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For Arctic estuaries that are characterized by landfast sea ice cover during the winter season, processes generating estuarine circulation and residual stratification have not yet been investigated, although some of the largest estuaries in the world belong to this class. Landfast sea ice provides a no-slip surface boundary condition in addition to the bottom boundary, such that frictional effects are expected to be increased. For this study of estuarine circulation and residual stratification under landfast sea ice, first, a simple linear analytical model is used. To include tidally varying scenarios, a water-column model is applied with a second-moment turbulence closure to juxtapose free-surface and ice-covered estuaries. Well-mixed and strongly stratified tidally periodic scenarios are analyzed by means of a decomposition of estuarine circulation into contributions from gravitational circulation, eddy viscosity–shear covariance (ESCO), surface stress, and river runoff. A new method is developed to also decompose tidal residual salinity anomaly profiles. Estuarine circulation intensity and tidally residual potential energy anomaly are studied for a parameter space spanned by the Simpson number and the unsteadiness number. These are the major results of this study that will support future scenario studies in Arctic estuaries under conditions of accelerated warming: (i) residual surface drag under ice opposes estuarine circulation; (ii) residual differential advection under ice destabilizes the near-surface flow; (iii) reversal of ESCO during strong stratification does not occur under landfast sea ice; (iv) tidal pumping (s-ESCO) contributes dominantly to residual stratification also with sea ice cover. Significance Statement Our work gives a first qualitative and quantitative understanding of how landfast sea ice cover on tidal estuaries impacts on the generation of estuarine circulation and residual stratification. Along the Arctic coasts, where some of the world’s largest estuaries are located, these processes play a significant role for the economy and ecology by means of transports of sediments, nutrients and pollutants. Due to Arctic amplification, the conditions for ice-covered estuaries are strongly changing in a way that the ice-covered periods may be shorter in the future. Our results intend to motivate field observations and realistic model studies to allow for better predicting the consequences of these changes.

The relationship between the salinity mixing, the diffusive salt transport, and the diahaline exchange flow is examined using salinity coordinates. The diahaline inflow and outflow volume transports are defined in this study as the integral of positive and negative values of the diahaline velocity. A numerical model of the Pearl River Estuary (PRE) shows that this diahaline exchange flow is analogous to the classical concept of estuarine exchange flow with inflow in the bottom layers and outflow at the surface. The inflow and outflow magnitudes increase with salinity, while the net transport equals the freshwater discharge Qr after sufficiently long temporal averaging. In summer, intensified salinity mixing mainly occurs in the surface layers and around the islands. The patchy distribution of intensified diahaline velocity suggests that the water exchange through an isohaline surface can be highly variable in space. In winter, the zones of intensification of salinity mixing occur mainly in deep channels. Apart from the impact of freshwater transport from rivers, the transient mixing is also controlled by an unsteadiness term due to estuarine storage of salt and water volume. In the PRE, the salinity mixing and exchange flow show substantial spring–neap variation, while the universal law of estuarine mixing m = 2SQr (with m being the sum of physical and numerical mixing per salinity class S) holds over longer averaging period (spring–neap cycle). The correlation between the patterns of surface mixing, the vorticity, and the salinity gradients indicates a substantial influence of islands on estuarine mixing in the PRE.

I will present an analytical relation that directly shows how mixing locally drives the overturning circulation. The theory is based on the application of the well-known Water Mass Transformation framework to each local water column. The budgets for volume and tracer content mapped to tracer space are supplemented by a budget for the squared tracer. Mixing is defined by the destruction term of squared tracer, which is equivalent to the decay of tracer variance. I will present maps of the simulated diahaline mixing and the associated diahaline exchange velocity in the Baltic Sea. In addition, our numerical model offers to separately diagnose the mixing due to turbulence parameterizations and the spurious mixing due to discrete transport schemes. This enables us to also quantify the amount of spuriously induced overturning circulation. The planned application to diapycnal exchange and the global overturing circulation will be outlined.

