Modeling lateral circulation and its influence on the along-channel flow in a branched estuary

A numerical modeling study of the influence of the lateral flow on the estuarine exchange flow was conducted in the north passage of the Changjiang estuary. The lateral flows show substantial variabilities within a flood-ebb tidal cycle. The strong lateral flow occurring during flood tide is caused primarily by the unique cross-shoal flow that induces a strong northward (looking upstream) barotropic force near the surface and advects saltier water toward the northern part of the channel, resulting in a southward baroclinic force caused by the lateral density gradient. Thus, a two-layer structure of lateral flows is produced during the flood tide. The lateral flows are vigorous near the flood slack and the magnitude can exceed that of the along-channel tidal flow during that period. The strong vertical shear of the lateral flows and the salinity gradient in lateral direction generate lateral tidal straining, which are out of phase with the along-channel tidal straining. Consequently, stratification is enhanced at the early stage of the ebb tide. In contrast, strong along-channel straining is apparent during the late ebb tide. The vertical mixing disrupts the vertical density gradient, thus suppressing stratification. The impact of lateral straining on stratification during spring tide is more pronounced than that of along-channel straining during late flood and early ebb tides. The momentum balance along the estuary suggests that lateral flow can augment the residual exchange flow. The advection of lateral flows brings low-energy water from the shoal to the deep channel during the flood tide, whereas the energetic water is moved to the shoal via lateral advection during the ebb tide. The impact of lateral flow on estuarine circulation of this multiple-channel estuary is different from single-channel estuary. A model simulation by blocking the cross-shoal flow shows that the magnitudes of lateral flows and tidal straining are reduced. Moreover, the reduced lateral tidal straining results in a decrease in vertical stratification from the late flood to early ebb tides during the spring tide. By contrast, the along-channel tidal straining becomes dominant. The model results illustrate the important dynamic linkage between lateral flows and estuarine dynamics in the Changjiang estuary.     

Hydrodynamic effects at the entry of tidal waves into estuaries

The phenomenon of an increase in tidal wave height in cone-shaped estuaries is studied. The effect of estuary narrowing in the direction of tidal wave propagation (the hydrodynamic effect of confusor) is among the factors amplifying the tide. An opposite effect of turbulent friction, whose manifestation increases with decreasing bay’s depth, conversely, reduces tide amplitude because of the dissipation of tidal wave energy. Stokes diffusion layer also plays a significant role in the formation of wave transformation regime. In an estuary with a median depth, which is much greater than the Stokes layer thickness, the confusor effect is stronger and tide amplitude increases at estuary head. At depths lesser than Stokes layer thickness, the turbulent friction dominates over the confusor effect and the amplitude of tidal wave decreases at the head of the estuary. The depths of the order of Stokes layer thickness cause an interesting intermediate phenomenon—at the entrance into the estuary, first the effect of friction manifests itself, resulting in a decrease in the amplitude of tidal wave, but later, the effect of confusor starts dominating, and the amplitude of tidal wave again increases toward estuary head. When the period of tidal wave coincides with seiche period, a resonance enhancement of seiche oscillations takes place in the estuary.     

Cross-shelf transport into nearshore waters due to shoaling internal tides in San Pedro Bay, CA

In the summer of 2001, a coastal ocean measurement program in the southeastern portion of San Pedro Bay, CA, was designed and carried out. One aim of the program was to determine the strength and effectiveness of local cross-shelf transport processes. A particular objective was to assess the ability of semidiurnal internal tidal currents to move suspended material a net distance across the shelf. Hence, a dense array of moorings was deployed across the shelf to monitor the transport patterns associated with fluctuations in currents, temperature and salinity. An associated hydrographic program periodically monitored synoptic changes in the spatial patterns of temperature, salinity, nutrients and bacteria. This set of measurements show that a series of energetic internal tides can, but do not always, transport subthermocline water, dissolved and suspended material from the middle of the shelf into the surfzone. Effective cross-shelf transport occurs only when (1) internal tides at the shelf break are strong and (2) subtidal currents flow strongly downcoast. The subtidal downcoast flow causes isotherms to tilt upward toward the coast, which allows energetic, nonlinear internal tidal currents to carry subthermocline waters into the surfzone. During these events, which may last for several days, the transported water remains in the surfzone until the internal tidal current pulses and/or the downcoast subtidal currents disappear. This nonlinear internal tide cross-shelf transport process was capable of carrying water and the associated suspended or dissolved material from the mid-shelf into the surfzone, but there were no observation of transport from the shelf break into the surfzone. Dissolved nutrients and suspended particulates (such as phytoplankton) transported from the mid-shelf into the nearshore region by nonlinear internal tides may contribute to nearshore algal blooms, including harmful algal blooms that occur off local beaches.     

