The vertical structure of tidal currents

Abstract

The accuracy to which the vertical structure of tidal currents can be predicted is examined. Theoretical models for current structure are developed employing (a) a constant eddy viscosity E = ε and (b) an eddy viscosity varying linearly with height above the sea bed z; E(z)=βz. By requiring these models to satisfy the commonly accepted quadratic friction law, the condition ε>½k is deduced where k is the bed friction coefficient, W a representative velocity and D the depth.

The sense of rotation of a current ellipse is shown to be related to the configuration of co-tidal charts. The vertical structure of the current ellipse is illustrated from the theoretical models and the sensitivity of this structure is examined for the following variables: (a) eddy viscosity ε or βz, (b) the bed friction parameter kW, (c) rotation of the prescribed pressure gradients and (d) tidal period. While reasonable agreement between observed and calculated current profiles may often be reported, precise agreement is shown to depend upon accurate specification of both eddy viscosity and the bed stress condition.     

Vesicle zonation and vertical structure of basalt flows

Observation and measurement of vertical sections of thin (< 10 m) basaltic lava flows show that the vertical structure of basalt flows, regardless of variation in chemical composition or thickness, can be divided into three, previously unrecognized, zones consisting of a fundamental and regular pattern in vesicle size and abundance. These zones can be characterized as follows: (1) an upper vesicular zone, (2) a middle nonvesicular or dense zone, and (3) a lower vesicular zone. The thickness of the upper vesicular zone is generally about one-half of the total vertical section, and the thickness of the lower vesicular zone is generally 30–40 cm regardless of the total flow thickness. In the upper vesicular zone, vesicles increase in diameter and decrease in number per unit cross-sectional area downward attaining a maximum diameter near the base of the upper vesicular zone. In the lower vesicular zone, vesicles increase in diameter and decrease in number per unit cross-sectional area upward attaining a maximum diameter at the top of the lower vesicular zone.Numerical simulations, performed for this study, suggest that these characteristic patterns of vesicle zonation are the result of the growth and rise of gas bubbles in cooling lavas rather than the result of dynamic conditions such as flow movement or convection. As a bubble grows, it begins to ascend, and continues to ascend until it is overtaken by solidification progressing inward from either the upper or lower cooling surfaces of the flow. Bubbles that start out high in the flow will ascend ahead of the lower solidification front and cease rising only after encountering the downward-advancing upper solidification front, and bubbles near the base of a flow will be entrapped by the upward-advancing lower solidification front. Bubbles that start and rise just above the lower solidification front form the lower part of the upper vesicular zone. Such bubbles will also have longer times in which to grow than bubbles that are either higher or lower and are therefore among the largest in the flow. A zone free of vesicles will remain between the last bubbles to ascend to the upper solidification front and the last bubbles to be overtaken by the lower solidification front.     

A depth-dependent study of the topographic rectification of tidal currents

Abstract

A depth-dependent model for the topographic rectification of tidal currents in a homogeneous rotating fluid is used to examine the dependence of the rectified mean flow on various tidal, topographic and frictional parameters. Friction is parameterized through a vertically-uniform, time-independent vertical eddy viscosity and a bottom stress law applied near the top of the constant stress layer. The model neglects the interaction of mean and tidal currents, assumes uniformity along isobaths, and is closed with the assumption of zero depth-averaged mean flow across isobaths.

In the limit of depth-independence, the model reduces to that considered by Huthnance (1973) and Loder (1980) which, for weak friction, favours anticyclonic mean circulation around shallow regions and Lagrangian flow which is significantly reduced from the Eulerian. With the inclusion of vertical structure, the magnitude of the anticyclonic flow is amplified suggesting that depth-independent models may underestimate the along-isobath flow. For strong friction the direction of the mean flow depends on the orientation of the tidal ellipse relative to the isobaths. The depthindependent model again underestimates the magnitude of the along-isobath flow, but this can be offset with an appropriate reduction of the bottom friction coefficient.

The cross-isobath mean flows are one to two orders of magnitude weaker than the along-isobath flows and generally have more vertical structure. There is also a significant Stokes drift in the cross-isobath direction. Although there is some tendency for the cross-isobath mean bottom current to be down the cross-isobath mean pressure gradient, it appears that it is not generally possible to infer this current from depth-independent models.     

