Tidal and residual currents over abrupt deep-sea topography based on shipboard ADCP data and tidal model solutions for three popular bathymetry grids

The response of tidal and residual currents to small-scale morphological differences over abrupt deep-sea topography (Seine Seamount) was estimated for bathymetry grids of different spatial resolution. Local barotropic tidal model solutions were obtained for three popular and publicly available bathymetry grids (Smith and Sandwell TOPO8.2, ETOPO1, and GEBCO08) to calculate residual currents from vessel-mounted acoustic Doppler current profiler (VM-ADCP) measurements. Currents from each tidal solution were interpolated to match the VM-ADCP ensemble times and locations. Root mean square (RMS) differences of tidal and residual current speeds largely follow topographic deviations and were largest for TOPO8.2-based solutions (up to 2.8 cm?s^?1) in seamount areas shallower than 1,000 m. Maximum RMS differences of currents obtained from higher resolution bathymetry did not exceed 1.7 cm?s^?1. Single depth-dependent maximum residual flow speed differences were up to 8 cm?s^?1 in all cases. Seine Seamount is located within a strong mean flow environment, and RMS residual current speed differences varied between 5 % and 20 % of observed peak velocities of the ambient flow. Residual flow estimates from shipboard ADCP data might be even more sensitive to the choice of bathymetry grids if barotropic tidal models are used to remove tides over deep oceanic topographic features where the mean flow is weak compared to the magnitude of barotropic tidal, or baroclinic currents. Realistic topography and associated flow complexity are also important factors for understanding sedimentary and ecological processes driven and maintained by flow–topography interaction.     

The impacts of the large-scale hydraulic structures on tidal dynamics in open-type bay: numerical study in Jakarta Bay

The construction of a Giant Sea Wall (GSW) complex in Jakarta Bay has been proposed to protect Jakarta against flood in the Master Plan for National Capital Integrated Coastal Development (NCICD). However, these large-scale hydraulic structures could significantly change the tidal dynamics in Jakarta Bay. This research investigates the potential impacts of a GSW on the tidal dynamics, including tides, currents, and residual currents in Jakarta Bay using a validated numerical model (Finite Volume Coastal Ocean Model (FVCOM)). Results show that the bay is diurnal with a maximum tidal range of ~0.9 m. The flow is mainly in an east-west direction with a maximum depth-mean current speed of up to 0.3 ms^?1. The construction of a GSW would modulate the tidal dynamics by changing the bathymetry, tidal prism, wind effect, and tidal choking effect in the bay. The maximum tidal range would be slightly increased due to the reduced tidal prism of the bay and the increased tidal choking effect. The current would penetrate into the west reservoir through the gates and channels between the artificial islands, with peak speed jets appearing at the gates (~0.3 ms^?1), due to tidal choking. A similar peak current speed appears near the right wing of the GSW due to the pressure gradient would be created by the wing of the GSW. Closing the gates would mainly affect the currents inside the west reservoir. The residual current would be slightly increased after the construction of the GSW. An eddy would be formed at the bottom level near the right wing of the GSW. The direction of the residual current is landward instead of seaward at the surface level outside the GSW. The impact of wind on surface currents would be much reduced due to the decreased water surface area. Although this study is site specific, the findings may have a wider applicability to the impacts of large-scale hydraulic structures on tidal dynamics in open-type bays.     