Nonlinear advection,Coriolis force,and frictional influence in the South Channel of the Yangtze Estuary,China

Observation data of along-estuary and lateral current velocities over a transect located at the South Channel of the Yangtze estuary was obtained during a spring tide in August 2011.Harmonic analysis was done on the current velocities to get a mean component and a semi-diurnal component.Based on these two components,the driving mechanisms of mean lateral flow and M2 lateral tidal flow are shown and analyzed respectively.The dominant driving force of mean lateral flow is nonlinear advection and that of lateral M2 tidal flow is Coriolis force.The friction plays an important role near the bottom and surface for both lateral mean flow and M2 tidal flow.     

Tidal waves at Mezen mouth and surge-wave formation conditions

The factors that govern the distribution and transformation of tidal waves in the macrotidal estuary of the Mezen River have been considered, including tide range in the mouth section, water discharge in the river’s lower reaches, estuary shape, and bed resistance coefficient. Data on variations of water discharge over period 1920–2008 are given. The parameters of estuary channel narrowing in horizontal and vertical sections have been considered. The effect of narrowing and bed hydraulic friction on tide wave amplitude has been evaluated. Froude number values for the tidal estuary suggest that tidal bore can form at the Mezen mouth. The conditions of the propagation of tidal waves to the mouths of different rivers and tidal bore formation in them are considered.     

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.     

Performance of a nowcast/forecast system for Prince William Sound,Alaska

A coastal ocean extended Prince William Sound nowcast/forecast system (EPWS/NFS) has been running semi-automatically for an extended domain of Prince William Sound (PWS), Alaska for 2 years. To determine the performance of this modeling system, an assessment is conducted. EPWS/NFS and PWS/NFS (viz., its predecessor) nowcasts are compared with observed time series of sea surface temperature (SST) and coastal sea level (CSL) at a few stations, and to velocity profiles from a moored ADCP. With the extension of the model domain to include the continental shelf outside PWS and forced by an operational global ocean model (Global-Navy Coastal Ocean Model (Global-NCOM)) and a 2D tidal model at the open boundary, EPWS/NFS has achieved significant improvement over PWS/NFS, which covered only PWS per se, for most of the predicted variables in this study. In both magnitude and phase, EPWS/NFS accurately predicts the coastal tide fluctuations, as well as M2 tidal currents in Central Sound, although significant errors in coastal tides exist during some spring and neap tide cycles. Other than for the tidal motions, EPWS/NFS generally produces less energetic CSL and velocity variations than those observed. In comparison, although PWS/NFS well predicts the coastal tides, it suffers from the absence of low-frequency CSL variations, as well as misprediction of M2 tidal currents in Central Sound. For 40 h low-passed PWS/NFS and EPWS/NFS velocities, significant phase error occurs during the model–date comparison period, while EPWS/NFS nowcasts generally produce less root-mean-square-error (rmse) and smaller correlations with the observations than PWS/NFS does. Both observations and EPWS/NFS have similar vertical profiles of baroclinic velocity standard deviations, but some substantial discrepancies occur in the velocity direction. Also, in the Central Sound, EPWS/NFS predicts well the SST seasonal cycle and a major cooling event during the summer 2005. However, for periods shorter than 1 week, both PWS/NFS and EPWS/NFS SST underestimated the observed fluctuations by an order of magnitude.     

Flow across reefs or between islands, and effects on shelf-sea motions

Oscillatory (e.g., tidal) flow over and around shallow reefs and islands is considered. Overall matching conditions (between sea levels and flows across the reef) are derived, to represent reef effects in models of larger regions.Analyses include various reef forms of uniform cross-section and water depth h(x), both narrow (uniform cross-reef transport) and broad (decoupled motions on either side). Simple island chains, or reefs broken by passages conducting all the flow, are also considered.In all cases, cross-reef transport is “down” the sea-surface slope, phase-shifted by 0 to 1/4 cycle. The transport is sufficient to render broken reefs effectively transparent to tides, unless the reefs are unusually far from the coast (> 100km, say), dense (> 90%) and broad (> 25km).The matching conditions are consistent with (expected) energy losses for unforced trapped waves propagating along a continental shelf with a long-shelf reef. There is a corresponding change of phase speed, if these effects are small, as is generally so for Kelvin waves. Continental shelf waves, particularly near their maximum frequency, may be strongly retarded and damped by a shelf-edge reef.     

