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Hans Burchard and Henk M. Schuttelaars

Abstract

Tidal straining, which can mathematically be described as the covariance between eddy viscosity and vertical shear of the along-channel velocity component, has been acknowledged as one of the major drivers for estuarine circulation in channelized tidally energetic estuaries. In this paper, the authors investigate the role of lateral circulation for generating this covariance. Five numerical experiments are carried out, starting with a reference scenario including the full physics and four scenarios in which specific key physical processes are neglected. These processes are longitudinal internal pressure gradient forcing, lateral internal pressure gradient forcing, lateral advection, and the neglect of temporal variation of eddy viscosity. The results for the viscosity–shear covariance are correlated across different experiments to quantify the change due to neglect of these key processes. It is found that the lateral advection of vertical shear of the along-channel velocity component and its interaction with the tidally asymmetric eddy viscosity (which is also modified by the lateral circulation) is the major driving force for estuarine circulation in well-mixed tidal estuaries.

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Yoeri M. Dijkstra and Henk M. Schuttelaars

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The salinity structure in estuaries is classically described in terms of the salinity structure as well mixed, partially mixed, or salt wedge. The existing knowledge about the processes that result in such salinity structures comes from highly idealized models that are restricted to either well-mixed and partially mixed cases or subtidal salt wedge estuaries. Hence, there is still little knowledge about the processes driving transitions between these different salinity structures and the estuarine parameters at which such a transition is found. As an important step toward a unified description of the dominant processes driving well-mixed, partially mixed, and salt wedge estuaries, a subtidal width-averaged model applicable to all these salinity structures is developed and systematically analyzed. Using our model, we identify four salinity regimes, resulting from different balances of dominant processes. It is shown that each regime is uniquely determined by two dimensionless parameters: an estuarine Froude and Rayleigh number, representing freshwater discharge and tidal mixing, respectively, resulting in a classification of the regimes in terms of these two parameters. Furthermore, analytical expressions to approximate the salt intrusion length in each regime are developed. These expressions are used to illustrate that the salt intrusion length in different regimes responds in a highly different manner to changes in depth and freshwater discharge. As one of the key results, we show that there are only very weak relations between the process-based regime of an estuary and the salt intrusion length and top–bottom stratification. This implies that the salinity structure of an estuary cannot be uniquely matched to a regime.

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Xiaoyan Wei, Mohit Kumar, and Henk M. Schuttelaars

Abstract

A semianalytical three-dimensional model is set up to dynamically calculate the coupled water motion and salinity for idealized well-mixed estuaries and prognostically investigate the influence of each physical mechanism on the residual salt transport. As a study case, a schematized estuary with an exponentially converging width and a channel–shoal structure is considered. The temporal correlation between horizontal tidal velocities and tidal salinities is the dominant process for the landward residual salt transport. The residual salt transport induced by residual circulation is locally significant, but the induced salt transport integrated over the cross section is small. The impacts of the estuarine geometry, Coriolis force, and bathymetry on the salt dynamics are studied using three dedicated experiments, in which the impact of each of these factors is studied separately. To assess the impact of width convergence, a convergent estuary without bathymetric variations or Coriolis force is considered. In this experiment, the temporal correlation between tidal velocities and salinities is the only landward salt transport process. In the second experiment, Coriolis effects are included. This results in a significant residual salt transport cell due to the advection of the tidally averaged salinity by residual circulation, with salt imported into the estuary from the left side and exported on the right (looking seaward). In the last experiment, a lateral channel–shoal structure is included while the Coriolis effects are excluded. This results in a significant landward salt transport through the deeper channel and a seaward salt transport over the shoals due to the advection of the tidally averaged salinity by residual circulation.

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Elisabeth Schulz, Henk M. Schuttelaars, Ulf Gräwe, and Hans Burchard

Abstract

The dependency of the estuarine circulation on the depth-to-width ratio of a periodically, weakly stratified tidal estuary is systematically investigated here for the first time. Currents, salinity, and other properties are simulated by means of the General Estuarine Transport Model (GETM) in cross-sectional slice mode, applying a symmetric Gaussian-shaped depth profile. The width is varied over four orders of magnitude. The individual along-channel circulation contributions from tidal straining, gravitation, advection, etc., are calculated and the impact of the depth-to-width ratio on their intensity is presented and elucidated. It is found that the estuarine circulation exhibits a distinct maximum in medium-wide channels (intermediate depth-to-width ratio depending on various parameters), which is caused by a maximum of the tidal straining contribution. This maximum is related to a strong tidal asymmetry of eddy viscosity and shear created by secondary strain-induced periodic stratification (2SIPS): in medium channels, transverse circulation generated by lateral density gradients due to laterally differential longitudinal advection induces stable stratification at the end of the flood phase, which is further increased during ebb by longitudinal straining (SIPS). Thus, eddy viscosity is low and shear is strong in the entire ebb phase. During flood, SIPS decreases the stratification so that eddy viscosity is high and shear is weak. The circulation resulting from this viscosity–shear correlation, the tidal straining circulation, is oriented like the classical, gravitational circulation, with riverine outflow at the surface and oceanic inflow close to the bottom. In medium channels, it is about 5 times as strong as in wide (quasi one-dimensional) channels, in which 2SIPS is negligible.