Dynamics,sediment transport,and morphology in a tide-dominated embayment

Western Port, Victoria, Australia is a tide-dominated embayment with an unusual and complex shape. Bottom currents and circulation and their effects on sediment processes were examined using instrumented tripods to measure currents, tides and wave activity, and to estimate sediment transport at nine locations in the bay. Overall bottom water movement patterns were determined by use of seabed drifters. The characteristics of the bay reflect a small catchment and low freshwater and sediment input. A complex system of channels is flanked by extensive intertidal areas. Tidal range varies up to more than 3 m, generating bottom currents up to 70cm s^?1. Flow directions generally conform to channel alignments but major deviations are important. Net circulation in the bay is clockwise around the large central island. The ratio of tidal range to half-tidal period (ΔH/ΔT) when compared with measured currents gave a method of prediction of the annual frequency distribution of maximum bottom current velocities. Determination of threshold current velocities enabled prediction of annual frequency of bedload movement (generally 50–100 per cent of tide cycles). Bedload mass transport for all observed tide cycles was calculated, and estimates of annual mass transport capacity (between 10² and 10⁶ g cm^?1 a^?1( were obtained from a relationship between predicted tidal conditions and mass transport. Seabed drifters delineated the major bottom water movements in the bay and adjacent Bass Strait, and also detailed circulation patterns. This linked the data from the tripod stations, in particular patterns of ebb- and flood-dominance. A coherent picture of the processes operating in Western Port is presented by integrating these studies with corroborative studies of sediment distribution and morphology, hydrochemistry, and mathematical modelling. Some morphological characteristics related to tide-dominance are discussed.     

The influence of tidal currents on the asymmetry of tide-dominated ebb–tidal deltas

An idealized numerical model is developed to study the spatial asymmetry of ebb–tidal deltas under influence of large-scale alongshore tidal currents. It is shown that the asymmetry of the delta depends on the magnitude of the cross-shore and large scale alongshore tidal currents, their phase difference, and on the width of the inlet. Model results are compared with observations of ebb–tidal deltas of the tidal inlet systems of the Dutch Wadden Sea and with the ebb–tidal delta of the Eastern Scheldt, located in the southwestern part of the Netherlands. The modeled current and residual sediment transport patterns agree well with observed ones. The modeled asymmetry of the ebb–tidal delta also agree with observed ones. Furthermore, bottom patterns are consistent with those found with a previous version of the idealized model which focused on the modeling of symmetric ebb–tidal deltas. However, the model is not able to reproduce the observed ebb-dominated channel. The underlying physical processes are explained in terms of vorticity dynamics. The convergence of the mean vorticity flux generates mean vorticity and thereby residual circulation. An analysis shows there is competition between two contributions to the convergence of the mean vorticity flux. This competition explains the sensitivity of the results to the model parameters.     

Lateral friction in the oceans as an effect of potential vorticity mixing

Abstract

Applying a mixing-length calculation to potential vorticity rather than to momentum a new type of lateral friction appears in the oceanic mass transport equations. This friction is evaluated for the special case of horizontally homogeneous, quasi-geostrophic turbulence. The main effect is a westward force arising from the so-called β-term. This produces an additional southward interior transport and a strengthening of the western boundary current. A turbulent exchange coefficient K^H = 10⁸ em²s^?1 is sufficient to give a Gulf Stream transport twice that obtained by the classical Sverdrup model.     

On the exact shape of the horizontal profile of a topographically rectified tidal flow

Abstract

Starting from the nonlinear shallow water equations of a homogeneous rotating fluid we derive the equation describing the evolution of vorticity by a fluctuating bottom topography of small amplitude, using a multiple scale expansion in a small parameter, which is the topographic length scale relative to the tidal wave length. The exact response functions of residual vorticity for a sinusoidal bottom topography are compared with those obtained by a primitive perturbation series and by harmonic truncation, showing the former to be invalid for small topographic length scales and the latter to be only a fair approximation for vorticity produced by planetary vortex stretching. In deriving the exact shape of the horizontal residual velocity profile at a step-like break in the bottom topography, it is shown that the Lagrangian profile only exists in a strip having the width of the amplitude of the tidal excursion at both sides of the break, and that it vanishes outside that interval. Moreover, in the limit of small amplitude topography at least, it vanishes altogether for the generation mechanism by means of planetary vortex stretching. The Eulerian profile is shown to extend over twice the interval of the Lagrangian profile both for production by vortex stretching and by differential bottom friction. These finite intervals over which the residual velocity profiles exist for a step-like topography are not reproduced by harmonic truncation of the basic equation. This method gives exponentially decaying profiles, indicating spurious horizontal diffusion of vorticity. In terms of orders of magnitude, the method of harmonic truncation is reliable for residual velocity produced by vortex stretching but it overestimates the residual velocity produced by differential bottom friction by a factor 2.     

