Calculating bottom orbital velocity beneath waves

Methods are presented for calculating directly from a known wave height, period and water depth the orbital velocity produced at the sea bed by surface waves. Two curves are sufficient to allow the root-mean-square bottom orbital velocity to be calculated for wave-spectra having any one of the JONSWAP, Pierson-Moskowitz, Bretschneider, ISSC or ITTC forms. A third curve covers the monochromatic case. Other curves allow the ratio of the peak periods of bottom orbital velocity and surface elevation to be calculated for the above five spectral forms. Values are deduced for the height and period of the monochromatic wave which most closely matches the bottom orbital velocity obtained from a full spectral representation, optimised over water depths ranging from deep water to breaking.     

Wave attenuation characteristics of a tethered float system

Wave attenuation characteristics of a tethered float system have been investigated for various wave heights, wave periods, water depths, depths of submergence of floats and float sizes. As the floats are similar in size and shape, only a single tethered spherical float is considered for the theoretical analysis. Float motion is determined through the dynamical equation of motion, developed for a single degree of freedom. From incident and transmitted wave powers, transmission coefficients are computed. The results show that transmission coefficient does not vary with changes in wave height or water depth. When depth of submergence of float increases, wave attenuation decreases, showing that the system performs well when it is just submerged. As float velocity decreases with increase in float size, transmission coefficient increases with increase in float size. The influence of wave period on wave attenuation is remarkable compared to other parameters. The effect of drag on wave attenuation is studied for varying drag coefficient values. Theoretical results are compared with experimental values and it is found that theory overestimates wave attenuation which may probably be due to various linearisations involved in the theoretical formulation.     

海南新村港潟湖表层沉积物粒度特征及其沉积环境

对2013年8月在海南新村港潟湖采集的表层沉积物样品进行粒度分析,揭示了该区表层沉积物的粒度特征和沉积物类型,结合高空间分辨率的水动力和水深数据,采用系统聚类和主成分相结合的方法划分现代沉积环境。结果表明,研究区表层沉积物主要有4种类型,以粉砂和粉砂质砂为主,分别分布在潟湖中部和近岸浅水区域。沉积物平均粒径变化较大(0~8.0 Ф),均值为4.6 Ф,沉积物随水深增大而逐渐变细;沉积物粒度组分以砂(平均含量43%)和粉砂(平均含量为52%)为主,黏土含量较少,平均含量为5%。聚类结果表明,平均粒径可分为两组:第一组平均粒径均大于5.5 Ф,均值为6.8 Ф;而第二组平均粒径均小于3.5 Ф,均值为2.2 Ф。此外,平均粒径与分选、偏态和峰态系数之间呈现出两种不同的相关关系。研究区大潮和小潮期间的均方根流速(RMSV)均值是7.5和6.9 cm/s,标准偏差分别是15.3和14.9 cm/s。当RMSV大于4 cm/s,RMSV与极细砂(63~125 μm)含量呈明显的正相关关系,这表明RMSV决定了潟湖沉积物中极细砂含量。聚类和主成分分析结果表明,平均粒径、峰态和分选系数是对沉积环境最为敏感的粒度参数组合,同时结合高空间分辨率的水动力和水深数据,将研究区沉积环境划分为3类。这样划分充分考虑了水动力、物源、地形及其相互作用,更能有效地揭示沉积环境的差异,尤其体现了适宜的粒度参数组合和高空间分辨率的水动力数据在沉积环境划分中的重要性。     

埕北海域底质沉积物粒度分布特征及其动力环境意义

通过分析181个埕北海域底质沉积物样品的粒度资料,并应用Flemming三角图示法对研究区进行沉积动力环境分区,结果表明:研究区底质沉积物主要为粉砂质砂、砂质粉砂、粉砂和黏土质粉砂4种类型,整体上由岸向海粒度呈现细-粗-细的分布特征,且呈条带状与岸线平行;粒度相对较粗,粒径频率曲线多以单峰为主,分选中等偏差,多为正偏;沉积动力环境分区表明该海域沉积物多以悬浮和跃移为主;粒度特征和沉积动力强度以6 m和12 m等深线为轴对称分布,12 m水深等值线两侧沉积物的分布类型和运移趋势主要受季节的风浪变化控制,6 m水深等值线两侧沉积物分布和运移趋势主要受波浪破碎的紊流作用控制。     

Significance of relative velocity in the estimation of drag force of a tethered spherical float

In the present study, a tethered spherical float undergoing oscillatory motion in regular waves is analysed. Float velocity is computed through dynamical equation of motion and particle velocity using linear wave theory. The results show that variation of particle velocity with respect to wave period, wave height or water depth is small compared to the variation of float velocity with respect to the same parameters. The results further indicate that the difference between float velocity and particle velocity is considerable and, in such cases, the relative velocity instead of the particle velocity has to be considered for drag force or drag power estimation. However, it is suggested that float velocity must be higher than the particle velocity in order to use relative velocity in drag force or drag power estimation.     