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Hans Burchard, Henk M. Schuttelaars, and W. Rockwell Geyer

Abstract

In this idealized numerical modeling study, the composition of residual sediment fluxes in energetic (e.g., weakly or periodically stratified) tidal estuaries is investigated by means of one-dimensional water column models, with some focus on the sediment availability. Scaling of the underlying dynamic equations shows dependence of the results on the Simpson number (relative strength of horizontal density gradient) and the Rouse number (relative settling velocity) as well as impacts of the Unsteadiness number (relative tidal frequency). Here, the parameter space given by the Simpson and Rouse numbers is mainly investigated. A simple analytical model based on the assumption of stationarity shows that for small Simpson and Rouse numbers sediment flux is down estuary and vice versa for large Simpson and Rouse numbers. A fully dynamic water column model coupled to a second-moment turbulence closure model allows to decompose the sediment flux profiles into contributions from the transport flux (product of subtidal velocity and sediment concentration profiles) and the fluctuation flux profiles (tidal covariance between current velocity and sediment concentration). Three different types of bottom sediment pools are distinguished to vary the sediment availability, by defining a time scale for complete sediment erosion. For short erosion times scales, the transport sediment flux may dominate, but for larger erosion time scales the fluctuation sediment flux largely dominates the tidal sediment flux. When quarter-diurnal components are added to the tidal forcing, up-estuary sediment fluxes are strongly increased for stronger and shorter flood tides and vice versa. The theoretical results are compared to field observations in a tidally energetic inlet.

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Hans Burchard, Robert D. Hetland, Elisabeth Schulz, and Henk M. Schuttelaars

Abstract

The generation of residual circulation in a tidally energetic estuary with constant longitudinal salinity gradient and parabolic cross section is examined by means of a two-dimensional cross-sectional numerical model, neglecting river runoff and Stokes drift. It is shown how the longitudinal and lateral residual circulation can be decomposed into contributions from various processes such as tidal straining circulation, gravitational circulation, advectively driven circulation, and horizontal mixing circulation. The sensitivity of the residual circulation and its components from various processes to changes in forcing is investigated by varying the Simpson number (nondimensional longitudinal buoyancy gradient) and the unsteadiness parameter (nondimensional tidal frequency), as well as the bed roughness and the width of the estuary. For relatively weak salinity gradient forcing, the tidal straining circulation dominates the residual exchange circulation in support of classical estuarine circulation (up-estuary flow near the bed and down-estuary flow near the surface). The strength of the longitudinal estuarine circulation clearly increases with increased salinity gradient forcing. However, when the Simpson number exceeds 0.15, the relative contributions of both gravitational circulation and advectively driven circulation to estuarine circulation increase substantially. Lateral residual circulation is relatively weak for small Simpson numbers and becomes flood oriented (divergent flow near the bed and convergent flow near the surface) for larger Simpson numbers because of increasing contributions from gravitational and advectively driven circulation. Increasing the unsteadiness number leads to decreased longitudinal and lateral residual circulation. Although changes in bed roughness result in relatively small changes in residual circulation, results are sensitive to the width of the estuary, mainly because of changes in residual exchange circulation driven by tidal straining.

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Xiaoyan Wei, George P. Schramkowski, and Henk M. Schuttelaars

Abstract

Understanding salt dynamics is important to adequately model salt intrusion, baroclinic forcing, and sediment transport. In this paper, the importance of the residual salt transport due to tidal advection in well-mixed tidal estuaries is studied. The water motion is resolved in a consistent way with a width-averaged analytical model, coupled to an advection–diffusion equation describing the salt dynamics. The residual salt balance obtained from the coupled model shows that the seaward salt transport driven by river discharge is balanced by the landward salt transport due to tidal advection and horizontal diffusion. It is found that the tidal advection behaves as a diffusion process, and this contribution is named tidal advective diffusion. The horizontal diffusion parameterizes processes not explicitly resolved in the model and is called the prescribed diffusion. The tidal advective diffusion results from the correlation between the tidal velocity and salinity and can be explicitly calculated with the dominant semidiurnal water motion. The sensitivity analysis shows that tidal advective diffusivity increases with increasing bed roughness and decreasing vertical eddy viscosity. Furthermore, tidal advective diffusivity reaches its maximum for moderate water depth and moderate convergence length. The relative importance of tidal advective diffusion is investigated using the residual salt balance, with the prescribed diffusion coefficient obtained from the measured salinity field. The tidal advective diffusion dominates the residual salt transport in the Scheldt estuary, and other processes significantly contribute to the residual salt transport in the Delaware estuary and the Columbia estuary.