Tidally-induced sediment transport patterns in the upper Bay of Fundy: A numerical study

The Minas Basin, the eastern end of the Bay of Fundy, is well known for its high tide ranges and strong tidal currents, which can be exploited to extract electricity power. The properties of the tidally-induced sediment transport in the Minas Basin, where significant changes in tidal processes may occur due to a recently proposed tidal power project, have been studied with a three-dimensional hydrodynamic model, an empirical bed load sediment transport model and surface sediment concentrations derived from the remotely-sensed images. The hydrodynamic model was evaluated against independent observational data, which include tidal elevation, tidal current (in the full water column and bottom layer), residual current profile and tidal asymmetry indicators. The evaluation shows that the model is in good agreement with the observations.The sediment transport includes two components, bed load and suspended particulate load. The bed load is calculated using the modelled bottom shear stress and the observed grain size data. The estimated features of bed load transport roughly agree with the observed patterns of the erosion and deposition in the Minas Basin and Cobequid Bay. The transport of the suspended load is estimated using the modelled velocity fields and the surface sediment concentration derived from remote-sensing images. The comparisons between the modelled results and the limited observations illustrate that the observed directions of suspended sediment transport are basically reproduced by the model. The modelled net suspended sediment input into the Minas Basin through Minas Passage is 2.4×10⁶ m³ yr^?1, which is comparable to the observed value of 1.6×10⁶ m³ yr^?1.The variations of the bed load and the suspended load in space and time are also presented. The total net transport, defined as the mean value of the sum of bed and suspended load transports during the tidal cycle, shows strong spatial variability. The magnitude of the transport flux ranges from 0.1 to 0.2 kg m^?1 s^?1 in Minas Channel and Minas Passage, 0.1 kg m^?1 s^?1 in Cobequid Bay, to 0.01 kg m^?1 s^?1 in the central Minas Basin and Southern Bight. In Minas Channel, the sediment transport follows the structure of the tidal residual circulation, which features a large anticlockwise gyre. The sediment in Minas Passage moves eastward and deposits into the central Minas Basin. However, the sediment from the eastern part of the Basin moves westward and deposits in the central Minas Basin as well. In the Cobequid Bay, sediment moves eastward and deposits in the upper bay.     

Residual circulation and stratification in the Liverpool Bay region of freshwater influence

Wind and tidal straining are proposed as key mechanisms influencing the magnitude and timing of the horizontal flux of freshwater across regions of freshwater influence (ROFIs). Evidence for this hypothesis is presented in estimates of the tidally averaged residual current profile, obtained from 5 years of continuous acoustic doppler current profiler measurements in the Liverpool Bay ROFI. The modified horizontal Richardson number (R_x^wtR_{x}^{wt}), which includes both the tidal and the wind forcing, was assessed as a measure of stratification. R_x^wtR_{x}^{wt} was found to be a good indicator of the timing of the evolution and destruction of stratification, but was not as successful as an indicator of the magnitude of stratification, both enduring and periodic. The observed mean residual velocities are compared to those predicted by a classical solution, and the eddy viscosity (N _z ) is shown to be a control on differences between the observed and predicted circulation. Principal component analysis is used to show that the strongest residual currents occur when the water column periodically alternates between a well-mixed and stratified state, a consequence of straining, rather than simply related to the density gradient. Evidence of wind straining was found in the correspondence between the wind direction and the near surface and near bed residual current direction.     