Harmonic generation past a submerged porous step

Experiments were conducted in a wave flume to study the differences between harmonic evolution of monochromatic waves as they propagate over a submerged impermeable or porous step under non-breaking conditions. Results are used as a preliminary analysis to establish some engineering design criteria on harmonic generation on submerged porous structures. The root-mean-squared wave height evolution is also studied and compared to linear models as a first approximation. It is shown that porous structure increases the effective relative depth and decreases the relative wave height, resulting in a lower Ursell number and a lower chance to generate harmonics. The effective water depth over a step as defined in the paper, provides information to evaluate the potential harmonic generation.     

Boundary roughness and bedforms in the surf zone

Hydrodynamical models of the nearshore system frequently assume that a single friction coefficient is sufficient to represent flow conditions at a point in the surf zone. Furthermore, models attempting to relate bed configuration to surf zone flows have relied primarily upon the wave orbital velocity as an indicator of potential bedforms, and thus as the control on boundary roughness. The data presented here point out potential errors arising from either of these approaches. The results of a field experiment conducted at Wendake Beach, Ontario, show that at a single location in an active surf zone, the Darcy-Weisbach friction coefficient, f, varied by approximately 250% (in this case between 0.016 and 0.041).

It is also shown that existing bedform models, based upon primary wave motions alone, do not accurately predict conditions at this study site. For a relatively constant wave orbital velocity and velocity asymmetry, it is found that changes in bed roughness, as a result of bedform development, are reflected mainly in the vertical profile of the long-shore current velocity. A sequence of bedforms, from oscillatory ripples through flat bed, is inferred from the data, and found to be supported by diver observations and preserved primary sedimentary structures.     

On the largest wave height in water of constant depth

Experimental evidence of the fact that, both in the laboratory and in the field, the largest wave height to water depth ratio realisable for oscillatory waves propagating in water of constant depth is about 0.55, has been published recently (Nelson, 1985); (Nelson, 1987); (Nelson, 1994). This paper presents various theoretical approaches to estimate this maximum value. In particular, the higher approximations of the Stokes and cnoidal theories give a much higher limiting wave height, close to 0.78 h, which is commonly used in engineering practice.However, the inclusion of higher harmonics, generated by a wave-maker paddle, into the analysis provides maximum wave height less than ≈ 0.6 h, which is in good agreement with observations.     

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.     

The statistical distribution of nearbed wave orbital velocity in intermediate coastal water depth

The statistical distribution of wave orbital velocity in intermediate coastal water depth has been quantitatively determined from the comprehensive field velocity data collected near the seabed in this study. Two ocean ADV current meters, which were mounted at 0.5 m above the seabed on two separate stainless steel tripods sitting on the seabed, were used to measure instantaneous water particle velocities at a 2 Hz sampling rate for 17.07 min every hour in two coastal water depths of 11 m and 23 m in nine field deployments over a period of 2 years. The zero-crossing method is applied to analyse the field velocity data collected in each field deployment to obtain a large sample of wave orbital velocity amplitudes of individual waves. Based on the collected field velocity data, it is found that the histogram of instantaneous wave orbital velocities perfectly follows the Gaussian distribution as commonly assumed, while the histogram of wave orbital velocity amplitudes is less accurately described by the Rayleigh distribution than the modified Rayleigh and the Weibull distribution. It is also found that large orbital velocity amplitudes are generally overestimated by the Rayleigh distribution, but well predicted by the modified Rayleigh and the Weibull distribution. The expected value of maximum orbital velocity in a velocity record of finite size is also derived from the three distributions and found to agree well with the present field data.     

波、流及其共同作用下桩墩局部冲刷问题试验研究现状

要研究波流共同作用下桩墩的基础冲刷问题,首先需要了解水流和波浪单独作用下桩墩冲刷的机理和特征。针对波、流及其共同作用下桩墩的局部冲刷问题,从流速、水深、桩径、波长、波高、相对底层流速、粒径和粒径级配等方面系统地简述了恒定流、波浪和波流作用下桩、墩局部冲刷的研究进展。根据实验资料比较了各家经典计算公式的计算结果发现我国规范65-1式计算值偏大,65-2式计算值偏小等结论。桩墩局部冲刷是一个复杂的过程,今后可以针对淤泥质海岸底床、粉沙质海岸底床、复杂桩群结构、物理模型比尺效应、非恒定水动力条件、复杂基础形式方面对波流作用下基础冲刷的最大冲刷深度、冲刷过程、冲刷范围进行研究,以弥补桩墩局部冲刷在这些方面的不足。     

Reconstruction of ancient sea conditions with an example from the Swiss Molasse

Ancient sea conditions can be estimated from the grain size, spacing and steepness of preserved ripple-marks. The element of greatest uncertainty in such reconstructions is the relationship between near-bed orbital diameter of water particles and the ripple spacing. This relationship is simple for vortex ripples of high steepness but is problematical for the low-steepness forms known as post-vortex, rolling-grain or anorbital ripples.

