Structure Of Tidal Currents Research Articles

Effect of variable winds on current structure and Reynolds stresses in a tidal flow: analysis of experimental data in the eastern English Channel

Abstract. Wind and wave effects on tidal current structure and turbulence throughout the water column are examined using an upward-looking acoustic Doppler current profiler (ADCP). The instrument has been deployed on the seafloor of 18-m mean depth, off the north-eastern French coast in the eastern English Channel, over 12 tidal cycles, and covered the period of the transition from mean spring to neap tide, and forcing regimes varied from calm to moderate storm conditions. During storms, we observed gusty winds with magnitudes reaching 15 m s−1 and wave heights reaching up to 1.3 m. Analysis of velocity spectra revealed a noticeable contribution of wind-induced waves to spectral structure of velocity fluctuations within the subsurface layer. Near the surface, stormy winds and waves produced a significant intensification of velocity fluctuations, particularly when the sustained wind blew against the ebb tide flow. As during wavy periods, the variance-derived Reynolds stress estimates might include a wave-induced contamination, we applied the Variance Fit method to obtain unbiased stresses and other turbulent quantities. Over calm periods, the turbulent quantities usually decreased with height above the seabed. The stresses were found to vary regularly with the predominantly semidiurnal tidal flow. The along-shore stress being generally greater during the flood flow (~2.7 Pa) than during the ebb flow (~−0.6 Pa). The turbulent kinetic energy production rate, P, and eddy viscosity, Az, followed a nearly regular cycle with close to a quarter-diurnal period. As for the stresses, near the seabed, we found the maximum values of estimated quantities of P and Az to be 0.1 Wm−3 and 0.5 m2 s−1, respectively, during the flood flow. Over the storm periods, we found the highest unbiased stress values (~−2.6 Pa) during ebb when tidal currents were opposite to the southwesterly winds while, during the flood, the surface stresses slightly exceeded those estimated for a calm period. A comparison of obtained results gives a good agreement with those of other researchers working on direct measurements of turbulence in tidal flows.

Skill tests of three‐dimensional tidal currents in a global ocean model: A look at the North Atlantic

We present and apply several skill tests to assess tidal currents generated within a global ocean model compared to an archive of current meter records spanning 40 years. Within the North Atlantic we have identified over 1800 velocity records available for comparison to model output. The skill tests identify those regions where tidal ellipse parameters (semi‐major/minor axis, inclination and Greenwich phase) fall within 95% confidence intervals derived from observations. Additional skill tests examine the vertical and horizontal structure of the tidal currents using the correlation and root mean square error between the observations and model. The skill tests account for grid misrepresentation within the model by comparing model values in a local 9‐point neighborhood. Both the three‐dimensional structure of model tidal currents and barotropic model tidal currents are compared to the altimetry based barotropic model TPXO 7.2. Our results indicate that the non‐data assimilative ocean model performance is comparable to TPXO 7.2. The semi‐major axes of the semi‐diurnal constituents lie within the 95% confidence intervals between 40% and 60% of the time in some regions of the North Atlantic. The performance degrades when all tidal ellipse parameters are considered. Root mean square errors between the model and observations distributed through the water column are generally less than 1 cm s−1 representing an error of less than ∼10% for constituent M2. The model tides also exhibit high correlation with observations in the horizontal planes. The skill tests could be adapted to other sets of observations and other models.

Vertical structure and seasonal variation of tidal and residual currents in the northern Huanghai Sea

Analysis of tidal current and sea level has been made based on the observations from the summer of 2006 to the winter of 2007, respectively. The result indicates that a two-layer structure of residual current exists in summer, with its upper layer going northwestward and the lower layer southeastward. In addition, some strong residuals exist in the neighboring depth of the pycnocline during the current period of astronomical tide. In winter, except some individual layersthe residual currents mostly direct to the northwest, from which we can see the fluctuation of abnormal sea-level and the appearance of associated current because of the changes of the wind field. The analysis of tidal ellipse indicates that the direction of the maximum semidiurnal component is clockwise from summer to winter, with an angle of 16°–18°. Moreover, in summer the semidiurnal component rotates with depth clockwise while the diurnal component counterclockwise. However, the vertical structure is almost homogeneous in winter.