Tidal residual eddies and their effect on water exchange in Puget Sound

Tidal residual eddies are one of the important hydrodynamic features in tidally dominant estuaries and coastal bays, and they could have significant effects on water exchange in a tidal system. This paper presents a modeling study of tides and tidal residual eddies in Puget Sound, a tidally dominant fjord-like estuary in the Pacific Northwest coast, using a three-dimensional finite-volume coastal ocean model. Mechanisms of vorticity generation and asymmetric distribution patterns around an island/headland were analyzed using the dynamic vorticity transfer approach and numerical experiments. Model results of Puget Sound show that a number of large twin tidal residual eddies exist in the Admiralty Inlet because of the presence of major headlands in the inlet. Simulated residual vorticities near the major headlands indicate that the clockwise tidal residual eddy (negative vorticity) is generally stronger than the anticlockwise eddy (positive vorticity) because of the effect of Coriolis force. The effect of tidal residual eddies on water exchange in Puget Sound and its subbasins was evaluated by simulations of dye transport. It was found that the strong transverse variability of residual currents in the Admiralty Inlet results in a dominant seaward transport along the eastern shore and a dominant landward transport along the western shore of the inlet. A similar transport pattern in Hood Canal is caused by the presence of tidal residual eddies near the entrance of the canal. Model results show that tidal residual currents in Whidbey Basin are small in comparison to other subbasins. A large clockwise residual circulation is formed around Vashon Island near entrance of South Sound, which can potentially constrain the water exchange between the Central Basin and South Sound.     

A numerical study of horizontal dispersion in a macro tidal basin

Tidal circulation in Cobscook Bay, a macro tidal basin, is simulated using the three-dimensional, nonlinear, finite element ocean model, QUODDY_dry. Numerical particles are released from various transects in the bay at different tidal phases and tracked for several tidal cycles. Initially, nearby particles in the main tidal channel experience a great deal of spreading and straining, and after a few tidal cycles, they are separated in different parts of the bay. The fundamental mechanism for particle dispersion is the chaotic advection that arises from long tidal excursions passing through many residual eddies. A loosely correlated, inverse relationship between the two dimensionless parameters, ν (the ratio of the residual current to the tidal current) and λ (the ratio of the tidal excursion to the main topographic scale), can be constructed for large values of ν. Several Lagrangian statistical measures are used to quantify and distinguish dispersion regimes in different parts of Cobscook Bay. It is found that the effective Lagrangian dispersion coefficient can be estimated using the product of the magnitude of residual currents and the tidal excursion.     

Tidally generated internal waves in partially mixed estuaries

The generation of internal waves in the partially mixed estuaries is examined. The numerical experiments consider the barotropic tidal currents interacting with isolated obstacles in an open channel. The bottom boundary layer and longitudinal salinity gradient are included. Internal lee (arrested) waves are excited when the accelerating barotropic tidal current approaches the first-mode internal wave speed. The arrested waves are amplified, and are subsequently released when the decelerating tidal current falls below the first-mode internal wave speed. The power input from the barotropic tidal energy into internal wave energy is calculated. It is on the order of 10⁻² W/m², and is comparable to the estimated interior dissipation rate. This suggests that the tidally generated internal waves could be a significant energy source for mixing in the halocline.     

Numerical computation of the tidally induced Lagrangian residual current in a model bay

With a depth-averaged numerical model, the tidally induced Lagrangian residual current in a model bay was studied. To correctly reflect the long-term mass transport, it is appropriate to use the Lagrangian residual velocity (LRV) rather than the Eulerian residual velocity (ERV) or the Eulerian residual transport velocity (ETV) to describe the residual current. The parameter κ, which is defined as the ratio of the typical tidal amplitude at the open boundary to the mean water depth, is considered to be the indicator of the nonlinear effect in the system. It is found that the feasibility of making the mass transport velocity (MTV) approximate the LRV is strongly dependent on κ. The error between the MTV and the LRV tends to increase with a growing κ. An additional error will come from the various initial tidal phases due to the Lagrangian drift velocity (LDV) when κ is no longer small. According to the residual vorticity equation based on the MTV, the Coriolis effect is found to influence the residual vorticity mainly through the curl of the tidal stress. A significant difference in the flow pattern indicates that the LRV is sensitive to the bottom friction in different forms.     