The existence field for wave ripples is between the threshold velocity for sediment movement and the onset of sheet flow, most low-steepness forms occurring close to the bed planation threshold. A range of maximum period of formative waves can be obtained using combinations of orbital diameter and orbital velocity, assuming linear wave theory to be a reasonable approximation.

Probable wave heights, wave lengths and water depths can be investigated using the transformation of wave parameters in shallowing waters and the constraints on wave dimensions provided by the wave-breaking condition. Given reasonable estimates of wave height, crude estimates of wave power allow a comparison of ancient wave-influenced sequences with modern counterparts.

Wave ripple-marks preserved in the Upper Marine Molasse of western Switzerland have been investigated. Results, which are in agreement with regional geology, suggest deposition in a seaway of approximately 100 km width, where moderate period waves (T = 3–6 s) were generated. The depositional facies belts were adjusted to the prevailing waves, tides and fluvial outflows.     

Sediment grains moved by passing tsunami waves: Tsunami deposits in deep water

Tsunamis propagating in the open ocean have associated horizontal particle velocities that do not change with depth — yet the limiting water depth where a tsunami of given characteristics will initiate sediment motion remains unknown. Based upon linear wave theory and a parametrization of the Shields curve, equations are derived and solved, using an iterative scheme, to address the topic of grain movement by tsunami waves as a function of water depth and wave amplitude. The focus is on waves in deep water where tsunami waves behave linearly and on non-cohesive sediment grains. Furthermore, the question is addressed of which grain sizes are picked up on a sloping beach as the wave shoals. According to the results, even the Boxing Day tsunami in 2004 was incapable of moving fine sand in water deeper than 985 m in the Bay of Bengal and 335 m in the Indian and Pacific oceans. The results suggest that tectonic tsunamis of size equal to or smaller than the Boxing Day tsunami cannot initiate motion of deep-water cohesionless sediments that can be correlated on an oceanic basin-wide scale.     

A three-dimensional theory for the development and migration of deep sea sedimentary waves

A perturbation model is presented for a velocity field of a bottom current flowing over a sinusoidal topography or an obstacle. The model extends existing theory by taking into account the three-dimensional Coriolis vector and an initial horizontal velocity vector at any orientation. One possible mechanism of the development of sedimentary waves in the vicinity of an obstacle by an arbitrarily oriented initial horizontal current is analyzed in detail. Space-stationary fluid particle oscillations are initiated on the downstream side of an obstacle, which can result in sedimentary waves. The model shows that their wavelength depends on latitude, water depth, obstacle width and orientation as well as the initial current direction and intensity. The model defines intervals for current velocities normal to the wave crest, for which the sedimentary waves grow (or are destroyed) or migrate in a certain direction. Information derived from bathymetric and seismic surveys, such as wavelength, height, orientation and migration direction of mudwaves, can be used to calculate the velocity component across the wave crest and to estimate the current direction, as is demonstrated for an example from the Argentine Basin (Project MUDWAVES, Site 5).     

系统聚类和主成分分析在现代沉积环境划分中的应用-以海南新村港潟湖为例

An understanding of the sedimentary environment in relation to its controlling factors is of great importance in coastal geomorphology,ecology,tourism and aquaculture studies.We attempt to deal with this issue,using a case study from the Xincun Lagoon,Hainan Island in southern China.For the study,surficial sediment samples were collected,together with hydrodynamic and bathymetric surveys,during August 2013.Numerical simulation was carried out to obtain high-spatial resolution tidal current data.The sediment samples were analyzed to derive mean grain size,sorting coefficient,skewness and kurtosis,together with the sand,silt and clay contents.The modern sedimentary environments were classified using system cluster and principal component analyses.Grain size analysis reveals that the sediments are characterized by extremely slightly sandy silty mud(ESSSM) and slightly silty sand(SSS),which are distributed in the central lagoon and near-shore shallow water areas,respectively.Mean grain size varies from 0 to 8.0Ф,with an average of 4.6Ф.The silt content is the highest,i.e.,52% on average,with the average contents of sand and clay being 43% and 5%,respectively.There exists a significant correlation between mean size and water depth,suggesting that the surficial sediments become finer with increasing water depth.Cluster analyses reveals two groups of samples.The first group is characterized by mean grain size of more than 5.5Ф,whilst the second group has mean grain size of below 3.5Ф.Further,these groups also have different correlations between mean grain size and the other grain size parameters.In terms of the tidal current,the average values of the root mean square velocity(RMSV) are 7.5 cm/s and 6.9 cm/s on springs and neaps,respectively.For the RMSVs that are higher than 4 cm/s,a significant positive correlation is found between the content of the 63–125 μm fraction and the RMSV,suggesting that the RMSV determines the variability of the very fine sand fraction.Based on system cluster and principal component analyses(PCA),the modern sedimentary environments are classified into three types according to the grain size parameters,RMSVs and water depth data.The results suggest the importance of grain size parameters and high-spatial resolution hydrodynamic data in differentiating the coastal sedimentary environments.     