Vertical structure of the M2 tidal current in the Yellow Sea

The vertical structure of the M2 tidal current in the Yellow Sea is analyzed from data acquired using an acoustic Doppler current profiler. The observed vertical profiles of the M2 tidal current are decomposed into two rotating components of counter-clockwise and clockwise, and restructured using a simple one-point model with a constant vertical eddy viscosity. The analyzed results show that the internal fictional effect dominates the vertical structure of the tidal current in the bottom boundary layer. In the Yellow Sea, the effect of the bottom friction reduces the current speed by about 20–40% and induces the bottom phase advance by about 15–50 minutes. In the shallower coastal regions, the effects of bottom topography are more prominent on the vertical structure of tidal currents. The vertical profile of the tidal current in summer, when the water column is strongly stratified, is disturbed near the pycnocline layer. The stratification significantly influences the vertical shear and distinct seasonal variation of the tidal current.

Complex EOF Analysis as a Method to Separate Barotropic and Baroclinic Velocity Structure in Shallow Water

Abstract Defining the vertical depth average of measured currents to be barotropic is a widely used method of separating barotropic and baroclinic tidal currents in the ocean. Away from the surface and bottom boundary layers, depth-averaging measured velocity is an excellent estimate of barotropic tidal flow, and internal tidal dynamics can be well represented by the difference between the measured currents and their depth average in the vertical. However, in shallow and/or energetic tidal environments such as the shelf of the South Atlantic Bight (SAB), bottom boundary layers can occupy a significant fraction of the water column, and depth averaging through the bottom boundary layer can overestimate the barotropic current by several tens of centimeters per second near bottom. The depth-averaged current fails to capture the bottom boundary layer structure associated with the barotropic tidal signal, and the resultant estimate of baroclinic tidal currents can mimic a bottom-trapped internal tide. Complex empirical orthogonal function (CEOF) analysis is proposed as a method to retain frictional effects in the estimate of the barotropic tidal currents and allow an improved determination of the baroclinic currents. The method is applied to a midshelf region of the SAB dominated by tides and friction to quantify the effectiveness of CEOF analysis to represent internal structure underlying a strong barotropic signal in shallow water. Using examples of synthesized and measured data, EOF estimates of the barotropic and baroclinic modes of motion are compared to those made using depth averaging. The estimates of barotropic tidal motion using depth-averaging and CEOF methods produce conflicting predictions of the frequencies at which there is meaningful baroclinic variability. The CEOF method preserves the frictional boundary layer as part of the barotropic tidal current structure in the gravest mode, providing a more accurate representation of internal structure in higher modes. The application of CEOF techniques to isolate internal structure co-occurring with highly energetic tidal dynamics in shallow water is a significant test of the method. Successful separation of barotropic and baroclinic modes of motion suggests that, by fully capturing the effects of friction associated with the barotropic tide, CEOF analysis is a viable technique to facilitate examination of the internal tide in similar environments.

Vertical structure of tidal currents over Espartel and Camarinal sills, Strait of Gibraltar

ADCP velocity data collected in the two main sills of the Strait of Gibraltar (Camarinal and Espartel sills) have been used for analysing the vertical structure of main tidal constituents (M 2, S 2, O 1 and K 1) currents in this area. Two different periods (winter and summer) were considered in correspondence to seasonal variations in density profiles. Amplitudes and phases of the various tidal constituents have been compared for both periods and locations. Barotropic and baroclinic parts of the tidal currents have been extracted using the dynamical mode decomposition technique and the relative importance of each mode has been established in terms on the energy associated. In Espartel sill, the barotropic mode is more energetic in wintertime for all constituents except for K 1. Baroclinic modes have smaller contribution to total energy. Second and third baroclinic modes tend to be more energetic than the first one, especially during winter, this indicating a relatively complex vertical structure of the tidal currents. Over Camarinal sill, barotropic mode accounts for more than 90% of total energy in all the tidal constituents, the highest value (97%) observed for M 2.