Apparent tidal influence on magmatic activity at Oldoinyo Lengai volcano,Tanzania, as observed in Moderate resolution Imaging Spectroradiometer (MODIS) data

This paper investigates the relative timing of solid Earth tides and thermal anomalies associated with volcanic activity at Oldoinyo Lengai (OL), Tanzania, from 2000 to 2008. The low viscosity of OL's carbonatite magmas may make it particularly susceptible to tidal stresses. Thermal data from the Moderate resolution Imaging Spectroradiometer (MODIS) were filtered using the MODLEN algorithm and Earth tides were modeled using TSoft. Application of the Schuster and Chi-squared tests resulted in apparent correlations between times of thermal anomalies and the phase of the semi-diurnal and biannual solid Earth tides. However, for semi-diurnal and biannual tides limited acquisition times of the MODIS data account for the apparent correlations. Re-examining the data while accounting for the bias introduced by the limited acquisition times, correlations are no longer found. Onset times of eruptive events and times of thermal anomalies show no statistically significant correlation with the fortnightly tide, indicating this is not an influence on activity at OL. Tidal influences on magmatic activity, if at all present, cannot be observed in coarse resolution thermal data on semi-diurnal and fortnightly time scales. Based on the available data, correlations on biannual timescales cannot be ruled out.     

Multi-scale modeling of Puget Sound using an unstructured-grid coastal ocean model: from tide flats to estuaries and coastal waters

Water circulation in Puget Sound, a large complex estuary system in the Pacific Northwest coastal ocean of the United States, is governed by multiple spatially and temporally varying forcings from tides, atmosphere (wind, heating/cooling, precipitation/evaporation, pressure), and river inflows. In addition, the hydrodynamic response is affected strongly by geomorphic features, such as fjord-like bathymetry and complex shoreline features, resulting in many distinguishing characteristics in its main and sub-basins. To better understand the details of circulation features in Puget Sound and to assist with proposed nearshore restoration actions for improving water quality and the ecological health of Puget Sound, a high-resolution (around 50 m in estuaries and tide flats) hydrodynamic model for the entire Puget Sound was needed. Here, a three-dimensional circulation model of Puget Sound using an unstructured-grid finite volume coastal ocean model is presented. The model was constructed with sufficient resolution in the nearshore region to address the complex coastline, multi-tidal channels, and tide flats. Model open boundaries were extended to the entrance of the Strait of Juan de Fuca and the northern end of the Strait of Georgia to account for the influences of ocean water intrusion from the Strait of Juan de Fuca and the Fraser River plume from the Strait of Georgia, respectively. Comparisons of model results, observed data, and associated error statistics for tidal elevation, velocity, temperature, and salinity indicate that the model is capable of simulating the general circulation patterns on the scale of a large estuarine system as well as detailed hydrodynamics in the nearshore tide flats. Tidal characteristics, temperature/salinity stratification, mean circulation, and river plumes in estuaries with tide flats are discussed.     

A coupled oscillator model of shelf and ocean tides

The resonances of tides in the coupled open ocean and shelf are modeled by a mechanical analogue consisting of a damped driven larger mass and spring (the open-ocean) connected to a damped smaller mass and spring (the shelf). When both masses are near resonance, the addition of even a very small mass can significantly affect the oscillations of the larger mass. The influence of the shelf is largest if the shelf is resonant with weak friction. In particular, an increase of friction on a near-resonant shelf can, perhaps surprisingly, lead to an increase in ocean tides. On the other hand, a shelf with large friction has little effect on ocean tides. Comparison of the model predictions with results from numerical models of tides during the ice ages, when lower sea levels led to a much reduced areal extent of shelves, suggests that the predicted larger tidal dissipation then is related to the ocean basins being close to resonance. New numerical simulations with a forward global tide model are used to test expectations from the mechanical analogue. Setting friction to unrealistically large values in Hudson Strait yields larger North Atlantic _M2$M_2$ amplitudes, very similar to those seen in a simulation with the Hudson Strait blocked off. Thus, as anticipated, a shelf with very large friction is nearly equivalent in its effect on the open ocean to the removal of the shelf altogether. Setting friction in shallow waters throughout the globe to unrealistically large values yields even larger open ocean tidal amplitudes, similar to those found in simulations of ice-age tides. It thus appears that larger modeled tides during the ice ages can be a consequence of enhanced friction in shallower water on the shelf in glacial times as well as a reduced shelf area then. Single oscillator and coupled oscillator models for global tides show that the maximum extractable power for human use is a fraction of the present dissipation rate, which is itself a fraction of global human power consumption.     