Some observations of internal wave current fluctuations at the shelf-edge and their implications for sediment transport

Observations of internal wave current fluctuations at a site on the European continental shelf are described. These have revealed current ‘pulses’ of regular tidal (M₂) phase which may be associated with internal tides generated at the shelf-edge. Current ‘pulses’ have been observed with amplitudes of 30 to 40 cm s^?1 superimposed on peak spring tidal currents of the order 60 to 70 cm s^?1. The measurements have shown that these fluctuations extended throughout the bottom mixed layer to within at least 2 m of the sea bed where they may play an important role in modifying sediment transport rates.     

Tides off‐shore: Transition from California coastal to deep‐sea waters‡

Abstract

Tidal pressures and currents were measured with self‐contained capsules dropped to the sea floor for one month at distances of 175, 190, and 500 nautical miles from San Diego. These observations, together with a one‐week bottom pressure record by Filloux at 750 n miles, and three half‐week bottom current records by Isaacs et al, at intermediary distances, were analyzed for tidal components by cross‐correlation with a noise‐free reference time series. (For short records this method has some merit over classical tide analysis.) It was found that the tide decays seaward to e^‐1 times the coastal amplitude over a distance of order 1000 km for the semidiurnal species, slower for the diurnal species. Tidal currents turn counterclockwise, and are polarized with maximum flow parrallel to shore in the direction of tidal propagation (320°T) at local high tide. The current amplitude is roughly 2 cm/sec for the semidiurnal component, 1 cm/sec for the diurnal component. Superimposed baroclinic tidal currents lead to poor signal: noise ratios (between 1:1 and 10:1) for the barotropic currents. In contrast, the ratio is typically 1000:1 for the bottom pressures and generally exceeds that for coastal tide stations of comparable duration. Published I.H.B. tidal constants for exposed California coastal stations indicate “upshore” (towards 320°T) propagation at 140 m/sec for semidiurnal tides. 214 m/sec for diurnal tides.

To interpret these diverse observations, we have computed the dispersion laws for all possible rotationally‐gravitationally trapped waves against a straight coast with shelf. Trapped solutions are conveniently portrayed in terms of a parameter μ such that ? = sin μ = iu/v and f = ‐ cos μ = η/v define the ellipticity and impedance of the wave motion, η, u and v being off‐shelf dimensionless elevation, normal‐to‐shore and longshore components of velocity, respectively. We then attempt to fit the observations by a superposition of the possible wave classes, all of the same tidal frequency: (a) a free Kelvin‐like edge wave with small μ (mostly trapped by rotation, but somewhat slowed by the shelf); (6) a free Poincare‐like leaky wave; and (c) a forced wave (the distortion of the sea bottom by the tide producing forces plays a significant role). The mod el can account for the main features of the observed tidal heights, and gives relative amplitudes at the coast of 54:16:4 cm for components a:b:c in the case of the semidiurnal tides, 21:24:9 cm for the diurnal tides. The results place a semidiurnal amphidrome about midway between San Diego and Hawaii. Tidal currents are not well fitted by the model, and there are problems associated with the separation of barotropic and baroclinic modes, and with the benthic boundary layer. Coastal energy dissipation is small in the sea under investigation, but a “ capacitive “ phase delay appears to be associated with Northern California harbors and inland waters.     