Threshold of erosion of submarine bedrock landscapes by tidal currents

Since sea level stabilized 7000 yr bp , shelf seas experiencing semi‐diurnal tides will have been affected by streaming four times per day. If tidal erosion of bedrock were even only marginally efficient, the ~10 million streamings since then should have left geomorphological imprints. We examine high‐resolution multibeam sonar data from three areas with extreme tidal currents. The Minas Passage (Bay of Fundy) experiencing 8‐knot surface tidal currents was surveyed in 2007 with a multibeam sonar. In an area near to transverse dunes, which are evidence for bedload transport, the data show local overhanging surfaces near to the sediment‐rock contact, potentially created by abrasion by saltating particles. However, they are uncommon. In the Straits of Messina, where surface currents reach 10 knots, surveying revealed ridges lying oblique to the flow that are not obviously broken into separate outcrops by erosion. In the Bristol Channel, UK, sonar data collected where currents reach 3·4 knots at 1·5 m above the bed reveal outcrops of limestone with superimposed sand dunes, but only minor rounding of blocks. Holocene tidal currents have apparently been generally ineffective at eroding bedrock. We examine this issue further by compiling extreme tidal streams around the UK and from them estimate shear stresses, representing a macro‐tidal environment where peak surface currents reach 9·7 knots. Those data are compared with shear stresses in mountainous rivers where long‐term rates of erosion are comparable with tectonic uplift rates and are thus geomorphologically significant. Whereas river stresses reach 10²–10³ Pa, the largest tidal stresses are generally 10¹ and only rarely approach 10² Pa, too small for quarrying to operate generally. However, the vertical faces in the Minas Passage may represent the onset of abrasion. Given this limited evidence for abrasion, we explore conditions in the geological past for tides that may have locally eroded bedrock. Copyright © 2012 John Wiley & Sons, Ltd.     

Experiments with a numerical model of coastal currents and tidal mixing fronts

A three-dimensional numerical model is used to simulate the development of disturbances on shelf-sea coastal currents and fronts. The model, which has a free surface, uses a finite difference grid ☐ scheme based on sigma coordinates. It has a semi-implicit scheme for the barotropic flow and a hydrid advection scheme to retain sharp fronts. The results demonstrate that (i) eddy formation follows changes at the inflow of a coastal current, (ii) a simple radiation boundary condition at the outflow produces nearly identical results for different outflow boundary positions, (iii) eddy growth, with matching behaviour of surface and bottom fronts, follows a small displacement on a tidal mixing front and (iv) effects of friction and mixing can significantly alter the behaviour of the front and the relative strength of the cyclonic and anticyclonic eddies formed.     

三门湾沿海声层析潮流观测实验

2009年9月6日至9日在三门湾进行了沿海声层析(Coastal Acoustic Tomography,CAT)潮流观测实验.实验由7台沿海声层析仪组网进行,并分别由渔船定点抛锚于7个站位.实验期间,还进行了定点ADCP(Acoustic Doppler Current Profiler)观测.通过建立逆模式对声传播时间差进行解析,引入权重因子,用L-curve法确定阻尼因子的最佳值,继而根据阻尼最小二乘法得到流速的最佳解.根据逆模式得到的流速分布可知该海区的潮流以半日潮(M2)为主,M2潮流椭圆呈东南-西北走向,潮流基本都是顺着水道,即涨潮为西北流向,退潮为东南流向.西北向与东南向最大流速分别为1.03 m·s-1和1.09 m·s-1.实验期间该区域的余流是从湾外流入湾内,平均流速约为0.05 m·s-1.CAT与定点ADCP流速的东分量和北分量的均方差均小于0.18 m·s-1.这样大面积的潮流和余流水平分布的同步观测,用传统观测手段很难实现.通过以上结果可以得出,沿海声层析技术可以作为一种新的测流方法对强潮海区进行大面积潮流观测,可在我国沿海的海洋环境监测等方面发挥重要作用.     