In this study we present new insights into the overturning circulation in non-tidal, fjord-type estuarine systems driven by diahaline mixing. As a realistic example we analyze two years of numerical model results for the Baltic Sea, a brackish semi-enclosed marginal sea, characterized by strong freshwater surplus. An isohaline water mass transformation framework is applied to quantify and decompose the diahaline exchange flow. Time-averaged effective vertical diahaline velocity is directly calculated from the divergence of the transports below the respective isohaline surface. It is furthermore indirectly estimated from the gradient of local mixing per salinity class with respect to salinity. Under the assumption of negligible horizontal salt transports both estimates should be identical. Our analysis shows a high correlation between the spatial patterns of the two estimates for the diahaline exchange flow. Two dominant types of diahaline exchange flow are analyzed. First of all there is a large scale overturning circulation with inflow at places where the isohaline surface is close to the bottom and with outflow at places where the isohaline is surfacing. Secondly, there is the well-known small-scale overturning circulation localized inside the bottom boundary layer over sloping bathymetry, driven by boundary mixing. Both types of circulation are visualized across selected vertical transects in physical and in salinity space. One major result is that about 50% of the diahaline exchange flow patterns are generated by numerical mixing caused by the truncation error of the advection scheme, despite the fact that an anti-diffusive advection scheme and vertically-adaptive coordinates are used.

Recent studies could link the quantities of estuarine exchange flows to the volume-integrated mixing inside an estuary, where mixing is defined as the destruction of salinity variance. The existing mixing relations quantify mixing inside an estuary by the net boundary fluxes of volume, salinity, and salinity variance, which are quantified as Knudsen or total exchange flow bulk values. So far, river runoff is the only freshwater flux included, and the freshwater exchange due to precipitation and evaporation is neglected. Yet, the latter is the driving force of inverse estuaries, which could not be described by the existing relations. To close this gap, this study considers evaporation and precipitation to complete the existing mixing relations by including cross-surface salinity variance transport. This allows decomposing the mixing into a riverine and a surface transport contribution. The improved relations are tested against idealized two-dimensional numerical simulations of different combinations of freshwater forcing. The mixing diagnosed from the model results agrees exactly with the derived mixing relation. An annual hindcast simulation of the Persian Gulf is then used to test the mixing relations, both exact and approximated, e.g., long-term averaged, for a realistic inverse estuary. The results show that the annual mean mixing contributions of river discharge and evaporation are almost equal, although the freshwater transport due to evaporation is about one order of magnitude larger than the river runoff.

The coastal area is one of the most vulnerable areas that is connecting lands and seas under the intensive human activities subjecting to the ocean forces. Nowadays, as the climate conditions are highly concerned, coastal morphodynamics, one of the most important elements for coastal areas, would become more uncertainty under the climate changes due to its non-linear interaction to the water forces. Therefore, an investigation of tide-wave-morphodynamic interactions is required by including sea level rise in order to involve various responses of morphodynamics to changing climate. In the conference, we will present results from our process-based coupled framework of tide-wave-morphodynamics modelling to consider the climate impacts on the morphodynamic changes in application on Wadden Sea of German Bight, which is one of the most vulnerable coastal areas subjects to sea level rise. The well-evaluated third-generation phase-resolved wave model WAVEWATCH III (WW3) is set up, coupled to the well-validated General Estuary Circulation Model (GETM) including the sediment transport and morphology modules. We applied ensemble-based simulations to reduce the uncertainties of climate effects in downscaling procedure. It is proved that this process-based model is capable for application on climate scenarios in a long term aspect as long as involving specific data analysis. It is desired that the process-based numerical investigation could be one of the most promising methods for studying the coastal morphodynamic responses to climate change as the physical processes could be examined straightforward for this non-linear interactions.Based on the preliminary results from the framework, it is indicated that the wave could propagate further more under sea level rise while the currents are observed to be increased at some locations, particularly at the region (i.e. ebb flats) of North Frisian Wadden Sea (NFW). As a result, the NFW becomes more dynamic under the sea level rise conditions especially at the intertidal areas, whereas the Elbe mouth might has less exchange of sediment far field to east and north Frisian Sea but might be highly dynamic in local, which is much similar to the pattern of observed datasets. The damthat connecting Sylt and main land, interested by lots of previous studies, also shows impact on both hydrodynamic and morphodynamic pattern under climate conditions. Based on the sea level rise scenarios, the significance of bed level changes at most areas of German Bight would be more seriousby keeping the identical pattern of morphological changes as that in present scenarios. However, it might also correlate to storminess, where we could looking in detail based on the process-based modelling. When considering the entire German Bight, it is found that the predominant forces from tide and wave might vary between the North Frisian Sea and East Frisian Sea due to the specific geometry. Tide-predominated and wave-dominated coastal system would be able to coexist in the German Bight. The detailed quantitative and qualitative results would be present in the conference.

