved wind drag estimations. A new drag coefficient formulation is proposed, based on existing wind dependent drag expressions, but including also spectral wave properties (a spectral width parameter) that highlights the characteristics of wind-wave generation under pre-existing swell. Such a formulation, once properly validated with field observations, is expected to improve wind-wave predictions.     

Wave damping over artificial Posidonia oceanica meadow: A large-scale experimental study

An experimental study, conducted in the large wave flume of CIEM in Barcelona, is presented to evaluate the effects of Posidonia oceanica meadows on the wave height damping and on the wave induced velocities. The experiments were performed for irregular waves from intermediate to shallow waters with the dispersion parameter h/λ ranging from 0.09 to 0.29. Various configurations of the artificial P. oceanica meadow were tested for two stem density patterns (360 and 180 stems/m²) and for plant's height ranging from 1/3 to 1/2 of the water depth.The results for wave height attenuation are in good agreement with the analytical expressions found in literature, based on the assumption that the energy loss over the vegetated field is due to the drag forces. Based on this hypothesis, an empirical relationship for the drag coefficient related to the Reynolds number, Re, is proposed. The Reynolds number, calculated using the artificial P. oceanica leaf width as the length scale and the maximum orbital velocity over the meadow edge as the characteristic velocity scale, ranges from 1000 to 3500 and the drag coefficient C_d ranges from 0.75 to 2.0.The calculated wave heights, using the analytical expression from literature and the proposed relationship for the estimation of C_d, are in satisfactory agreement with those measured. Wave orbital velocities are shown to be significantly attenuated inside the meadow and just above the flume bed as indicated by the calculation of an attenuation parameter. Near the meadow edge, energy transfer is found in spectral wave velocities from the longer to the shorter wave period components. From the analysis it is shown that the submerged vegetation attenuates mostly longer waves.     

Significant wave height forecasting using wavelet fuzzy logic approach

Wave heights and periods are the significant inputs for coastal and ocean engineering applications. These applications may require to obtain information about the sea conditions in advance. This study aims to propose a forecasting scheme that enables to make forecasts up to 48 h lead time. The combination of wavelet and fuzzy logic approaches was employed as a forecasting methodology. Wavelet technique was used to separate time series into its spectral bands. Subsequently, these spectral bands were estimated individually by fuzzy logic approach. This combination of techniques is called wavelet fuzzy logic (WFL) approach. In addition to WFL method, fuzzy logic (FL), artificial neural networks (ANN), and autoregressive moving average (ARMA) methods were employed to the same data set for comparison purposes. It is seen that WFL outperforms those methods in all cases. The superiority of the WFL in model performances becomes very clear especially in higher lead times such as 48 h. Significant wave height and average wave period series obtained from buoys located off west coast of US were used to train and test the proposed models.