南海东北部末次冰期以来的沉积环境演变

利用南海东北部上陆坡处所取的D孔柱样进行硅藻分析,结合粒度与碎屑矿物分析结果,探讨该海域末次冰期以来沉积环境演变过程.结果表明：粒度与硅藻分析结果较为吻合,共同显示D孔柱样可分为上下两层.上表层（0～2 cm）的砂质沉积层为冰后期海进过程改造的晚更新世残留沉积层,即变余沉积;下层（2～130 cm）主要是末次冰期形成的浅海沉积.整个柱样可反映出海洋同位素MIS 4期海退至MIS 3期海进与MIS 2期海退至冰后期海进的沉积变化韵律.     

淤泥质潮流深槽最大冲刷深度的一个概念模型

以概念模式方法计算了淤泥质潮流深槽的最大深度,探讨了涨落潮流速、涨落潮历时、深槽淤泥质物质粒径、深槽顶底部原始深度、水道长度等因素对潮流深槽最大深度的影响。概念模式的假设条件是:(1)深槽形态为长方体,底部纵向坡度为0;(2)沉积物粒径无垂向变化;(3)只考虑潮流作用的影响,涨、落潮流速在时间序列上呈正弦分布;(4)不考虑细颗粒物质的粘性和絮凝作用。模拟结果显示:(1)涨、落潮历时对深槽最大深度的影响很小。(2)优势潮流流速与最大深槽深度之间存在着幂函数关系。(3)深槽的底质粒径、深槽的长度均与最大冲刷深度呈正相关关系。(4)深槽顶部水深与最大深度呈负相关关系。(5)由于潮汐水道深度与潮流流速和沉积物侵蚀强度之间具有负反馈关系,因此水道冲刷存在着一个极限,即最终可以达到均衡状态。潮流深槽的均衡态特征和达到均衡态所需的时间可运用沉积动力学方法来确定;同时,若应用深槽的真实参数,进一步减少模型的假设条件,可望使该模型具有实际的应用价值。     

Tidal-cycle changes in oscillation ripples on the inner part of an estuarine sand flat

Oscillation ripples form on subaqueous sand beds when wave-generated, near-bottom water motions are strong enough to move sand grains. The threshold of grain motion is the lower bound of the regime of oscillation ripples and the onset of sheet flow is the upper bound. Based on the relation between ripple spacing and orbital diameter, three types of symmetrical ripples occur within the ripple regime. In the lower part of the ripple regime (orbital ripples), spacing is proportional to orbital diameter; in the upper part (anorbital ripples) spacing is independent of orbital diameter. Between these regions occurs a transitional region (suborbital ripples).

Oscillation ripples develop on a sandy tidal flat in Willapa Bay, Washington, as a result of waves traversing the area when it is submerged. Because wave energy is usually low within the bay, the ripples are primarily orbital in type. This means that their spacing should respond in a systematic way to changes in wave conditions. During the high-water parts of some tidal cycles, ripples near the beach decrease in spacing during the latter stage of the ebb tide while ripples farther offshore do not change. Observations made over several tidal cycles show that the zone of active ripples shifts on- or offshore in response to different wave conditions.

Detailed bed profiles and current measurements taken during the high-water part of spring tides show the manner in which the oscillation ripples change with changes in orbital diameter. Changes in ripple spacing at the study site could be correlated with changes in orbital diameter in the manner suggested by the criterion for orbital ripples. However, there appeared to be a lag time between a decrease in orbital diameter and the corresponding decrease in ripple spacing. Absence of change during a tidal cycle could be attributed to orbital velocities below the threshold for grain motion that negated the effects of changes in orbital diameter.

Because changes in sand-flat ripples depend both upon changes in orbital diameter and upon the magnitude of the orbital velocity, exposed ripples were not necessarily produced during the preceding high tide. In fact, some ripples may have been just produced, while others, farther offshore, may have been produced an unknown number of tides earlier. Therefore, when interpreting past wave conditions over tidal flats from low-tide ripples, one must remember that wave periods have to be short enough to produce velocities greater than the threshold velocity for the orbital diameters calculated from the observed ripple spacings.