The relationship between the diahaline mixing, the diffusive salt transport, and the diahaline exchange flow is examined using salinity coordinates. The diahaline inflow and outflow volume transports are defined in this study as the integral of positive and negative values of the diahaline velocity. A numerical model of the Pearl River Estuary (PRE) shows that this diahaline exchange flow is analogous to the classical concept of estuarine exchange flow with inflow in the bottom layers and outflow at the surface. The inflow and outflow magnitudes increase with salinity, while the net transport equals the freshwater discharge Qr after sufficiently long temporal averaging. In summer, intensified diahaline mixing mainly occurs in the surface layers and around the islands. The patchy distribution of intensified diahaline velocity suggests that the water exchange through an isohaline surface can be highly variable in space. In winter, the zones of intensification of diahaline mixing occur mainly in deep channels. Apart from the impact of freshwater transport from rivers, the transient isohaline mixing is also controlled by an unsteadiness term due to estuarine storage of salt and water volume. In the PRE, the diahaline mixing and exchange flow show substantial spring-neap variation, while the universal law of estuarine mixing m=2SQr (with m being the sum of physical and numerical mixing per salinity class S) holds over longer averaging period (spring-neap cycle). The correlation between the patterns of surface mixing, the vorticity, and the salinity gradients indicates a substantial influence of islands on estuarine mixing in the PRE.

The Total Exchange Flow (TEF) analysis framework computes the exchange flow in estuaries using isohaline coordinates. The TEF represents a paradigm for exchange flow estimates that is consistent with (steady-state) Knudsen-bulk values, and naturally allows quantifying mixing, which in turn controls the inflow and outflow fluxes of water and salinity.This study provides preliminary estimates of TEF along the Guadalquivir River Estuary (Spain) at seven notable cross-sections during low river flows. The analysis combines observations recorded between 2008 and 2011 by a real time monitoring network and analytical model output for a well-mixed M2+M4 tidal flow with oscillating salinity. Exchange profiles and volume and salinity transports sorted by salinity classes are computed.The results indicate that bulk along-channel TEF estimates decrease upstream. Incoming and outgoing water volume transports are about 10% larger than previous estimates based on gravitational circulation only. The largest net incoming water volume transport, viz. approx. 300 m3s-1, is attained at the lower part of the estuary, near where the largest salinity gradient is observed. This value is about 12-fold the normal river flow from the head dam at Alcalá del Río. Its corresponding representative TEF bulk salinity value is 20 psu, whereas the representative value for outflows at the same location is about 16 psu. In the middle part of the estuary, incoming TEF bulk volume values below 150 m3s-1 are obtained. As expected, negligible values are obtained in the upper part of the estuary near the head dam. Mixing completeness is larger than 75% at all cross-sections, thereby evidencing the poorly-stratified character of the Guadalquivir estuary.Regarding the effects of tidal asymmetry, the inclusion of the M4 tidal constituent in the analysis does not improve significantly the TEF estimates (less than 1% at all cross-sections), although it might be the case in other estuaries or coastal seas. This ensues that the covariance between salinity and current seems to play a more important role in exchange flow in the Guadalquivir estuary.

In this talk we present new insights into the overturning circulation of the Baltic Sea. Based on a state-of-the-art 3D numerical model for the entire Baltic Sea, we analyse the estuarine circulation and water mass transformation in salinity space. State and diagnostic variables are binned to salinity classes and conservatively averaged already during model runtime such that exact budgets for local isohaline volumes can be evaluated. Derived maps in salinity space for entrainment velocities, diahaline diffusive fluxes as well as physical and spurious numerical mixing contributions will be shown. The latter is based on a unique separation and quantification of mixing due to turbulence parameterisations and discretisation errors from the applied numerical advection schemes. Finally it is demonstrated that integration of the different new local diagnostics confirms existing bulk theories (e.g. Knudsen theorem, universal law of estuarine mixing).