Measurements of upper and lower tidal currents at Banc de la Chapelle

Summary Measuring and analysis techniques are described for two sets of measurements of tidal currents near the surface and near the bottom at Banc de la Chapelle, a location 165 m. deep above the edge of the West European Continental Shelf. Reliable results are obtained for the semi-diurnal currents, but the scatter of the data is too great for consistent results to be extracted for the small diurnal and quarter-diurnal tidal constituents. The major axes of the mean semidiurnal current ellipses are aligned at about 30°. This direction is normal to the line of greatest slope of the shelf edge and to the main alignment of the large sand waves on the bank, which accords with a theory of formation of the latter. Bottom currents are on the average about 69% of the surface currents in magnitude. There is also some evidence for a residual drift of about 0·2 knot towards the West. An analysis is made of the errors involved in estimating the drift of a ship from Radar sights on moored buoys.

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Messungen der oberen und unteren Gezeitenströmungen bei der La-Chapelle-Bank

Zusammenfassung Es werden Meß- und Analysemethoden beschrieben für zwei Serien von Gezeitenstrommessungen nahe der Oberfläche und in Bodennähe auf der La-Chapelle-Bank, einer 165 m tiefen Stelle am Rand des West-Europäischen Kontinentalabhangs. Für halbtägige Gezeitenströme wurden zuverlässige Ergebnisse erzielt, die Streuung der Werte ist jedoch zu groß, um übereinstimmende Ergebnisse für die kleinen ganztägigen und vierteltägigen Tiden aus ihnen ableiten zu können. Die Hauptachsen der mittleren halbtägigen Gezeitenstrom-Ellipse bilden einen Winkel von rechtweisend 30⁰. Diese Richtung verläuft senkrecht zur Linie der größten Neigung des Schelfrandes und zur Hauptrichtung der großen Sandwellen auf der Bank, was mit der Theorie über die Entstehung der Bank übereinstimmt. Die Bodenströmungen betragen ungefähr 69% der Oberflächenströmungen. Es scheint auch ein Reststrom von ungefähr 0,2 kn in westlicher Richtung vorhanden zu sein. Die Fehler, die bei Errechnung der Abdrift eines Schiffes mit Hilfe von Radar-Beobachtungen von einer verankerten Boje aus auftreten, werden untersucht.

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La mesure des courants supérieurs et inférieurs de marée sur la banque de la Chapelle

Résumé On décrit des méthodes de mesure et d'analyse pour deux séries de mesures des marées près de la surface et au voisinage du fond sur la banque de la Chapelle, un endroit situé à 165 m de profondeur au bord de la marge continentale de l'Europe occidentale. Des résultats authentiques ont été obtenus en ce qui concerne les marées semi-diurnes, leurs valeurs, cependant, diffèrent à un tel point que l'on ne peut en dériver des résultats conformes pour les petites marées quart-diurnes ou pour celles qui se produisent seulement une fois par jour. Les axes principaux de l'ellipse de la marée semi-diurne forment un angle vrai de 30 degrés. Cette direction suit un cours perpendiculaire à la ligne de la plus grande pente de la marge continentale et à la direction principale de grandes rides de sable sur la banque ce qui s'accorde bien avec la théorie de sa genèse. Les courants au voisinage du fond font 69% des courants superficiels. En outre, il paraît qu'il existe un courant résiduel orienté vers l'ouest dont la vitesse est de 0,2 noeud. Les erreurs se produisant lorsqu'on calcule la dérive du bâtiment à l'aide des observations de radar faites à bord d'une bouée ancrée sont étudiées.

     

Dynamic links between shape of the eddy viscosity profile and the vertical structure of tidal current amplitude in bays and estuaries

Several field studies in bays and estuaries have revealed pronounced subsurface maxima in the vertical profiles of the current amplitude of the principal tidal harmonic, or of its vertical shear, over the water column. To gain fundamental understanding about these phenomena, a semi-analytical model is designed and analysed, with focus on the sensitivity of the vertical structure of the tidal current amplitude to formulations of the vertical shape of the eddy viscosity. The new analytical solutions for the tidal current amplitude are used to explore their dependence on the degree of surface mixing, the vertical shape of eddy viscosity in the upper part of the water column and the density stratification. Sources of surface mixing are wind and whitecapping. Results show three types of current amplitude profiles of tidal harmonics, characterised by monotonically decreasing shear towards the surface, “surface jumps” (vertical shear of tidal current amplitude has a subsurface maximum) and “subsurface jets” (maximum tidal current amplitude below the surface), respectively. The “surface jumps” and “subsurface jets” both occur for low turbulence near the surface, whilst additionally the surface jumps only occur if the eddy viscosity in the upper part of the water column decreases faster than linearly to the surface. Furthermore, “surface jumps” take place for low density stratification, while and “subsurface jets” occur for high density stratification. The physics causing the presence of surface jumps and subsurface jets is also discussed.     