A multistation coastal acoustic tomography system with coherent operation

A multistation coastal ocean acoustic tomography (CAT) system with coherent operation has been developed and applied to field experiments over ten times in the last 8 years. The system is designed to measure both temperature and current velocity fields in the coastal ocean. As is well known, an ocean acoustic tomography is generally based on travel time measurements. In the CAT system, the clock accuracy for travel time measurement is most important to realize coherent transmission from multistations and to measure especially current velocity. For highly accurate coherent transmission from multistations, each station is equipped with a timing module synchronized by the clock signals of global positioning system (GPS). As a result, time error is maintained less than 0.1 μs. In the sound transmission from multistations, the code division multiple access (CDMA) and spread spectrum technology are applied. The coded signals also improved remarkably the signal‐to‐noise ratio of the CAT system. With detecting not only the amplitude, but also the phase of received signals, the accuracy of travel time measurement is improved within a sampling interval of data. This multistation CAT system served to map 2‐D time‐varying tidal current structures in Tokyo Bay (Kaneko et al., 2005).

Current structure measurements by the coastal acoustic tomography

The coastal acoustic tomography (CAT), coastal-sea application of deep-sea acoustic tomography (Munk and Wunsch, 1978), is proposed as an advanced technology to map current structures in the coastal sea. A sequence of successful experiments was recently carried out in the coastal seas with various oceanographic conditions around Japan (Yamaguchi et al., 2005; Kaneko et al., 2005; Lin et al., 2005). In the Tokyo Bay experiment of November 2002, the 2-D tidal currents inducing a clockwise residual circulation were mapped by eight CAT systems, located at both the eastern and western coasts of the bay. The vortex-embedded tidal currents with a maximum velocity of 5 ms−1 were targets in the Kanmon Strait experiment of March 2003. In the Hiroshima Bay experiment of September 2003, the stratified sea was shifted to the homogenized sea after the passage of a typhoon. The transition of tidal current structures before and after the typhoon was well measured by seven CAT systems, located at the northern coast and on the southern oyster rafts. The procedure of 2-D current mapping for the coastal seas with depths shallower than about 30 m is well established through a sequence of CAT experiments mentioned above.

Vertical structure and bottom-intensification of tidal currents off Northwestern Spain

Four-month current and temperature observations collected in two different positions and at four different depths in the Golfo Artabro, off the NW corner of the Iberian Peninsula, have been analysed in order to investigate some aspects of tides in this area. Tidal currents in the deepest stations are much greater than expected for a purely barotropic tide, a result that is even more outstanding if the bottom decay of the interior currents is allowed for. The near-bottom tidal enhancement is confirmed by the large tidal fluctuations of temperature at M2 frequency, equivalent to internal oscillations of some tens of metres of amplitude. The phase of these oscillations suggests propagation of the internal tide parallel to the depth gradient. The slope of the bottom profile is comparable to the slope of the internal rays and favours the generation of internal tides of considerable amplitude. The existence of areas of supercritical slope shoreward of the mooring lines is able to reflect seawards the energy of the incoming internal waves along trajectories nearly parallel to the sea floor, a mechanism that is put forward as responsible for the considerable concentration of tidal energy in the bottom layer.

The structure of tides in the Western Iberian region

A s-coordinate three-dimensional model, regional ocean modeling system (ROMS), was implemented in the Western Iberian region ranging from the coast to 11°W aiming high-resolution tidal simulations for an homogeneous ocean. The features for tidal heights and ellipses for the principal constituents, M 2, S 2, N 2, K 2, K 1, O 1, P 1 and Q 1, were imposed at the boundaries of the model. A tidal analysis for heights and tidal currents was done allowing to calculate two-dimensional distribution of amplitudes and three-dimensional structure of tidal currents. The amplitudes and phases for heights agree with previous results and observations, showing a good precision on the tidal propagation in the interior of the domain. Tidal kinetic energy is dominated by the semi-diurnal components, mainly M 2, and increases on the shelf. Over the Lisbon Promontory the diurnal component K 1 is however the second more energetic harmonic. Vertical variation of tidal ellipse parameters evidences the different structure of semi-diurnal and diurnal tidal components, as well as differences between the open sea and shelf tidal circulation.

