Study on the double-logarithmic profile of tidal flow velocity in the near-bed layers

Tidal current velocity profile in the near-bed layers has been widely studied. The results showed that velocity profile in the near-bed layer obviously departure from the traditional logarithmic profile, due to the acceleration or deceleration. Although the logarithmic linear profile can reduce the rate of deviation from this, only it is a lower-order approximate solution. In this paper, considering the unsteady and non-linear features of tidal motion, the double logarithmic profile near-bed layers in estuarine and coastal waters is established on the assumption that the turbulent shear stress along the water depth was parabolic distribution, and on the basis of Prandtl''s mixing length theory and von Karman''s self-similar theory. Having been verified the data observed at the West Solent in the south of England, and comparison of the logarithmic linear profile, it found that the double logarithmic profile is more precious than the latter. At last, the discussed results showed that:(1) The parabolic distribution of the tidal shear stresses verified good by the field data and experimental data, can be better reflected the basic features of the tidal shear stress deviating from linear distribution that is downward when to accelerate, upward when to decelerate. (2) The traditional logarithmic velocity profile is the zero-order approximation solution of the double logarithmic profile, the logarithmic linear profile is the first order, and the logarithmic parabolic profile is the second order. (3) Ignoring the conditions of diffusion and convection in the tidal movement, the double logarithmic profile can reflect the tidal properties of acceleration or deceleration, so that the calculation of the friction velocity and roughness length are more reasonable. When the acceleration or the deceleration is about zero, the double logarithmic profile becomes the logarithmic profile.     

潮滩水流加减速阶段边界层流速剖面的比较

江苏大丰地区潮滩由于水深较浅,潮流、波浪等动力较强,整个水层可视为边界层,其主体部分是对数层,即水流流速在垂向上呈对数分布。在潮流的加减速阶段,流速剖面将可能偏离对数分布,从而使对数剖面法计算出来的边界层参数造成误差。使用MIDAS-400用户化数据采集系统,在大丰潮滩获得了多层流速、浊度等同步高频观测数据,基于修正后的von Karman-Prandtl模型对u-lnz进行回归分析、数据内部一致性分析来定义流速对数剖面并与未修正前经典理论得到的边界层参数进行比较。分析结果表明,修正后的流速剖面更符合实际情况,边界层参数除了受水流加速度的影响外,还和沙纹等因素有关。另外,边界层参数的变化量与特征加速度负相关。     

Hydraulic roughness over simple subaqueous dunes

Detailed studies of flow over subaqueous dunes in laboratory flumes were used to suggest a virtual near-bed layer of twice the dune height in which the mean velocity is accelerated towards the crest by contraction. The mean flow velocity in this layer above the crest, transformed into friction velocity by means of the surface skin roughness, is shown to give values consistent with measured values. The resulting dimensionless shear stress due to skin friction is depth-independent, in contrast to that derived by means of often cited traditional methods. As a result of the relationship between dune height and the thickness of the near-bed layer, an expression for the expansion loss behind dunes was formulated and used to relate form resistance directly to dune height.     

台风期间厦门湾潮流边界层特征研究

本文基于2007年8月圣帕台风影响台湾海峡期间的厦门湾垂向海流流速剖面观测资料,运用Karman-Prandtl模型统计和分析了流速对数剖面的出现频率和边界层参数（摩阻流速与粗糙长度）．结果表明流速剖面满足对数分布出现频率都超过50％,但进行内部一致性原则分析后,流速剖面满足对数分布情况均不足30％．造成流速剖面偏离对数分布的因素主要有：台风、径流、流速加减速、水体分层、底床结构、海底悬沙浓度等等．台风期间的摩阻流速和粗糙长度都大于非台风期间的数值．     

Effects of time dependence in unstratified tidal boundary layers: results from large eddy simulations

A three-dimensional Large Eddy Simulation (LES) model is used to simulate oscillating tidal boundary layers and test previous results obtained from one-dimensional boundary layer models and turbulence measurements in tidal channels. The LES model produces low-order turbulence statistics in agreement with the semi-analytic theory and observations. It shows a logarithmic layer in the mean velocity profile and a linear distribution of Reynolds stress with water depth. However, the eddy viscosity profile predicted by the LES model is not parabolic but better matches a parabolic profile modified by wake effect observed in the outer part of depth-limited steady boundary layers. Low-order turbulence statistics can be scaled by the instantaneous friction velocity at the bottom boundary. Although turbulence intensities in three directions fluctuate over a tidal cycle, their normalized values are in good agreement with those determined from laboratory experiments of steady open-channel flows. The LES model confirms that tidal turbulence is in quasi-equilibrium. However, it also demonstrates the importance of flow acceleration/deceleration term in the depth-integrated momentum balance for the mean flow. Phase differences are found between flows at different heights above the bottom boundary.     