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Dante M. L. Horemans, Yoeri M. Dijkstra, Henk M. Schuttelaars, Patrick Meire, and Tom J. S. Cox

Abstract

Sediment transport in estuaries and the formation of estuarine turbidity maxima (ETM) highly depend on the ability of suspended particulate matter (SPM) to flocculate into larger aggregates. While most literature focuses on the small-scale impact of biological flocculants on the formation of larger aggregates, the influence of the flocculation process on large-scale estuarine SPM profiles is still largely unknown. In this paper, we study the impact of flocculation of SPM on the formation of ETM. For this, a semianalytical width-integrated model called iFlow is utilized and extended by a flocculation model. Starting from a complex one-class flocculation model, we show that flocculation may be described as a linear relation between settling velocity and suspended sediment concentration to capture its leading-order effect on the ETM formation. The model is applied to a winter case in the Scheldt estuary (Belgium, Netherlands) and calibrated to a unique, long-term, two-dimensional set of turbidity (cf. SPM) observations. First, model results with and without the effect of flocculation are compared, showing that the spatial and temporal variations of the settling velocity due to flocculation are essential to reproduce the observed magnitude of the suspended sediment concentrations and its dependence on river discharge. Second, flocculation results in tidally averaged land-inward sediment transport. Third, we conduct a sensitivity analysis of the freshwater discharge and floc breakup parameter, which shows that flocculation can cause additional estuarine turbidity maxima and can prevent flushing of the ETM for high freshwater inflow.

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Ronald L. Brouwer, George P. Schramkowski, Yoeri M. Dijkstra, and Henk M. Schuttelaars

Abstract

Using an idealized width-averaged process-based model, the role of a mud pool on the bed and time-varying river discharge on the trapping of fine sediment is systematically investigated. For this purpose, a dynamically and physically motivated description of erodibility is presented, which relates the amount of sediment on the bed to the suspended sediment concentration (SSC). We can distinguish between two states: in the availability-limited state, the SSC is limited by the amount of erodible sediment at the bed. Over time, under constant forcing conditions, the estuary evolves to morphodynamic equilibrium. In the erosion-limited state, there is an abundant amount of sediment at the bed so that sediment pickup occurs at the maximum possible rate. The SSC is then limited by the local hydrodynamic conditions. In this state, the estuary keeps importing sediment, forming an erodible bottom pool that grows in time. These two states can be used to explain the response of an estuary to changing river discharge. Under availability-limited conditions, periods of high river discharge push estuarine turbidity maxima (ETMs) downstream, while drier periods allow ETMs to move upstream. However, when the estuary is in an erosion-limited state during low river discharge, a bottom pool is formed. When the discharge then increases, it takes time to deplete this pool, so that an ETM located over a bottom pool moves with a significant time lag relative to changes in the river discharge. Good qualitative agreement is found between model results and observations in the Scheldt Estuary of surface SSC using a representative year of discharge conditions.

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Xiaoyan Wei, Henk M. Schuttelaars, Megan E. Williams, Jennifer M. Brown, Peter D. Thorne, and Laurent O. Amoudry

Abstract

Asymmetric tidal turbulence (ATT) strongly influences estuarine health and functioning. However, its impact on the three-dimensional estuarine dynamics and the feedback of water motion and salinity distribution on ATT remain poorly understood, especially for short estuaries (estuarine length ≪ tidal wavelength). This study systematically investigates the abovementioned interactions in a short estuary for the first time, considering periodically weakly stratified conditions. This is done by developing a three-dimensional semi-analytical model (combining perturbation method with finite element method) that allows a dissection of the contributions of different processes to ATT, estuarine circulation, and salt transport. The generation of ATT is dominated by (i) strain-induced periodic stratification and (ii) asymmetric bottom-shear-generated turbulence, and their contributions to ATT are different both in amplitude and phase. The magnitude of the residual circulation related to ATT and the eddy viscosity–shear covariance (ESCO) is about half of that of the gravitational circulation (GC) and shows a “reversed” pattern as compared to GC. ATT generated by strain-induced periodic stratification contributes to an ESCO circulation with a spatial structure similar to GC. This circulation reduces the longitudinal salinity gradients and thus weakens GC. Contrastingly, the ESCO circulation due to asymmetric bottom-shear-generated turbulence shows patterns opposite to GC and acts to enhance GC. Concerning the salinity dynamics at steady state, GC and tidal pumping are equally important to salt import, whereas ESCO circulation yields a significant seaward salt transport. These findings highlight the importance of identifying the sources of ATT to understand its impact on estuarine circulation and salt distribution.

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