Tidal circulation and energy dissipation in a shallow, sinuous estuary

The tidal dynamics in a pristine, mesotidal (>2 m range), marsh-dominated estuary are examined using moored and moving vessel field observations. Analysis focuses on the structure of the M ₂ tide that accounts for approximately 80% of the observed tidal energy, and indicates a transition in character from a near standing wave on the continental shelf to a more progressive wave within the estuary. A slight maximum in water level (WL) occurs in the estuary 10–20 km from the mouth. M ₂ WL amplitude decreases at 0.015 m/km landward of this point, implying head of tide approximately 75 km from the mouth. In contrast, tidal currents in the main channel 25 km inland are twice those at the estuary mouth. Analysis suggests the tidal character is consistent with a strongly convergent estuarine geometry controlling the tidal response in the estuary. First harmonic (M ₄) current amplitude follows the M ₂ WL distribution, peaking at mid-estuary, whereas M ₄ WL is greatest farther inland. The major axis current amplitude is strongly influenced by local bathymetry and topography. On most bends a momentum core shifts from the inside to outside of the bend moving seaward, similar to that seen in unidirectional river flow but with point bars shifted seaward of the bends. Dissipation rate estimates, based on changes in energy flux, are 0.18–1.65 W m⁻² or 40–175 μW kg^–1. A strong (0.1 m/s), depth-averaged residual flow is produced at the bends, which resembles flow around headlands, forming counter-rotating eddies that meet at the apex of the bends. A large sub-basin in the estuary exhibits remarkably different tidal characteristics and may be resonant at a harmonic of the M ₂ tide.     

Nonlinear interaction of the Tsugaru Warm Current and tide in the Tsugaru Strait

The Tsugaru Strait, which connects the Sea of Japan with the Pacific Ocean, is characterized by the eastward Tsugaru Warm Current (TWC) and oscillating tidal currents of similar magnitude. A 15-day current observation was conducted in one of the two narrow channels in the strait, at the northwest tip of the Shimokita Peninsula. The observation revealed that the spectral energy of the semidiurnal current exceeds that of the diurnal current, contrary to the conventional view. The Tsugaru Strait regional model was developed to study the mechanism of this spectral energy reversal (140–141.5° E, 40.4–42.6° N, 500?m grid resolution). At the eastern and western open boundaries, the model was driven by the constant Tsugaru warm current and tidal elevation, which was adjusted by comparing the model with tidal gauge observations within the channel. The relative magnitude of the spectral energies differed from that of the observation when the model was driven by tide only. However, the spectral energy levels were reversed when the model was driven by both tide and current. The nonlinear interaction of periodic tidal currents and the steady TWC was explained by the vorticity equation, which describes the production and advection of residual currents from tidal currents. According to the model results, flow separation and advection of vorticity by the TWC was the most prominent factor in this phenomenon. Because of the strong nonlinearities, flow separation around the headland occurred during the tidal period with dominant current magnitude and furnished the main difference between the diurnal and semidiurnal interactions. These phenomena were enhanced by the complex topography, and demonstrate the importance of scale interaction, especially when developing high-resolution regional models.     

Internal hydraulic control in rotating fluids—applications to oceans

Abstract

Laboratory experiments and analysis of shallow water equations in a rotating fluid show that channel flow is governed by the ratio of the width of the channel to the Rossby radius of deformation R= √[g&Delta;ρH/ρf ²]. Flows through narrow ocean openings exhibit blocking and clear evidence of hydraulic control. These imply that formulae can be derived for width, volume flux, and velocity scales of the currents. A new version of the constant potential vorticity problem is solved, and it is shown to predict volume flux within 22% of the zero potential vorticity results. Next a systematic method of predicting volume flux through ocean passages is described. Some examples are given from the Denmark Straits overflow and the flow of Antarctic Bottom Water into the western Atlantic Ocean. Two-layer flows and counter-flows with rotation in a narrow passage, the so-called lock exchange flow problem, duplicate flows at a number of important straits and openings to bays. A potential vorticity formulation is reviewed. The flows in the mouths of various bays such as Funka Bay in Hokkaido, Japan, Spencer Gulf in South Australia, and Chesapeake Bay in the United States has R < width of the mouth, and the two currents are separated by a front. The width of the front and the density difference can be predicted with good results.     

Turbulent transport of magnetic fields. V. Distribution of magnetic energy in a simple α2-dynamo

Abstract

In this paper we analyse the stationary mean energy density tensor T_ij = B_iB_j for the x ²-sphere. This model is one of the simplest possible turbulent dynamos, originally due to Krause and Steenbeck (1967): a conducting sphere of radius R with homogeneous, isotropic and stationary turbulent convection, no differential rotation and negligible resistivity. The stationary solution of the (linear) equation for T_ij is found analytically. Only T_rr , T _θθ and T _φφ are unequal to zero, and we present their dependence on the radial distance r.