A Computational Model for Velocity Separation in Shallow Sea

Based on the hydrodynamical feature and the theoretical velocity profiles of tidal flow and vvind-induced flow in shal-low sea, a computational model is established for the first time, which can separate observed velocity into tidal velocity and wind-induced velocity by use of the least square method. With the model, not only the surface velocities of tidal flow and vvind-induced flow are obtained, but also the bed roughness height is determined and the wind velocity above the wa-ter surface is estimated. For verification of the model, the observed velocity in the Yellow River Estuary and the laborato-ry test is separated, then it is applied to the Yangtze River Estuary. All the results are satisfactory. The research results show that the model is simple in method, feasible in process and reasonable in result. The model is a valid approach to analysis and computation of field dala, and can be applied to separate the observed velocity in shallow sea; at the same time, reasonable boundary conditions of th     

江苏大丰潮间带粉砂滩的潮流边界层特征

对江苏大丰潮间带粉砂滩的潮流观测数据，运用Karman-parndtl模型分析了流速对数剖面的出现频率和边界层参数（摩阻流速与粗糙长度）。结果表明，不同时间尺度（10^1-10^3s）的平均流速对计算u-lnz线性关系出现频率的影响不大，而不同层位组合的影响较为显著，影响流速对数剖面分布的自然因素为波浪、风、潮流旋转、表底层流向差异、滩面坡度和水流加减速等。相邻层位的流速在时间序列上存在很高的线性关系，回归直线的斜率与水层距底床的高度、粗糙长度和摩阻流速有关。涨潮阶段床面粗糙长度大于落潮阶段，涨潮阶段摩阻流速小于落潮阶段。     

长江河口区边界层参数的观测与分析

2003年11月在长江口南槽用ADCP进行定点水文观测,结果表明研究区为不规则半日潮,在水流转向期流速较低时常出现悬沙浓度峰值。根据流速对数剖面分布模型与悬沙分布模型,分别计算了海底边界层参数,其中潮周期内摩阻流速可达0.15 m/s,粗糙长度为0.01~1.2 m,拖曳系数为10-3~10-4,边界层厚度为2~4 m,悬沙的沉降速率为0.2~6 mm/s。     

江苏近海潮流湍流切应力研究

潮流的流速分布和湍流切应力的分布密切相关。为了研究潮流湍流切应力的特征和变化规律,本文从潮流运动方程推导出随潮流呈周期性变化的湍流切应力随深度的分布表达式。从江苏近海现场实测流速剖面中计算得到一个潮周期内的湍流切应力的变化过程。通过将实测值与本文理论解的比较发现,计算值能很好地反映出实测值的变化特征,尤其是能正确地反映潮流在加速和减速过程中,湍流切应力偏离线性分布呈现上凹和下凹的现象,以及只有在加减速转换的时候切应力才呈现线性分布的特点。最后,通过分析湍流切应力振幅及相位沿水深的变化情况,认为反映潮流周期、涡粘性和水深之间关系的参数Ri是决定湍流切应力弯曲程度及分布形态的重要参数。对于近海潮流,水深是影响湍流切应力偏离线性程度的主要因素。     

Hydrodynamics and associated sediment transport over coastal wetlands in Quanzhou Bay,China

Coastal salt marshes represent an important coastal wetland system.In order to understand the differences between boundary layer parameters of vegetated and unvegetated areas,as well as the mechanisms of sediment transport,several electromagnetic current meters (AEM HR,products of Alec Electronics Co.Ltd.) were deployed in coastal wetlands in Quanzhou Bay,China,to measure current velocity.During the low tide phase,the surficial sediment was collected at 10 m intervals.In situ measurements show that the current velocities on the bare flat were much higher than those in the Spartina alterniflora marsh.Current velocity also varied with distance from marsh edge and plant canopy height and diameter.Around 63% of the velocity profiles in the tidal creek can be described by a logarithmic equation.Over the bare flat and Spartina alterniflora marsh,a logarithmic profile almost occurs during the flood tide phase.Sediment analysis shows that mean grain size was 6.7 Φ along the marsh edge,and surface sediments were transported from bare flat to marsh;the tidal creeks may change this sediment transport pattern.The hydrodynamics at early flood tide and late ebb tide phases determined the net transport direction within the study area.     