The tidal force function and tidal torques

Summary The tidal force function of the two-body system is defined. It is formed by two parts, reflecting the direct, as well as, the indirect tidal effects. It enables deriving the tidal torques due to both the tidal effects independently of density distributions. The Stokes parameters of both bodies, the Love numbers and phase lag angles are sufficient for the solution.     

地中海涡旋的垂向结构与物理性质

本文利用地震海洋学新的反演结果,对地中海涡旋的温度、密度、声速以及波阻抗等物理性质进行了详细的分析与讨论,特别对地中海涡旋的一些细结构、混合过程进行了相关描述.研究分析取得以下认识:(1)涡旋具有涡旋核心水与涡旋混合水双层结构,这种结构特征可以在温度图、声速图和波阻抗图中识别出来;(2)涡旋核心水并不是均匀的稳定结构,内部有微弱的混合作用;(3)在涡旋上部以及周围边缘区域,海水的混合比较复杂;在涡旋下部边缘区域,除了有小尺度的盐指混合,内波也是非常重要的动力混合作用;(4)海水密度在涡旋核心水的分布比较稳定,成层性较强,在混合水区域由于不同的混合作用及其强烈程度不同,会发生波动甚至反转;(5)涡旋本身并不是一个严格对称的结构,涡旋与背景海水的上部以及周围边界比较模糊和复杂,而涡旋下部边界则比较明显.地震海洋学反演提供的涡旋物理性质数据能够为涡旋进一步的研究提供更为准确、更高精度以及更高分辨率的参考数据,同时对涡旋的运动学以及动力学研究提供了更进一步的研究方法和研究方向.     

Shallow water tidal currents in close proximity to the seafloor and boundary-induced turbulence

Velocity measurements with vertical resolution 0.02 m were conducted in the lowest 0.5 m of the water column using acoustic Doppler current profiler (ADCP) at a test site in the western part of the East China Sea. The friction velocity u _* and the turbulent kinetic energy dissipation rate ε _wl(ζ) profiles were calculated using log-layer fits; ζ is the height above the bottom. During a semidiurnal tidal cycle, u _* was found to vary in the range (1–7) × 10⁻³ m/s. The law-of-the-wall dissipation profiles ε _wl(ζ) were consistent with the dissipation profiles ε _mc(ζ) evaluated using independent microstructure measurements of small-scale shear, except in the presence of westward currents. It was hypothesized that an isolated bathymetric rise (25 m height at a 50-m seafloor) located to the east of the measurement site is responsible for the latter. Calculation of the depth integrated internal tide generating body force in the region showed that the flanks of the rise are hotspots of internal wave energy that may locally produce a significant turbulent zone while emitting tidal and shorter nonlinear internal waves. This distant topographic source of turbulence may enhance the microstructure-based dissipation levels ε _mc(ζ) in the bottom boundary layer (BBL) beyond the dissipation ε _wl(ζ) associated with purely locally generated turbulence by skin currents. Semi-empirical estimates for dissipation at a distance from the bathymetric rise agree well with the BBL values of ε _mc measured 15 km upslope.     

Growth of large-scale bed forms due to storm-driven and tidal currents: a model approach

An idealized morphodynamic model is used to gain further understanding about the formation and characteristics of shoreface-connected sand ridges and tidal sand banks on the continental shelf. The model consists of the 2D shallow water equations, supplemented with a sediment transport formulation and describes the initial feedback between currents and small amplitude bed forms. The behaviour of bed forms during both storm and fair weather conditions is analyzed. This is relevant in case of coastal seas characterized by tidal motion, where the latter causes continuous transport of sediment as bed load.The new aspects of this work are the incorporation of both steady and tidal currents (represented by an M₂ and M₄ component) in the external forcing, in combination with dominant suspended sediment transport during storms. The results indicate that the dynamics during storms and fair weather strongly differ, causing different types of bed forms to develop. Shoreface-connected sand ridges mainly form during storm conditions, whereas if fair weather conditions prevail the more offshore located tidal sand banks develop. Including the M₄ tide changes the properties of the bed forms, such as growth rates and migration speeds, due to tidal asymmetry. Finally a probabilistic formulation of the storm and fair weather realization of the model is used to find conditions for which both types of large-scale bed forms occur simultaneously. These conditions turn out to be a low storm fraction and the presence strong tidal currents in combination with strong steady currents during storms.     