The stationary solution depends on two coefficients describing the turbulent state: the diffusion coefficient β≈?u²?τ_c/3 and the vorticity coefficient γ ≈ ?|?×u|²?τ_c/3 where u(r, t) is the turbulent velocity and _c its correlation time. But the solution is independent of the dynamo coefficient α≈??u·?×u?τ_c/3 although α does occur in the equation for T_ij . This result confirms earlier conclusions that helicity is not required for magnetic field generation. In the stationary state, magnetic energy is generated by the vorticity and transported to the boundary, where it escapes at the same rate. The solution presented contains one free parameter that is connected with the distribution of B over spatial scales at the boundary, about which T_ij gives no information. We regard this investigation as a first step towards the analysis of more complicated, solar-type dynamos.     

Tidal currents and residual currents at Norderney,Elbe 1, and Aussen-Eider lightships and their variation under the influence of prevailing winds

Summary Four hourly current-and wind observations during the years 1924–1927 at the German lightvessels Norderney, Elbe 1, and Aussen-Eider were subjected to harmonic analysis with emphasis on the influence of the wind on the residual as well as on the tidal current. The tidal current is strongest at Elbe 1 and weakest at Aussen-Eider. The half-monthly inequality of the current is strongly influenced by a ₂ tidal component. Wind influences the velocity, phase and duration of ebb-and flow current in a systematic way at Norderney and Elbe 1. Deviations from the mean tidal current are caused mainly by the change in wind direction rather than by wind velocity. The mean residual current is weak at the three stations. But wind driven currents have a velocity up to 5 times as great as the mean residual current and reverse their direction with the wind. The annual variation of the mean residual current, however, is caused only to a small part by the annual wind variation.Abbreviations used in this paper Gr. M. Tr. Greenwich moon transit, i.e. Greenwich civil time of the upper or lower transit of the moon through the meridian of Greenwich - C _n computed tidal current at M1/2Hn - C _n ^m computed mean tidal current at M1/2Hn - M _n Moon-half hour mean, i.e. mean of all current velocities observed during M1/2Hn - M.A. Moon age of an observation, true Greenwich time of Gr.M.Tr. directly preceeding the time of observation, expressed in 12 integral numbers, each representing M.A. falling in 12 different hourly intervals - M1/2H Moon-half hour, 1/2 of the interval between one moon transit and the next, i.e. 1/24 of 12h25m - R _n ^o ,R _n ^' ,R _n ^" residual current computed by harmonic analysis ofn M1/2H means of the mean current, the current at weak winds, and the current at strong winds respectively - d.o.f. degrees of freedom - standard deviation ofC _n fromM _n - ^* mean standard deviation ofC _n fromM _n for analysis with weighted means - A _o Standard error of the residual currentA _o - AB standard error of the harmonic coefficientsA ₁,B ₁,A ₂,B ₂,... - S ₂ Phase of the current componentS ₂     

Tidal currents in the central Great Barrier Reef

Observations at 8 sites in the outer central Great Barrier Reef show M₂, S₂, K₁, and O₁ tidal currents flow directly off-shelf (northeast), when the corresponding tide at Townsville is at zero height and falling, with typical amplitudes of 12, 6, 3, and 2 cm s^?1. On the slope (at 300 m depth), the vertically averaged long-shelf component was small. On the shelf, the eccentricity of the tidal ellipses decreases shoreward and the tidal ellipses rotate anticlockwise. The major axes of the tidal ellipses tilt left of cross-shelf, especially for the diurnal constituents. There is satisfactory agreement between the observed and modelled cross-shelf currents. The long-shelf velocity is sensitive to the long-shelf changes in amplitude and phase of the tide heights and high quality tidal data for open boundary conditions will be required if numerical models are to model these currents satisfactorily.