ADCP Measurements of Momentum Balance and Dynamic Topography in a Constricted Tidal Channel

Abstract The dynamics of tidal flow through inlets are not fully understood; observations are scarce because of the small spatial scales over which the flow varies. This paper gives the first detailed measurements of the 2D structure of tidal currents and the dynamical terms of the momentum equation within a tidal inlet, leading to an improved understanding of the physics of tidal inlets. In the 180 cm s−1 peak flow the near-steady-state momentum balance is dominated by horizontal advection and the pressure gradient, with bottom friction playing a secondary role. At slack water, there is a balance between local acceleration and the pressure gradient. Numerical integration of the ADCP-measured terms in the momentum equation yields 60-m- resolution dynamic topography that shows a 7-cm variation at peak flood consistent with Bernoulli’s equation. The surface topography because of friction forms a linear ramp with a peak irreversible head loss of 2 cm over 600 m. Tidal velocities were extracted from the ADCP measurements by extending an existing spline analysis technique. This technique is known to be sensitive to the number and location of the nodes where weights are applied to the spline. Simulations with artificial data representative of the tidally varying ADCP measurements show that, provided there are sufficient nodes to resolve the smallest spatial scale of interest, velocities predicted by the spline technique are insensitive to the number or locations of the nodes.

Cross-Shore Internal Waves in Zanpa Coastal Region of Okinawa Island

Comprehensive field observations were made to establish a baseline of the existing tidal current structure and internal wave phenomena in a coastal region. Water temperature distributions at different depths and vertical profiles of horizontal current were examined in detail. Time series of horizontal current and near-bottom temperature fluctuations are explained by internal wave theories following two-layer and continuous density distributions. Study results show the propagation of cross-shore internal waves in an area where bottom topography is characterized by near-critical slope. Near-bottom cold internal current that flowed toward the shore significantly influenced the water temperature distributions in the region. The vertical structure of east-west horizontal current showed that its transmission was consistent with the phase propagation of theoretically calculated internal waves.

Tidal currents in the St. Lawrence Island region

Vertical and spatial variability of tidal currents in the northern part of the Bering Sea near St. Lawrence Island were examined using observations made at 17 new and historical current meter mooring locations. The semidiurnal currents dominate over the diurnal currents. Semidiurnal currents exhibit a seasonal modulation with currents being somewhat stronger during the summer and fall when the density structure displays two‐layer stratification. Diurnal currents exhibit a weak semiannual modulation. Examination of the vertical structure of tidal currents shows that maximum semidiurnal currents are observed in the upper or middle layers down to a depth of about 20 m, and below this depth the energy of the semidiurnal currents decreases rapidly. However, the energy of diurnal band currents remains almost constant with depth, decreasing only in close proximity to the bottom. Rotary spectral analysis applied to the records shows further differences: the M2 clockwise (CW) component of rotation dominates in the upper and middle water column but the counterclockwise component (CCW) dominates near the bottom. Interpretation of these observed results points to the different bottom boundary layers (BBL) for the CW and CCW motions in addition to the role of density stratification in organizing the BBL. We compare results of a vertically averaged two‐dimensional model to the observationally derived tidal ellipse parameters and show that the barotropic formulation provides a first‐order description of the tidal regime within the domain.

Accurate imaging and prediction of Kanmon Strait tidal current structures by the coastal acoustic tomography data

The Kanmon Strait acoustic tomography data acquired at a 5‐min interval are assimilated sequentially into a 2D ocean model on the basis of the ensemble Kalman filter scheme to image strong tidal current structures occurring in the strait. When the accurate range‐averaged currents obtained for the sound transmission lines connecting eight tomography stations are used as assimilation data, the complicated vortex‐imbedded currents are imaged with horizontal resolution and accuracy much better than the result of tomographic inversion. The assimilated currents are well compared to the shipboard ADCP data with a RMS difference of about 24 cm s−1 for both the horizontal velocity components. The assimilated volume transport across the strait also shows a good agreement with the transport estimated from the range‐averaged current on a pair of transmission lines crossing the strait, making a RMS difference of 3700 m3 s−1.

