The formation of tidal sand waves: Fully three-dimensional versus shallow water approaches

Tidal sand waves, also named tidal dunes, are large scale bedforms generated by the growth of perturbations of the sea bottom driven by tidal currents. Indeed, the interaction of an oscillatory tidal current with a bottom waviness gives rise to steady recirculating cells which tend to drag the sediment from the troughs towards the crests of the bottom perturbation. The net motion of the sediment towards the crests is opposed by gravity force and the growth of the perturbation is controlled by a balance between these two effects. In the literature, to determine the conditions which lead to the formation of sand waves and to determine the characteristics of the bedforms generated by this instability mechanism, both fully three-dimensional and shallow water approaches are employed. The shallow water approach is computationally less expensive than the fully three-dimensional one but, in many cases, it might be less accurate. This paper compares the quantitative predictions obtained by means of the two approaches and quantifies the range of the parameters such that the shallow water approximation provides reliable predictions.     

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.     

Observations of semidiurnal internal tidal currents off central Chile (36.6°S)

Observations of semidiurnal internal tidal currents from three moorings deployed on the continental shelf off central Chile during summer and winter of 2005 are reported. The spectra of the baroclinic currents showed large peaks at the semidiurnal band with a dominant counterclockwise rotation, which was consistent with internal wave activity. The amplitude of the barotropic tidal currents varied according to the spring–neap cycle following the sea level fluctuations. In contrast, the amplitudes of the internal tide showed high spatial-temporal variability not directly related to the spring–neap modulation. Near the middle of the continental shelf and near the coast (San Vicente Bay) the variance of the semidiurnal baroclinic current is larger than the variance of its barotropic counterpart. The vertical structure of the baroclinic tidal current fluctuations was similar to the structure of the first baroclinic internal wave mode. In general, in the three study sites the variance of the baroclinic current was larger near the surface and bottom and tended to show a minimum value at mid depths. Kinetic energy related to semidiurnal internal waves was larger in winter when stratification of the water column was stronger. During summer, upwelling and the decrease of freshwater input from nearby rivers reduced the vertical density stratification. The amplitude of the semidiurnal internal tide showed a tendency to be enhanced with increasing stratification as observed in other upwelling areas. The continental shelf break and submarine canyons, which limit the continental shelf in the alongshore direction, represent near-critical slopes for the semidiurnal period and are suggested to be the main internal tide generation sites in the study region.     

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.     

A parameterization of the wavelength of tidal dunes

The idealized model of Besio et al. (On the formation of sand waves and sand banks. Journal of Fluid Mechanics 2006; 557: 1–17) is used to predict the wavelength of tidal dunes (sand waves) generated by tidal currents in estuaries and shallow seas. The predictions are then analysed and a formula is proposed to estimate the wavelength of tidal dunes as a function of the parameters of the problem. The wavelength of the dunes is found to increase when the water depth is increased and/or the strength of the tidal current is decreased. On the other hand, the size of the bottom material (if medium sand is considered) and the tidal ellipticity are found to have a relatively small influence on the length of the bottom forms. The formula proposed provides results which are consistent with field observations of different authors. Copyright © 2011 John Wiley & Sons, Ltd.     

Variations of vertical velocity in the deep oceans simulated by a 1/10° OGCM

This paper analyzes variations of vertical velocity w simulated by the 1/10° Ocean General Circulation Model for the Earth Simulator (OFES). Strong w-variability is found in the deep oceans. When w is WKBJ-normalized, the standard deviation averaged over the Southern Ocean increases with depth and is larger than 8 × 10^− 3 cm/s throughout the water column below 1,500 m. Evidences are presented that link this w-variability to internal waves generated by quasi-steady currents over topography. The aliasing errors in lag-3-day correlations suggest a bottom generation of near-inertial waves. A scale analysis indicates that vertically propagating waves that can be resolved by the OFES model are waves with frequencies of the order of inertial frequency and wavelengths comparable to the order of the grid size. The vertical energy flux associated with these waves is substantial. When integrated globally, the vertical energy flux is upward in the upper 4 km and reaches maximum values of about 0.8 TW at about 1 to 2 km depth. Thus, the w-variability in the 1/10° OFES integration points not only to a strong bottom generation of near-inertial internal waves in the deep Southern Ocean but also to the possibility that the power provided by internal waves generated by non-tidal currents over topography can be comparable to the power provided by internal waves generated by tidal flows over topography.     