Melting of the Greenland ice sheet has a big influence on the climate system. Therefore, it is important to understand how the ice melts. Since direct measurements at the underside of floating ice tongues are sparse, high-resolution models for the interaction of ocean and glacial ice are needed to determine sub-glacial melt rates and to understand melt processes. A common problem is that model resolution is often too low, so that the meltwater plume is only represented by one or two layers, and thus the entrainment of warmer water into the plume is not well captured. However, this heat transport towards the ice is crucial for the sub-glacial melt rate.In this talk, we show how we solve this problem with the General Estuarine Transport Model (GETM). GETM features adaptive vertical coordinates that zoom automatically to areas of interest, in particular strong density gradients. A high density contrast exists in the entrainment layer between the relatively fresh and cold meltwater of the plume, and the ambient ocean water. By zooming towards this interface, our adaptive vertical coordinates resolve the meltwater plume with several layers, while keeping the total number of model layers at a modest level to ensure a feasible computation time. In addition, the coordinate levels align to the moving isopycnals – they “follow” the plume –, which strongly reduces numerical mixing and pressure gradient errors.We present this for the fjord of the 79°N-Glacier (79NG), which has the largest floating ice tongue in Greenland. In our idealized 2D-setup, we obtain layers as thin as 0.2 m to 1 m in the meltwater plume, for only 100 levels over a water column of several 100 m depth. Thanks to this high resolution of plume and entrainment layer, our model reproduces the overturning circulation in the glacier cavity correctly; in particular, it shows that the salinity stratification of the adjacent ocean determines the level at which the meltwater plume detaches from the ice tongue. Almost all sub-glacial melting occurs before this detachment, i.e., where the plume is directly at the ice–ocean interface. Furthermore, we can confirm that the highest melt rates exist near the grounding line of the glacier. Finally, our simulated melt rates are consistent with observations at 79NG.Our model, developed in the GROCE (Greenland ice sheet–ocean interaction) project, will form the basis of a realistic 3D-model of the 79NG-fjord in the future.

The Weser estuary has been subject to profound changes in topography in the past 100 years through natural variations and river engineering measures, leading to strong changes in hydrodynamics. These changes are also expected to have affected the dynamics of saltwater intrusion. Using numerical modelling, we examined saltwater intrusion in the Weser estuary in four different system states (1966, 1972, 1981, 2012). Models of each system state were set up with the respective topography and boundary values. We calibrated and validated each model individually to account for differences in sediments, bedforms, and the resolution of underlying bathymetric data between historical and recent system states. In simulations of 1 hydrological year, each with realistic forcing (hindcasting study), the influence of topography is overshadowed by the effects of other factors, particularly river discharge. At times of identical discharge, results indicate a landward shift of the salinity front between 1966 and 2012. Subsequent simulations with different topographies but identical boundary conditions (scenario study) confirm that topography changes in the Weser estuary affected saltwater intrusion. Solely through the topography changes, at a discharge of 300 m3 s−1, the position of the tidally averaged and depth-averaged salinity front shifted landwards by about 2.5 km between 1972 and 1981 and by another 1 km between 1981 and 2012. These changes are significant but comparatively small, since due to seasonal variations in run-off, the tidally averaged saltwater intrusion can vary by more than 20 km. An analysis of the salt flux through a characteristic cross section showed that saltwater intrusion in the Weser estuary is primarily driven by tidal pumping and only to a lesser degree due to estuarine circulation. However, results indicate that the contribution of individual processes has changed in response to anthropogenic measures.

A universal law of estuarine mixing is derived here, combining the approaches of salinity coordinates, Knudsen relations, total exchange flow, mixing definition as salinity variance loss, and the mixing–exchange flow relation. As a result, the long-term average mixing within an estuarine volume bounded by the isohaline of salinity S amounts to M(S) = S2Qr, where Qr is the average river runoff into the estuary. Consequently, the mixing per salinity class is m(S) = ∂SM(S) = 2SQr, which can also be expressed as the product of the isohaline volume and the mixing averaged over the isohaline. The major differences between the new mixing law and the recently developed mixing relation based on the Knudsen relations are threefold: (i) it does not depend on internal dynamics of the estuary determining inflow and outflow salinities (universality), (ii) it is exactly derived from conservation laws (accuracy), and (iii) it calculates mixing per salinity class (locality). The universal mixing law is demonstrated by means of analytical stationary and one-dimensional and two-dimensional numerical test cases. Some possible consequences for the salinity distribution in real estuaries are briefly discussed. Since the mixing per salinity class only depends on the river runoff and the chosen salinity, and not on local processes at the isohaline, low-mixing estuaries must have large isohaline volumes and vice versa.

The floating ice tongue of the 79° North Glacier (Nioghalvfjerdsfjorden Glacier) in Northeast Greenland has been found to thin over the past two decades. Recent studies suggest the warming of the ocean as one of the main drivers of destabilizing outlet glaciers of the Greenland ice sheet by enhanced subglacial melting. Using a horizontal two-dimensional numerical plume model, we study the hydrodynamic processes determining basal melt rates beneath the glacial tongue of the 79° North Glacier. We specifically investigate the spatial distribution of submarine melting and assess the importance of ice base morphology in controlling basal melting. For our study, we design a suite of simulations by implementing a synthetic network of basal channels. Additionally, we determine the role of subglacial discharge in driving melting along the glacier base. Our model results lead us to the conclusion that channelised basal topographies at the glacier base are the dominant control on the basal melt rates and its spatial distribution.