A Continuous Mapping of Tidal Current Structures in the Kanmon Strait

Tidal current structures at the Hayatomono-Seto of the Kanmon Strait are mapped continuously during March 17 to 20, 2003, including a spring tide, by the eight coastal acoustic tomography (CAT) systems distributed on both the sides of the strait. Detailed structures of strong tidal currents and their associated vortices are well reconstructed by the inverse analysis of travel-time difference data obtained from the reciprocal sound transmission between the paired CAT systems located at both sides of the strait mainly. The results are well compared to the shipboard acoustic Doppler current profiler (ADCP) data at the correlation rate of 0.84/0.82 and the RMS difference of 0.47/0.48 ms−1 for the east-west/north-south current after the selection of good data. During the observation period, the maximum hourly mean volume transport for the upper 7 m layer across the strait reached 13,314 m3 s−1 for the eastward and 5,547 m3 s−1 for the westward. The daily mean transport is directed to the eastward and estimated 1,470 m3 s−1 and 2,140 m3 s−1 for March 18 and 19, respectively, when a spring tide occurs.

Sediment trapping, turbidity maxima, and bathymetric stability in macrotidal estuaries

This paper examines how fine marine sediments are trapped in macrotidal estuaries and what processes coexist to maintain bathymetric stability. An analytical emulator is constructed integrating explicit formulations for tidal and residual current structures together with sediment erosion, suspension, and deposition. The emulator estimates suspended concentrations and net sediment fluxes and indicates the nature of their functional dependencies and corresponding sensitivities to tidal elevation amplitude (or tidal current ), channel depth D, bed friction coefficient f, sediment size (specifically, settling velocity Ws), and river flow velocity UR. Associated scaling analyses reveal the relative impacts of terms representing tidal nonlinearities, gravitational circulation, and “delayed” settling. Using the emulator to determine conditions consistent with zero net flux of sediments or bathymetric stability, we deduce Ws ≈ f. Overall, finer sediments are imported and coarser ones are exported, with more imports (extending to a coarser fraction) on spring tides than on neaps. The emulator indicates that the spring‐neap shifting of this coarse‐fine boundary corresponds to particle diameters between 30 and 50 μm. This constitutes selective sorting, maintaining a widely distributed source of continuously resuspended material in a size range commonly observed. By illustrating the acute sensitivity of sediment fluxes to the bed friction coefficient, we anticipate feedback adjustments between suspended and surficial sediments. Factors governing the generation, location, and characteristics of turbidity maxima are indicated, including dependence on /D. A direct link is shown between parameters that control sediment flux at a specific cross section and net upstream tidal energy dissipation.

Spatial structure of tidal and residual currents as observed over the shelf break in the Bay of Biscay

Theoretical and laboratory models show that internal-wave energy in continuously stratified fluids propagates in the vertical plane, at an angle set by the wave, buoyancy and Coriolis frequencies. Repeated Acoustic Doppler Current Profiler observations on three transects, crossing the shelf edge, now directly reveal this beam-wise propagation of internal tides in the Bay of Biscay. This confirms previous suggestions based on observations sampled more sparsely in space. The present observation is made by bin-wise harmonic analysis of horizontal currents, leading to the spatial resolution of barotropic and baroclinic semi-diurnal tidal and (time-averaged) residual flows. The observed barotropic tide has a cross-slope mass flux that is roughly constant. Its fast along-slope phase variations can only in part be explained by the spring-neap tidal cycle. The observed baroclinic tide compares favourably to that produced by a 2D numerical model. The observations reveal details of the internal tidal beam, including its spatial amplitude distribution, presence of amphidromes and direction of phase propagation. The cross-isobath structure of the along-slope barotropic mean flow shows a localized maximum near the shelf break. Over two transects it agrees in sign and magnitude with a theoretical tidally rectified flow. The baroclinic, cross-isobath mean flow shows a strong near-bottom downwelling flow, compensated by an on-shelf-directed flow in the upper part. The along-shelf mean flow displays subsurface intensification attributed here to frictional modification of a tidally rectified flow that is bottom-trapped due to stratification.