Sediment transport and resuspension due to combined motion of wave and current in the northern Adriatic Sea during a Bora event in January 2001: A numerical modelling study

The Adriatic Sea general circulation model coupled to a third generation wave model SWAN and a sediment transport model was implemented in the Adriatic Sea to study the dynamics of the sediment transport and resuspension in the northern Adriatic Sea (NAS) during the Bora event in January 2001. The bottom boundary layer (BBL) was resolved by the coupled model with high vertical resolution, and the mechanism of the wave–current interaction in the BBL was also represented in the model. The study found that, during the Bora event of 13–17 January 2001, large waves with significant wave height 2 m and period of 5 s were generated by strong winds in the northwestern shelf of the Adriatic where the direction of wave propagation was orthogonal to the current. The combined motion of the wave and current in the BBL increased the bottom stress over the western Adriatic shelf, resulting in stronger sediment resuspension there. Combining stronger bottom resuspension and strong upward vertical flux of resuspended sediments due to turbulent mixing, the model predicted that sediment concentration near the Po River was much higher than that predicted by the model run without wave forcing. The study also shows that wave–current interaction in the BBL reduced the western Adriatic Coastal Currents (WACCs) in the shallower north. It is concluded that wave forcing significantly changed the sediment distributions and increased the total horizontal fluxes over the western shelf. These results signified wave effect on sediment flux and distribution in the NAS, and suggested that waves cannot be neglected in the study of dynamics of sediment transport and resuspension in the shallow coastal seas. By including the tidal forcing in the coupled model, we also examined the effect of tides on the sediment transport dynamics in the NAS.     

Tsunami–tide interactions: A Cook Inlet case study

First, we investigated some aspects of tsunami–tide interactions based on idealized numerical experiments. Theoretically, by changing total ocean depth, tidal elevations influence the speed and magnitude of tsunami waves in shallow regions with dominating tidal signals. We tested this assumption by employing a simple 1-D model that describes propagation of tidal waves in a channel with gradually increasing depth and the interaction of the tidal waves with tsunamis generated at the channel's open boundary. Important conclusions from these studies are that computed elevations by simulating the tsunami and the tide together differ significantly from linear superposing of the sea surface heights obtained when simulating the tide and the tsunami separately, and that maximum tsunami–tide interaction depends on tidal amplitude and phase. The major cause of this tsunami–tide interaction is tidally induced ocean depth that changes the conditions of tsunami propagation, amplification, and dissipation. Interactions occur by means of momentum advection, bottom friction, and variable water flux due to changing total depth and velocity. We found the major cause of tsunami–tide interactions to be changing depth. Secondly, we investigate tsunami–tide interactions in Cook Inlet, Alaska, employing a high-resolution 2-D numerical model. Cook Inlet has high tides and a history of strong tsunamis and is a potential candidate for tsunami impacts in the future. In agreement with previous findings, we find that the impacts of tsunamis depend on basin bathymetries and coastline configurations, and they can, in particular, depend on tsunami–tide interactions. In regions with strong tides and tsunamis, these interactions can result in either intensification or damping of cumulative tsunami and tide impacts, depending on mean basin depth, which is regulated by tides. Thus, it is not possible to predict the effect of tsunami–tide interaction in regions with strong tides without making preliminary investigations of the area. One approach to reduce uncertainties in tsunami impact in regions with high tides is to simulate tsunamis together with tidal forcing.     