The hydrodynamics in estuaries is mainly governed by the competition between a horizontal density gradient, friction, and wind stress. The sensitivity of the estuarine exchange flow to the wind stress increases in the absence of tides, which is investigated here using the example of the weakly tidal Warnow river estuary in the southwestern Baltic Sea—the mouth of which is characterized by strongly varying salinities of 8 to 20 g kg−1. The interaction between a volatile salinity gradient and along-estuary wind forcing is found to cause temporary inversions of the estuarine circulation. Despite the highly dynamic conditions, the applicability of recent theories for isohaline mixing, using the framework of Total Exchange Flow, and the strength of the exchange flow, using a non-dimensional parameter space, could be confirmed. By analyzing salinity fluxes at the mouth of the estuary, a mixing completeness of 84% was calculated for the estuary. Furthermore, inversion of estuarine circulation was typically found for a local Wedderburn number (ratio of non-dimensional wind stress to non-dimensional horizontal density gradient) exceeding 0.33, indicating a high sensitivity to along-estuary wind.

Processes of stratification and destratification in the German Bight region of fresh water influence (ROFI) are investigated following an extreme river discharge event in June 2013. For this purpose, a high‐resolution baroclinic ocean model is set up and validated against field data. The model results are used to study the temporal and spatial variability of stratification and the duration of persistent stratification in 2013. The relevant processes affecting stratification are investigated by analyzing the potential energy anomaly budget, with a focus on mixing and tidal straining. It is shown that the stratification in the German Bight is highly affected by the spring‐neap tidal cycle, with generally less stratification at spring tides due to dominant tidal mixing. It is also shown that the location of the river plume can modify this pattern. During spring tides, if the river plume is confined to the eastern region, stratification decreases significantly, as expected, due to the dominance of mixing over tidal straining. On the other hand, if the river plume moves toward deeper regions at spring tides, strong tidal straining becomes present. In this condition, mixing is weak, and the dominant tidal straining results in persistent stratification., Key Points: Processes impacting the German Bight stratification are investigated using a high‐resolution baroclinic model. The position of the river plume highly affects the contribution of tidal straining and mixing to changes in stratification. Strong tidal straining can result in persistent stratification even during spring tides., Bundesministerium für Bildung und Forschung (BMBF) http://dx.doi.org/10.13039/501100002347, German Research Foundation http://dx.doi.org/10.13039/501100001659, German Environment Agency http://dx.doi.org/10.13039/501100010809

In straight tidal estuaries, residual overturning circulation results mainly from a competition between gravitational forcing, wind forcing, and friction. To systematically investigate this for tidally energetic estuaries, the dynamics of estuarine cross sections is analyzed in terms of the relation between gravitational forcing, wind stress, and the strength of estuarine circulation. A system-dependent basic Wedderburn number is defined as the ratio between wind forcing and opposing gravitational forcing at which the estuarine circulation changes sign. An analytical steady-state solution for gravitationally and wind-driven exchange flow is constructed, where tidal mixing is parameterized by parabolic eddy viscosity. For this simple but fundamental situation, is calculated, meaning that the up-estuary wind forcing needs to be 15% of the gravitational forcing to invert estuarine circulation. In three steps, relevant physical processes are added to this basic state: (i) tidal dynamics are resolved by a prescribed semidiurnal tide, leading to caused by tidal straining; (ii) lateral circulation is added by introducing cross-channel bathymetry, smoothly increasing from 0.47 (flat bed) to 1.3 (parabolic bed) due to an increasing effect of lateral circulation on estuarine circulation; and (iii) full dynamics of a real tidally energetic inlet with highly variable forcing, where results from a two-dimensional linear regression.