Incremental inference of boundary forcing for a three-dimensional tidal model: tides in the Taiwan Strait

Tides in the Taiwan Strait are predominantly semidiurnal. The semidiurnal tide propagates southward along the mainland (China) coast but is a standing wave on the Taiwan coast. The tidal amplitude is large, reaching about 2 m in the middle of the strait, but diminishing rapidly towards the deeper portion of the strait. An amphidromic point is located off the southwest coast of Taiwan. Tidal currents are strong near the open ends (especially on the Taiwan side) and diminish towards the middles of the strait. A fine-resolution (3 km×3 km), three-dimensional, coastal ocean model is being developed for the Taiwan Strait. In this study, the focus is on validation of tidal sea levels and currents. The limited-area model is driven by tidal elevations on two open ends, of which amplitudes and phases are optimized through a four-dimensional variational assimilation. Specifically, the model uses an incremental approach in which misfits between model results and coastal tidal observations are reduced incrementally through repeat applications of a linear two-dimensional model and its adjoint. The incremental approach is both effective and efficient. The root-mean-squared (rms) error for the dominant M 2 tide is reduced from about 0.15 to 0.06 m, a five-fold reduction in error variance. Moreover, this is achieved with only 3–4 iterations of the three-dimensional model; for comparison, a typical four-dimensional variational assimilation will require an order of magnitude more computation effort. The predicted tidal current ellipses are also compared with the observations from six bottom-mounted Acoustic Doppler Current Profilers (ADCP). The semi-major axis currents generally agree to within 0.05 m/s. The sensitivity of vertical tidal current structure to bottom friction also is examined.

Saline intrusion in partially mixed estuaries

Restricting interest to partially mixed estuaries, earlier studies of tidally averaged linearised theories relating to the vertical structure of salinity and velocities (accompanying saline intrusion) are extended to take account of tidal straining and associated convective overturning. The applicability of these theories is evaluated by reference to a ‘single-point’ numerical model in which the time-varying cycle of depth-averaged tidal current amplitude, Û, and a (temporally and vertically) constant saline gradient, S x , are specified. This model highlights the importance of convective overturning in counteracting unstable density structures introduced by tidal straining. By omitting overturning in the model, results agree closely with linearised theoretical derivations. However, incorporating overturning substantially increases tidally averaged surface-to-bed differences for both residual currents, δ u, and salinity, δ s. The vertical structure of tidal currents is a maximum, and hence the effect of tidal straining, in shallow macro-tidal estuaries. The propagation of tidal elevations and currents remains insensitive to saline intrusion in partially mixed estuaries. The applicability of the model was evaluated by simulation of recent measurements by Rippeth et al. (J. Phys. Oceanogr. 31 (2001) 2458). To explore the generality of estuarine responses, the model was run for a wide range of values of saline intrusion lengths, L, and water depths, D. Additional sensitivity analyses were made for changes in Û and bed stress coefficient, k. Response frameworks are shown for: δ u, δ s, potential energy anomaly φ, work done by bed friction and internal shear, rates and efficiency of saline mixing and ratios of relative mixing by diffusion to overturning. By equating the rate of mixing associated with vertical diffusion with river flow, Q, an expression for saline intrusion length L∝D 2/k U ̂ U o ( U o river flow velocity) was derived. This formulation agrees with an earlier derivation based on flume tests and showed reasonable agreement with observed values in six estuaries (eight cases). However, in funnel-shaped estuaries, axial migration of the intrusion introduces major variations in D, Û and U o, thereby complicating the application of the above expression for L. Moreover, the time lag involved in the adjustment of L to changes in Û and Q may explain much of the complexity encountered in the observations.

Tidal currents and mixing in the Lake Maracaibo estuarine system

The Lake Maracaibo estuarine system is a cooscillating coupled ocean-lake system connected through a partially mixed estuary. In this paper we examine the low frequency movements (w < 0.1 cycles/day) in the different water bodies within this system. The harmonic and rotary spectral analyses of velocity data indicates the importance of tidal forcing within the whole system and its interaction with winds and fresh water discharge. In particular, the results indicate the existence of dominant semi-monthly oscillations in Lake Maracaibo, likely of non-linear tidal origin, and suggest that vertical stratificaction plays an important role in controlling the three-dimensional structure of tidal currents.