Modeling studies of tidal dynamics and the associated responses to coastline changes in the Bohai Sea,China

Over the past 30 years, reclamation projects and related changes have impacted the hydrodynamics and sediment transport in the Bohai Sea. Three-dimensional tidal current models of the Bohai Sea and the Yellow Sea were constructed using the MIKE 3 model. We used a refined grid to simulate and analyze the effects of changes in coastline, depth, topography, reclamation, the Yellow River estuary, and coastal erosion on tidal systems, tide levels, tidal currents, residual currents, and tidal fluxes. The simulation results show that the relative change in the amplitude of the half-day tide is greater than that of the full-day tide. The changes in the tidal amplitudes of M₂, S₂, K₁, and O₁ caused by coastline changes accounted for 27.76–99.07% of the overall change in amplitude from 1987 to 2016, and water depth changes accounted for 0.93–72.24% of the overall change. The dominant factor driving coastline changes is reclamation, accounting for 99.55–99.91% of the amplitude changes in tidal waves, followed by coastal erosion, accounting for 0.05–0.40% of the tidal wave amplitude changes. The contribution of changes in the Yellow River estuary to tidal wave amplitude changes is small, accounting for 0.01–0.12% of the amplitude change factor. The change in the highest tide level (HTL) is mainly related to the amplitude change, and the correlation with the phase change is small. The dominant factor responsible for the change in the HTL is the tide amplitude change in M2, followed by S2, whereas the influence of the K1 and O1 tides on the change in the HTL is small. Reclamation resulted in a decrease in the vertical average maximum flow velocity (V_VAM) in the Bohai Sea. Shallower water depths have led to an increase in the V_VAM; deeper water depths have led to a decrease in the maximum flow velocity. The absolute value of the maximum flow velocity gradually decreases from the surface to the bottom, but the relative change value is basically constant. The changes in the tidal dynamics of the Bohai Sea are proportional to the degree of change in the coastline. The maximum and minimum changes in the tidal flux appear in Laizhou Bay (P-LZB) and Liaodong Bay (P-LDB), respectively. The changes in the tidal flux are related to the change in the area of the bay. Due to the reduced tidal flux, the water exchange capacity of the Bohai Sea has decreased, impacting the ecological environment of the Bohai Sea. Strictly controlling the scale of reclamation are important measures for reducing the decline in the water exchange capacity of the Bohai Sea and the deterioration of its ecological environment.     

Interaction between suspended sediment and tidal amplification in the Guadalquivir Estuary

Water level records at two stations in the Guadalquivir Estuary (Spain), one near the estuary mouth (Bonanza) and one about 77 km upstream (Sevilla), have been analysed to study the amplification of the tide in the estuary. The tidal amplification factor shows interesting temporal variation, including a spring-neap variation, some extreme low values, and especially the anomalous behaviour that the amplification factor is larger during a number of periods. These variations are explained by data analysis combined with numerical and analytical modelling. The spring-neap variation is due to the quadratic relation between the bottom friction and the tidal flow velocity. The river flood events are the direct causes of the extreme low values of the amplification factor, and they trigger the non-linear interaction between the tidal flow and suspended sediment transport. The fluvial sediment input during a river flood causes high sediment concentration in the estuary, up to more than 10 g/l. This causes a reduction of the effective hydraulic drag, resulting in stronger tidal amplification in the estuary for a period after a river flood. After such an event the tidal amplification in the estuary does not always fall back to the same level as before the event, indicating that river flood events have significant influence on the long-term development of this estuary.     