High-frequency vertical current observations in stratified seas

Although large-scale tidal and inertial motions dominate the kinetic energy and vertical current shear in shelf seas and ocean, short-scale internal waves at higher frequencies close to the local buoyancy frequency are of some interest for studying internal wave breaking and associated diapycnal mixing. Such waves near the upper limit of the inertio-gravity wave band are thought to have relatively short O (10²–10³ m) horizontal scales and to show mainly up- and downward motions, which contrasts with generally low aspect ratio large-scale ocean currents. Here, short-term vertical current (w) observations using moored acoustic Doppler current profiler (ADCP) are presented from a shelf sea, above a continental slope and from the open ocean. The observed w, with amplitudes between 0.015 and 0.05 m s⁻¹, all span a considerable part of the water column, which is not a small vertical scale O(water depth) or O (100–500 m, the maximum range of observations), with either 0 or π phase change. This implies that they actually represent internal waves of low vertical modes 1 or 2. Maximum amplitudes are found in layers of largest stratification, some in the main pycnocline bordering the frictional bottom boundary layer, suggesting a tidal source. These ‘pycnocline-w’ compose a regular train of (solitary) internal waves and linearly decrease to small values near surface and bottom.     

Flood–ebb and spring–neap variations of mixing,stratification and circulation in Chesapeake Bay

A three-dimensional hydrodynamic model is used to investigate intra-tidal and spring–neap variations of turbulent mixing, stratification and residual circulation in the Chesapeake Bay estuary. Vertical profiles of salinity, velocity and eddy diffusivity show a marked asymmetry between the flood and ebb tides. Tidal mixing in the bottom boundary layer is stronger and penetrates higher on flood than on ebb. This flood–ebb asymmetry results in a north–south asymmetry in turbulent mixing because tidal currents vary out of phase between the lower and upper regions of Chesapeake Bay. The asymmetric tidal mixing causes significant variation of salinity distribution over the flood–ebb tidal cycle but insignificant changes in the residual circulation. Due to the modulation of tidal currents over the spring–neap cycle, turbulent mixing and vertical stratification show large fortnightly and monthly fluctuations. The stratification is not a linear function of the tidal-current amplitude. Strong stratification is only established during those neap tides when low turbulence intensity persists for several days. Residual circulation also shows large variations over the spring–neap cycle. The tidally averaged residual currents are about 50% stronger during the neap tides than during the spring tides.     

Can tidal perturbations associated with sea level variations in the western Pacific Ocean be used to understand future effects of tidal evolution?

This study examines connections between mean sea level (MSL) variability and diurnal and semidiurnal tidal constituent variations at 17 open-ocean and 9 continental shelf tide gauges in the western tropical Pacific Ocean, a region showing anomalous rise in MSL over the last 20 years and strong interannual variability. Detrended MSL fluctuations are correlated with detrended tidal amplitude and phase fluctuations, defined as tidal anomaly trends (TATs), to quantify the response of tidal properties to MSL variation. About 20 significant amplitude and phase TATs are found for each of the two strongest tidal constituents, K₁ (diurnal) and M₂ (semidiurnal). Lesser constituents (O₁ and S₂) show trends at nearly half of all gauges. Fluctuations in MSL shift amplitudes and phases; both positive and negative responses occur. Changing overtides suggest that TATs are influenced by changing shallow water friction over the equatorial Western Pacific and the eastern coast of Australia (especially near the Great Barrier Reef). There is a strong connection between semidiurnal TATs at stations around the Solomon Islands and changes in thermocline depth, overtide generation, and the El Niño Southern Oscillation (ENSO). TATs for O₁, K₁, and M₂ are related to each other in a manner that suggests transfer of energy from M₂ to the two diurnals via resonant triad interactions; these cause major tidal variability on sub-decadal time scales, especially for M₂. The response of tides to MSL variability is not only spatially complex, it is frequency dependent; therefore, short-term responses may not predict long-term behavior.     

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.     

The effect of geometry and tidal forcing on hydrodynamics and net sediment transport in semi-enclosed tidal basins

A new depth-averaged exploratory model has been developed to investigate the hydrodynamics and the tidally averaged sediment transport in a semi-enclosed tidal basin. This model comprises the two-dimensional (2DH) dynamics in a tidal basin that consists of a channel of arbitrary length, flanked by tidal flats, in which the water motion is being driven by an asymmetric tidal forcing at the seaward side. The equations are discretized in space by means of the finite element method and solved in the frequency domain. In this study, the lateral variations of the tidal asymmetry and the tidally averaged sediment transport are analyzed, as well as their sensitivity to changes in basin geometry and external overtides. The Coriolis force is taken into account. It is found that the length of the tidal basin and, to a lesser extent, the tidal flat area and the convergence length determine the behaviour of the tidally averaged velocity and the overtides and consequently control the strength and the direction of the tidally averaged sediment transport. Furthermore, the externally prescribed overtides can have a major influence on tidal asymmetry in the basin, depending on their amplitude and phase. Finally, for sufficiently wide tidal basins, the Coriolis force generates significant lateral dynamics.     