Tidal boundary layer measurements in the presence of waves

Measurements of tidal current and wave velocity made at 0.69 and 1.85 m above a rough seafloor exhibit large current gradients (boundary layer) in the water column. The logarithmic boundary layer flow model was fitted to the measurements, and thus roughness (z₀) and friction velocity (u^*) parameters were derived. The roughness parameter values were generally consistent with the observed upstream physical roughness. The values of both parameters for conditions in the rough turbulence flow regime are generally larger (much larger for ebb) than earlier published values for similar measurements of currents in the absence of significant waves but are comparable to values from recent measurements of currents in the presence of storm waves. The high parameter values here appear to relate more to the magnitude of the current and to the upstream physical bottom roughness than to the magnitude of the seastate. Large boundary layers in the flow at the seabed have a profound effect on the design of offshore structures such as offshore pipelines.     

Bottom Boundary Layer Characteristics in the Hooghly Estuary Under Combined Wave-Current Action

The development of a theoretical model for estimating bottom boundary layer characteristics in the Hooghly estuary, located in the east coast of India, under combined effects of waves and currents is reported. Three numerical models, viz a depth averaged hydrodynamic model, SWAN wave model, and bottom boundary layer model, were integrated. In the bottom boundary layer parameters, maximum bottom stress, effective friction factor, and near-bed velocity both during ebb and flood phases of the tidal forcing are investigated and validated for the Haldia channel. The close match seen from results signifies applicability of this model for entire Hooghly basin.     

Three-dimensional structure of tidal current in the East China Sea and the Yellow Sea

A three-dimensional tidal current model is developed and applied to the East China Sea (ECS), the Yellow Sea and the Bohai Sea. The model well reproduces the major four tides, namely M₂, S₂, K₁ and O₁ tides, and their currents. The horizontal distributions of the major four tidal currents are the same as those calculated by the horizontal two-dimensional models. With its high resolutions in the horizontal (12.5 km) and the vertical (20 layers), the model is used to investigate the vertical distributions of tidal current. Four vertical eddy viscosity models are used in the numerical experiments. As the tidal current becomes strong, its vertical shear becomes large and its vertical profile becomes sensitive to the vertical eddy viscosity. As a conclusion, the HU (a) model (Davieset al., 1997), which relates the vertical eddy viscosity to the water depth and depth mean velocity, gives the closest results to the observed data. The reproduction of the amphidromic point of M₂ tide in Liaodong Bay is discussed and it is concluded that it depends on the bottom friction stress. The model reproduces a unique vertical profile of tidal current in the Yellow Sea, which is also found in the observed data. The reason for the reproduction of such a unique profile in the model is investigated.     

东海深部地层时深转换关系的分段优化拟合

在将钻井垂直地震剖面(VSP)数据的时深拟合公式应用于深部地层的时深转换时,拟合深度与计算的层速度常常不够准确。本文首先利用多项式和幂函数给出了东海陆架盆地中部某凹陷41口钻井VSP数据的时深拟合公式,并用双程旅行时(TWT)最深达8 s的三维地震速度体数据与多道地震剖面对拟合公式在深部地层的适用性进行分析。在TWT为8 s时,速度体数据表明41口钻井位置的平均深度为18 140 m,平均层速度为6 208 m/s,二次多项式的平均拟合深度较之偏高9.2%,计算的层速度偏高36.2%,幂函数则分别偏低28.9%与35.6%,拟合效果都不理想。对此,本文采用通过识别VSP数据的增速拐点并对增速拐点前的VSP数据进行二次多项式拟合,对增速拐点后的VSP数据进行幂函数拟合的分段拟合模型,将TWT为8 s时的平均拟合深度和层速度的误差降到3.3%与4.7%。地震剖面显示研究区莫霍面深度约为TWT=11 s,分段拟合模型在TWT=11 s的平均拟合深度为27 516 m,层速度为7 334 m/s,更接近前人研究成果,表明该模型能显著提高深部地层时深转换的精度。     

东大港水道流速垂线分布探讨

对辐射沙洲海域东大港水道4号站位连续2个潮次的流速测量资料进行了分析、研究,拟合给出了流速垂线分布关系,并根据实际测量资料率定了该站位各时刻6个水层的浑水水流的尾流函数项表达式,这些表达式表明浑水水流的尾流函数项是相对深度和摩阻速度的函数。     