A model study of tide- and wind-induced mixing in the Columbia River Estuary and plume

A numerical simulation of circulation in the Columbia River estuary and plume during the summer of 2004 is used to explore the mixing involved as river water is transformed into shelf water. The model is forced with realistic river flow, tides, wind stress, surface heat flux, and ocean boundary conditions. Simulated currents and water properties on the shelf near the mouth are compared with records from three moorings (all in 72 m of water) and five CTD sections. The model is found to have reasonable skill; statistically significant correlations between observed and modeled surface currents, temperature, and salinity are all 0.42–0.72 for the mooring records. Equations for the tidally averaged, volume-integrated mechanical energy budget (kinetic and potential) are derived, with attention to the effects of: (i) Reynolds averaging, (ii) a time varying volume due to the free surface, and (iii) dissipation very close to the bottom. It is found that convergence of tidal pressure work is the most important forcing term in the estuary. In the far field plume (which has a volume 15 times greater than that of the estuary), the net forcing is weaker than that in the estuary, and may be due to either tidal currents or wind stress depending on the time period considered. These forcings lead to irreversible mixing of the stratification (buoyancy flux) that turns river water into shelf water. This occurs in both the plume and estuary, but appears to be more efficient (17% vs. 5%), and somewhat greater (4.2 MW vs. 3.3 MW), in plume vs. estuary. This demonstrates the importance of both wind and tidal forcing to watermass transformation, and the need to consider the estuary and plume as part of a single system.     

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.     

Simulation of Tidal Effects on Contaminant Transport in Porous Media

A one-dimensional numerical model is developed with oscillating velocities and dispersions to simulate the migration process of a contaminant plume within tidally influenced aquifers. Model simulations demonstrate that a major effect the tidal fluctuation has on the migration process of a contaminant plume is the exit concentration discharging to the tidal estuary. Tidal fluctuation causes the exit concentration levels to be significantly diluted by the surface-water body of the estuary. Sensitivity analyses demonstrate that tidal fluctuation hastens the rate of plume migration near the bank of the estuary because of the relatively high advective and dispersive fluxes induced by tides. However, tides affect the migration process only over a short distance from the tidal-water interface (about 40 ft for the parameters used in this study). If the contaminant plume is located far beyond the interface, tidal fluctuations will not affect the rate of plume migration until an existing regional ground-water flow velocity brings the plume to the tidally active zone. With or without tides, the rate of contaminant migration increases with higher regional hydraulic gradient. Furthermore, the effects of tidal fluctuations on the transport process become insignificant with higher regional hydraulic gradients.     

Numerical modelling of morphodynamics—Vilaine Estuary

The main objective of this paper is to develop a method to simulate long-term morphodynamics of estuaries dominated by fine sediments, which are subject to both tidal flow and meteorologically induced variations in freshwater run-off and wave conditions. The method is tested on the Vilaine Estuary located in South Brittany, France. The estuary is subject to a meso–macrotidal regime. The semi-diurnal tidal range varies from around 2.5 to 5 m at neap and spring, respectively. The freshwater input is controlled by a dam located approximately 8 km from the mouth of the estuary. Sediments are characterised as mostly fines, but more sandy areas are also found. The morphology of the estuary is highly influenced by the dam. It is very dynamic and changes in a complicated manner with the run-off from the dam, the tide and the wave forcing at the mouth of the estuary. Extensive hydrodynamic and sediment field data have been collected in the past and provide a solid scientific basis for studying the estuary. Based on a conceptual understanding of the morphodynamics, a numerical morphological model with coupled hydrodynamic, surface wave and sediment transport models is formulated. The numerical models are calibrated to reproduce sediment concentrations, tidal flat altimetry and overall sediment fluxes. Scaling factors are applied to a reference year to form quasi-realistic hydrodynamic forcing and river run-off, which allow for the simulations to be extended to other years. The simulation results are compared with observed bathymetric changes in the estuary during the period 1998–2005. The models and scaling factors are applied to predict the morphological development over a time scale of up to 10 years. The influence of the initial conditions and the sequence of external hydrodynamic forcing, with respect to the morphodynamic response of the estuary, are discussed.     

Inversion for tides in the Eastern North Pacific Ocean

A regional model of tides in the Eastern North Pacific Ocean is developed through the use of inversion with two-dimensional finite element codes. Since global tide models are least accurate in coastal environments, modeling tides on a regional scale allows tidal propagation and interaction along the coast to be more accurately represented. In this respect, a regional model can act as a liaison between open ocean dynamics and physical processes more pertinent to coastal systems. The region of interest in this study extends from the Aleutian Islands to Southern California and includes deep ocean, continental shelf, and shallow water features. Boundary conditions are determined from nonlinear inversion of harmonic data from both shallow water and deep ocean tide gauges. Spatial patterns of amplitudes and phases from the model are examined for major constituents. Results are also compared to global tide models at selected stations.