Interactions among waves,current, and mud: Numerical and laboratory studies

Interactions between waves, current, mud and turbulence are very complicated in the coastal and estuarine turbid waters. It is still necessary to improve our understanding of the fundamental physical processes governing the cohesive sediment transport in the coastal and estuarine waters. A numerical model is developed to study the interactions among waves, current, and mud. An eddy viscosity model for wave and current is proposed in order to close the equations of wave motion or of current motion in a combined flow, respectively. The equations of mud transport are derived based on the visco-elastic properties of mud. Coupling the equations of wave motion or of current motion for water layer with those of mud layer can give (1) wave height; (2) distributions of current velocities in the water layer; (3) distributions of transport velocities at the water–mud interface; and (4) distributions of mass transport velocities within the mud layer. These modeled results are in a reasonable agreement with experimental results. Results suggest that (1) the rate of wave attenuation increases in the opposing currents (currents against in the direction in which the waves propagate) and decreases in the following currents (currents in the same direction as that in which the waves propagate); (2) the opposing currents would have more significant effects on the rate of wave height attenuation than the following currents; (3) the effect of current on the rate of wave attenuation on the muddy bottom is larger than that on the rigid bottom; (4) mud transport rate increased in the following currents but decreased in the opposing currents; and (5) the rate of wave height attenuation on the mud bottom is one order of magnitude larger than that on the rigid bottom.     

Coastal tides in West Greenland derived from tide gauge records

Based on pressure tide-gauge observations, sea-level records are derived for ten sites along the coast of West Greenland. The ocean tidal signal is extracted by a harmonic tidal analysis. The accuracy of the determined tidal constants is discussed in detail. The tides account for 85% of the observed sea-level standard deviation. The tide gauge records reveal significant shallow-water tidal effects, in particular compound and overtide amplitudes reaching 5 cm. The propagation of the tidal waves into the fjords depends strongly on local conditions and is in some cases accompanied by an amplification of the tidal amplitudes. The observed tidal signals are compared to the predictions of the global ocean tide model FES2004. At the outer coast, a good agreement is found. Inside the fjords, however, the model performs worse and tide gauge observations may still be indispensable when accurate tidal signals are required.     

On the generation and propagation of internal solitary waves in the southern Andaman Sea: A numerical study

Numerous internal solitary waves(ISWs) have been observed in the southern Andaman Sea. In this study, the two-dimensional Massachusetts Institute of Technology general circulation model is applied to investigate the dynamics of ISWs and explore the effects of the bottom topography and tidal forcing on the generation and propagation of ISWs in the southern Andaman Sea. The results show that the large-amplitude depression ISWs are mainly generated via the oscillating tidal flow over the sill of the Great Channel, and the generation of ISWs is subject to the lee wave regime. The Dreadnought Bank cannot generate ISWs itself; however, it can enhance the amplitudes of eastward-propagating ISWs generated from sill A, owing to constructive interference of internal tide generation between the sill of the Great Channel and the Dreadnought Bank. The eastward-propagating ISWs generated by the eastern shallow sill near the continental shelf can propagate to the shelf, where they evolve into elevation waves because of the shallow water. Sensitivity runs show that both the semidiurnal and diurnal tides over the sill of the Great Channel can generate ISWs in this area. However, the ISWs generated by diurnal tides are much weaker than those generated by semidiurnal tides. Mixed tidal forcing has no significant effect on the generation of ISWs.     