Estimating swash zone friction coefficients on a sandy beach

Video-based swash motions from three studies (on two separate beaches) were analyzed with respect to theoretical swash trajectories assuming plane beach ballistic motions under quadratic friction. Friction coefficient values for both the uprush and backwash were estimated by comparing measured swash space–time trajectories to these theoretical expectations given an initial velocity and beach slope. Observations were made spanning high tides, and in one case, during a light rain. Analysis of over 4500 individual swash events showed that the uprush friction coefficient was nearly constant during all three studies with a mean value of roughly 0.007 and showed no trends over a tidal cycle. In contrast, backwash friction coefficient values varied over the tidal cycles ranging between 0.01 and 0.07 with minimum values corresponding to the highest tides. Although these values are close to the theoretical estimates based on a Law of the Wall formulation and values commonly referenced in the literature, these observations show a consistent tendency for backwash friction estimates to greatly exceed uprush friction estimates. The disparity between uprush and backwash friction coefficients can be partially attributed to the exclusion of a pressure gradient term in the ballistic model. However, results indicate that backwash friction coefficients adjusted to account for this effect may be three times larger than the uprush friction values during lower tides. This tidal dependence for backwash friction coefficients is attributed to a complex interaction between swash infiltration and entrained sediment loads. These findings imply that friction estimates (necessary for sediment transport calculations and hydrodynamic predictions) based solely on grain roughness may not be correct for backwash flows.     

Observations of boundary layer parameters and suspended sediment transport over the intertidal flats of northern Jiangsu, China

A current-turbidity monitoring system (CTMS) was deployed on the intertidal flat at Wanggang, northern Jiangsu during October 16-17, 2000, to measure the tidal current speeds and seawater turbidities at 5 levels above the seabed. Based upon the logarithmic-prof‘de equation, the boundary layer parameters, i.e., u*, Z0 and C60, were obtained for 247 tidal flow velocity prof‘des. Around 90% of the profiles were logarithmic according to the critical correlation coefficient. Internal consistency analysis shows that these parameters derived by different methods are consistent with each other. In addition, the height of the bedforms observed is close to the seabed roughness lengths calculated from the velocity prof‘des, indicating that the boundary layer parameters obtained can reveal the conditions at the sedimentwater interface on the intertidal flats. Suspended sediment concentrations were obtained from the 5 CTMS turbidity meters using laboratory and in-situ calibrations. The results show that the in-situ calibrated SSCs have a much higher accuracy than the laboratory calibrated ones. Calculation of suspended sediment fluxes on the intertidal flats, with a magnitude of 104 kg/m per spring tidal cycle, indicates that suspended sediment moves towards the northwest, which is reversal to the transport pattern controlled by the southward Northern Jiangsu Coastal Current in the sub-tidal zone and adjacent shallow waters.     

海上不同高度风速换算关系的研究

本文用海上石油平台上观测的风梯度资料,计算了在不同风况下海面摩擦速度和粗糙高度。结果表明,海面摩擦速度u_*与海上10m高度处风速u_(10)的关系为u_*=0.055u_(10)-0.058。在4—5级风时,海面平均摩擦速度为50cm/s,粗糙度为0.022m,它相当于陆上的平均粗糙高度。在风速为2—3级时,二者与海上通常采用的数据接近。文中最后给出了上述两种风况下海上不同高度的换算系数。     

An investigation of the velocity field under regular and irregular waves over a sand beach

Near-bed horizontal (cross-shore) and vertical velocity measurements were acquired in a laboratory wave flume over a 1:8 sloping sand beach of finite depth. Data were acquired using a three-component acoustic Doppler velocimeter to measure the velocity field close to, but at a fixed distance from the bed. The near-bed velocity field is examined as close as 1.5 cm above a trough and crest of a ripple under three different types of wave forcing (Stokes waves, Stokes groups, and irregular waves). Although both horizontal and vertical velocity measurements were made, attention is focused primarily on the vertical velocity. The results clearly indicate that the measured near-bed vertical velocity (which was outside the wave-bottom boundary layer) is distinctly nonzero and not well predicted by linear theory. Spectral and bispectral analysis techniques indicate that the vertical velocity responds differently depending on the location over a ripple, and that ripple-induced effects on the velocity field are present as high as 4–8 cm above the bed (for vortex ripples with wavelengths on the order of 8 cm and amplitudes on the order of 2 cm). At greater heights above the bed, the observed wave-induced motion is adequately predicted by the linear theory.