The well-known Knudsen relations and the total exchange flow (TEF) analysis framework provide quantifications of exchange flow across an open boundary to the adjacent ocean in terms of bulk values (Knudsen theory: inflow and outflow volume or salinity) or with resolution in salinity space (TEF: profiles of volume and salt flux in salinity coordinates). In the present study, these theories are extended toward mixing of salinity, defined as the decay of salinity variance due to turbulent mixing. In addition to the advective fluxes, diffusive fluxes across the boundary are also considered now. These new Knudsen and TEF relations for mixing are derived by applying Gauss’s theorem to the salinity square and salinity variance equations. As a result of the analysis, four different Knudsen relations for the mixing in estuaries are derived. The first one is exact and considers nonperiodicity as well as nonconstancy of the inflow and outflow salinities. The other three formulations are approximate only, in the sense that either nonperiodicity or nonconstancy or both are relaxed. The simplest of those formulations has recently been derived by MacCready et al. and estimates the estuarine mixing as the product of inflow salinity, outflow salinity, and time-averaged river runoff. These four mixing estimates are systematically assessed by means of a number of idealized estuarine test cases. For periodic tidal flow, the simplest estimate still predicts the effective (physical plus numerical) mixing within an error of about 10%.

The activity of macrofauna on the sea floor is since long known to mediate deposition and erosion of sediment, but so far most studies addressed this effect at a local scale. In the present paper, the contribution of the observed macrofauna distribution (exemplified by a bivalve, the bean-like tellin Fabulina fabula, formerly known as Tellina fabula) on large-scale sediment transport in the southern North Sea is investigated by means of a model study. Macrofauna effects are considered with respect to the critical bed shear stress and erodibility, which are two important factors that control the resuspension rate. Simulation results for a typical winter month revealed for the first time that the suspended sediment concentration (SSC) is increased not only locally but beyond the inhabited zones. This alteration is not confined to near-bed zones but can be observed throughout the entire water column, especially during storm events. These effects are most prominent in the fine silt fraction, coarser and finer fractions are less affected. For a selected storm event in February 2010, we explain the counter-intuitive decrease in near-bed SSC in some areas with a high macrofauna abundance compared to a simulation excluding such macrofauna: A high macrofauna-induced entrainment rate leads to rapid exhaustion of available sediments at the bed in the model and consequently limits the near-bed SSC.

The Knudsen theorem for estuarine exchange flow, based on mass conservation of water and salt, and its generalization with resolution in salinity coordinates, the Total Exchange Flow (TEF) analysis framework, are reviewed here. The former had been developed, and applied to quantify exchange flow between the North Sea and the Baltic Sea, more than a century ago. In this paper, the underlying short research paper published in 1900 by Martin Knudsen, originally written in German, is translated into English. Reaching far beyond the Knudsen relation in particular, the extensive scientific achievements of Martin Knudsen on the salinity of seawater are reviewed. Using the Knudsen theorem and the TEF analysis framework, validated multi-decadal (years 1949–2013) model simulations are analyzed in terms of exchange flow through straits of the Western Baltic Sea. When comparing the model results to the original findings of Martin Knudsen, it is impressive to see how relevant his analysis of ratios of averaged inflowing and outflowing water masses still is today, given that they were based on just a few salinity observations. The model-based long-term Knudsen and TEF analyses of exchange flow in the Western Baltic Sea reproduces the Major Baltic Inflows (MBIs) that have occurred since the 1950s. For the complex inflow years 2002/2003, with two baroclinic summer inflows and one barotropic winter inflow in between, the strong underestimation of the exchange flow by Eulerian analysis as compared to TEF analysis is demonstrated.

The relationship between net mixing and the estuarine exchange flow may be quantified using a salinity variance budget. Here “mixing” is defined as the rate of destruction of volume-integrated salinity variance, and the exchange flow is quantified using the total exchange flow. These concepts are explored using an idealized 3D model estuary. It is shown that in steady state (e.g., averaging over the spring–neap cycle) the volume-integrated mixing is approximately given by Mixing ≅ SinSoutQr, where Sin and Sout are the representative salinities of in- and outflowing layers at the mouth and Qr is the river volume flux. This relationship provides an extension of the familiar Knudsen relation, in which the exchange flow is diagnosed based on knowledge of these same three quantities, quantitatively linking mixing to the exchange flow.

Estuarine turbidity maxima (ETMs) are generated by a large suite of hydrodynamic and sediment dynamic processes, leading to longitudinal convergence of cross-sectionally integrated and tidally averaged transport of cohesive and noncohesive suspended particulate matter (SPM). The relative importance of these processes for SPM trapping varies substantially among estuaries depending on topography, fluvial and tidal forcing, and SPM composition. The high-frequency dynamics of ETMs are constrained by interactions with the low-frequency dynamics of the bottom pool of easily erodible sediments. Here, we use a transport decomposition to present processes that lead to convergent SPM transport, and review trapping mechanisms that lead to ETMs at the landward limit of the salt intrusion, in the freshwater zone, at topographic transitions, and by lateral processes within the cross section. We use model simulations of example estuaries to demonstrate the complex concurrence of ETM formation mechanisms. We also discuss how changes in SPM trapping mechanisms, often caused by direct human interference, can lead to the generation of hyperturbid estuaries.