Analytical study of the transverse distribution of along-channel and transverse residual flows in tidal estuaries

We present an analytical model to decompose complex along-channel and transverse residual flows into components induced by individual mechanisms. The model describes the transverse distribution of residual flows in tidally dominated estuaries. Scaling and perturbation techniques are used to obtain analytical solutions for residual flows over arbitrary across-channel bed profiles. The flows are induced by horizontal density gradients, tidal rectification processes, river discharge, wind, channel curvature and the earth's rotation. These rectification processes induce residual flows that are up-estuary to the right and down-estuary to the left of an estuarine channel (looking up-estuary in the northern hemisphere). The tidal rectification processes fundamentally change the transverse structure of along-channel residual flows in many tidal estuaries, as these processes cause the flows to be internally asymmetric about the mid-axis of the channel for relatively large tidal velocities, steep channels or narrow estuaries. In addition, velocity scales are derived from the analytical solutions to estimate the relative importance of the various residual flow mechanisms from estuarine parameters. A case study of a transect across the Upper Chesapeake Bay showed that important features of the residual flow observed in that transect are reproduced and explained by the analytical model. The velocity scales were able to identify the relevant residual flow mechanisms as well. The tidal rectification processes considered here result from advection of along-channel tidal momentum by Coriolis-induced transverse tidal currents.     

An enhanced depth-averaged tidal model for morphological studies in the presence of rotary currents

A simple and efficient method to improve morphological predictions using depth-averaged tidal models is presented. The method includes the contribution of secondary flows in sediment transport using the computed flow field from a depth-averaged model. The method has been validated for a case study using the 3D POLCOMS model and ADCP data. The enhanced depth-averaged tidal model along with the SWAN wave model are applied to morphological prediction around the Lleyn Peninsula and Bardsey Island as a case study in the Irish Sea. Due to the presence of a headland in this area two asymmetrical tidal eddies are developed in which the cyclonic eddy is stronger as a result of Coriolis effects. The results show that the enhanced model can effectively predict formation of sand banks at the centre of cyclonic eddies, while the depth-averaged model, due to its inability to accommodate secondary flow, is inadequate in this respect.     

Mapping of tidal current and associated nonlinear currents in the Xiangshan Bay by coastal acoustic tomography

Ocean Dynamics - Herein, tidal current and associated nonlinear currents were measured using nine coastal acoustic tomography (CAT) systems surrounding the tomography domain in Xiangshan Bay from...     

Variability of baroclinic tidal currents on the Mackenzie Shelf,the Southeastern Beaufort Sea

Semidiurnal tidal currents on the outer shelf of the Mackenzie Shelf in the Beaufort Sea were found to be strongly influenced by the locally generated baroclinic tide. Two primary factors are involved in this process: (1) the sharp shelf break along the northeastern Mackenzie Shelf, promoting the generation of vigorous internal tidal waves; and (2) the proximity to critical latitudes for M₂ and N₂ motions locking these waves and preventing them from leaving the source region. As a result, internal tides are resonantly trapped between the shelf and critical latitudes. The physical properties and temporal variations of tidal motions were examined using current meter measurements obtained from 1987–1988 at four sites (SS1, SS2, SS3, and SS4) offshore of the shelf break at depths of ∼200 m. Each mooring had Aanderaa RCM4s positioned at ∼35 m below the surface and ∼50 m above the bottom. Complex demodulation was used to compute the envelopes (amplitude modulation) of these components. A striking difference in the variability of clockwise (CW) and counterclockwise (CCW) tidal currents was found. The CW tides are highly variable, have greater amplitude, exhibit a burst-like character associated with wind events and contain about 80% of the total energy of the semidiurnal tidal currents. In contrast, the CCW components have a more regular temporal regime with distinct monthly, fortnightly and 10-day modulation at astronomical periodicities associated with frequency differences M₂–N₂ (0.03629 cpd), S₂–M₂ (0.06773 cpd), and S₂–N₂ (0.10402 cpd). Significant horizontal correlation of the CW current envelopes was found only between stations near the northeast Mackenzie Shelf, indicating this to be the main area of baroclinic internal wave generation.