Numerical study of generation of the tidal shear front off the Yellow River mouth

Tidal shear front off the Yellow River mouth has been observed and modeled in the previous studies. However, a detailed investigation of the front generation has not been conducted. The aim of this paper is to use a three-dimensional tidal model coupled to a sediment transport module to examine the front formation. The model predicted a tidal shear front that propagated offshore and lasted 1–2 h at both flood and ebb phase off the Yellow River mouth. The sensitivity numerical experiments showed that the topography with a strong slope off the Yellow River mouth was a determining factor for the front generation, and a parallel orientation between the major axes of ellipses and co-tidal lines of maximum tidal current was a necessary condition. While the bottom friction and the river runoff had no effect on the front location but affected the front intensity, the front generation was not sensitive to the coastline variation. The study concluded that the bottom slope off the river mouth induces a strong variation in the bottom stress in a cross-shore direction, which produces both maximum phase gradient and sediment concentration variability across the tidal shear front. With the extending Yellow River delta, the tidal shear front under the new bathymetry of year 2003 has been strengthened and pushed further offshore due to an increased bottom slope.     

Influence of the back-barrier basin length on the geometry of ebb-tidal deltas

The characteristics of ebb-tidal deltas are determined by the local hydrodynamics. The latter depend, among others, on the geometry of the adjacent back-barrier basin. Therefore, interventions in the back-barrier basin can affect the geometry of ebb-tidal deltas. In this study, the effect of the length of the back-barrier basin on the sand volume and spatial symmetry of ebb-tidal deltas is quantified with the use of a numerical model. It is found that the length of the back-barrier basin affects the tidal prism, the amplitude and phase of the primary tide and its overtides, and the residual currents that, together, determine the sand volume of the ebb-tidal delta. In particular, it is found that no unique relationship exists between tidal prism and sand volume of an ebb-tidal delta. The spatial symmetry of ebb-tidal deltas is also found to be affected by the length of the back-barrier basin. This is because the basin length determines the phase difference between alongshore and cross-shore tidal currents. The numerical model results give a possible explanation for the changes that are observed in the geometry of the ebb-tidal deltas that are located seaward of the Texel Inlet and Vlie Inlet after the closure of the Zuiderzee.     

On the effect of subinertial phenomena on the internal lee waves generation in the Strait of Gibraltar

The generation of internal lee waves (ILW) in the Strait of Gibraltar takes place in the main sill where the tidal flow interacts with a submarine obstacle. The tidal flow is perturbed by subinertial phenomena of different nature summarized in the subinertial currents that can inhibit the ILW generation. The authors present an attempt to randomize the problem by the introduction of a Gaussian noise in the Taylor–Goldstein equation. The random number sets are generated from the statistical distribution of the previously isolated random part of the subinertial currents from experimental data taken in the area during the Gibraltar Experiment 94–96. The effect of the noise is translated into a continuous spreading of the spectrum around the solution of the noise-free problem. A stability analysis is carried out in order to determine the single neutral modes of oscillations and the phase space is divided onto regions of stability and instability as a function of the inflowing subinertial current. The methodology and results could be useful for the design and timing of oceanographic surveys in straits where the ILWs occur.     

Difference between the Lagrangian trajectories and Eulerian residual velocity fields in the southwestern Yellow Sea

The responses to tidal and/or wind forces of Lagrangian trajectories and Eulerian residual velocity in the southwestern Yellow Sea are investigated using a high-resolution circulation model. The simulated tidal harmonic constants agree well with observations and existing studies. The numerical experiment reproduces the long-range southeastward Eulerian residual current over the sloping bottom around the Yangtze Bank also shown in previous studies. However, the modeled drifters deployed at the northeastern flank of the Yangtze Bank in the simulation move northeastward, crossing over this strong southeastward Eulerian residual current rather than following it. Additional sensitivity experiments reveal that the influence of the Eulerian tidal residual currents on Lagrangian trajectories is relatively weaker than that of the wind driven currents. This result is consistent with the northeastward movement of ARGOS surface drifters actually released in the southwestern Yellow Sea. Further experiments suggest that the quadratic nature of the bottom friction is the crucial factor, in the southwestern Yellow Sea, for the weaker influence of the Eulerian tidal residual currents on the Lagrangian trajectories. This study demonstrates that the Lagrangian trajectories do not follow the Eulerian residual velocity fields in the shallow coastal regions of the southwestern Yellow Sea.