The impact of sea level rise (SLR) on the future morphological development of the Wadden Sea (North Sea) is investigated by means of extensive process-resolving numerical simulations. A new sediment and morphodynamic module was implemented in the well-established 3D circulation model GETM. A number of different validations are presented, ranging from an idealized 1D channel over a semi-idealized 2D Wadden Sea basin to a fully coupled realistic 40-year hindcast without morphological amplification of the Sylt-Romobight, a semi-enclosed subsystem of the Wadden Sea. Based on the results of the hindcast, four distinct future scenarios covering the period 2010–2100 are simulated. While these scenarios differ in the strength of SLR and wind forcing, they also account for an expected increase of tidal range over the coming century. The results of the future projections indicate a transition from a tidal-flat-dominated system toward a lagoon-like system, in which large fractions of the Sylt-Romobight will remain permanently covered by water. This has potentially dramatic implications for the unique ecosystem of the Wadden Sea. Although the simulations also predict an increased accumulation of sediment in the back-barrier basin, this accumulation is far too weak to compensate for the rise in mean sea level.

Simulations of the North Sea circulation by the global ocean model MPI-OM and the regional ocean models GETM, HAMSOM, NEMO, TRIM are compared against each other and with observational data for the period 1998–2009. The aim of the study is to evaluate the quality of the simulations in particular with respect to their suitability to drive biogeochemical shelf sea models. Our results demonstrate the benefit of the global model to avoid the specification of lateral open boundary conditions. Due to its stretched grid configuration, which provides a higher grid resolution at the Northwest European Shelf, the global model is able to reproduce the large-scale features, such as the water mass distribution and the thermal stratification in the central and northern North Sea, qualitatively similar to the regional models. The simulation of temperature and salinity near the coast however, shows large biases in almost all models because of the coarse meteorological forcing and too coarse vertical resolutions. The simulation of the Baltic Sea exchange and the spread of freshwater along the Norwegian coast proved difficult for all models except GETM, which reproduces impacts of the Baltic Sea outflow reasonably well.

We present a systematic analysis of generation mechanisms for exchange flows in partially stratified estuaries using water column (1DV) and width-averaged (2DV) numerical models. We focus on exchange flows generated by eddy viscosity-shear covariance (ESCO). We identify two distinctly different physical mechanisms. The first, tidal ESCO circulation, results from interactions between the barotropic tide and temporal variations of the eddy viscosity. While this flow is mostly generated by direct interactions between the tide and eddy viscosity variations at the main tidal frequency, a similarly important contribution can be attributed to indirect interactions. These are more complex interactions involving eddy viscosity variations at other frequencies than the main tidal frequency (e.g., M4). The second mechanism is called gravitational ESCO circulation. This results from an amplification of the gravitational circulation through indirect interactions between the gravitational circulation and temporal variations of the eddy viscosity at any time scale. Tidal and gravitational ESCO circulations are generated by different mechanisms and have a different dependency on the phase and frequency of eddy viscosity variations and the density gradient. The relative contributions of gravitational circulation and tidal and gravitational ESCO circulation to the exchange flow are typically 1/3 each in tidally energetic well-mixed or partially stratified estuaries. The results are generalized using an idealized width-averaged model of the Scheldt River estuary. This model confirms the results of the water column model and additionally shows that temporal variations of turbulence not captured in the water column model have a significant effect on the exchange flow.

The Total Exchange Flow analysis framework computes consistent bulk values quantifying the estuarine exchange flow using salinity coordinates since salinity is the main contributor to density in estuaries and the salinity budget is entirely controlled by the exchange flow. For deeper and larger estuaries temperature may contribute equally or even more to the density. That is why we included potential temperature as a second coordinate to the Total Exchange Flow analysis framework, which allows gaining insights in the potential temperature-salinity structure of the exchange flow as well as to compute consistent bulk potential temperature and therefore heat exchange values with the ocean. We applied this theory to the exchange flow of the Persian Gulf, a shallow, semienclosed marginal sea, where dominant evaporation leads to the formation of hypersaline and dense Gulf water. This drives an inverse estuarine circulation which is analyzed with special interest on the seasonal cycle of the exchange flow. The exchange flow of the Persian Gulf is numerically simulated with the General Estuarine Transport Model from 1993 to 2016 and validated against observations. Results show that a clear seasonal cycle exists with stronger exchange flow rates in the first half of the year. Furthermore, the composition of the outflowing water is investigated using passive tracers, which mark different surface waters. The results show that in the first half of the year, most outflowing water comes from the southern coast, while in the second half most water originates from the northwestern region.

We review the state of knowledge about offshore wind farm (OWF) development-related effects on hydrodynamics and their possible secondary effects on fishes derived from European studies. Theoretical, modeling, and observational studies of OWF developments are relatively advanced and identify potential impacts resulting from OWF changes to local or regional hydrodynamics through modification of (1) the wind fields, and (2) oceanographic parameters including turbulence, mixing, and vertical stratification. While limited, studies discuss local OWF (i.e., within the OWF footprint) impacts on fishes due to sediment resuspension or sedimentation, temperature change, nutrient transport, and substrate availability. These studies largely neglect possible effects further afield and generally conclude that any hydrodynamic impact of OWFs on fishes cannot be distinguished when compared to natural variability. To further understanding of the cumulative risk from extensive OWF developments requires additional research on OWF-related spillover effects on surrounding ecosystems and on natural oceanographic connectivity. The use of dynamic habitat or agentbased models coupled with refined hydrodynamic models can help quantify the scale of spatial and temporal effects of hydrodynamic cues on the movement of fishes and their habitats, which is not currently possible via conventional modeling, quantitative analysis approaches, or field-based observational studies and surveys.

A new parameterization for the estuarine turbulent eddy viscosity coefficient is developed considering the influence of wind forcing and feedback between stratification and shear. The emerging tidally averaged eddy viscosity profile A v T is parameterized as parabolic under well-mixed conditions, and is composed of a skewed-Gaussian-like form for the upper layer, and a parabolic form for the bottom layer under stratified conditions. The precise shape of the profiles depends parametrically on the bottom boundary layer thickness, the bulk Richardson number, and the Wedderburn number. The parameterized A v T profiles show excellent agreement with profiles obtained from numerical models. To explore the importance of vertically varying A v T with regard to exchange processes, an analytical model is designed. This one-dimensional model is based on a balance between frictional forces and pressure gradient. The resulting exchange flow is analyzed over the relevant parameter space that is associated with horizontal and vertical stratification through the bulk Richardson number, and the bi-directional wind stress via the Wedderburn number. Down-estuary wind enhances the up-estuary flow near the bottom and down-estuary flow near the surface driving an exchange flow pattern typically associated with gravitational circulation. Up-estuary wind results in either a two-layer inverted circulation opposing the gravitational circulation, or a three-layer flow that is up-estuarine at the surface with classical two-layer circulation underneath. Three-layer flow emerges with a weak wind. With increasing runoff velocity, three-layer flow transitions to a single layer flow under weak stratification conditions.

This paper discusses and explains the phenomenon of salinity inversions in the thermocline offshore from an upwelling region during upwelling-favorable winds. Using the non-tidal Central Baltic Sea as an easily accessible natural laboratory, high-resolution transect and station observations in the upper layers are analyzed. The data show local salinity minima in the strongly stratified seasonal thermocline during summer conditions under the influence of upwelling-favorable wind. A simple analytical box model using parameters (including variation by means of a Monte-Carlo method) estimated from a hindcast model for the Baltic Sea is constructed to explain the observations. As a result, upwelled water with high salinity and low temperature is warmed up due to downward surface heat fluxes while it is transported offshore by the Ekman transport. The warming of upwelled surface water allows maintenance of stable stratification despite the destabilizing salinity stratification, such that local salinity minima in the thermocline can be generated. Inspection of published observations from the Benguela, Peruvian and Eastern Tropical North Atlantic upwelling systems show that also there salinity inversions occur in the thermocline, but in these cases thermocline salinity shows local maxima, since upwelled water has a lower salinity than the surface water. It is hypothesized that thermocline salinity inversions should generally occur offshore from upwelling regions whenever winds are steady enough and surface warming is sufficiently strong.

Accelerated sea level rise may have serious implications for the Wadden Sea ecosystem in its present state. If sediment accumulation rates on the extensive intertidal flats stay behind sea level rise, the flats will eventually submerge. Drowning of the flats has negative consequences for nature conservation and for coastal risk management. Based upon an evaluation of steady state relations for Wadden Sea tidal basins, Hofstede (Zeitschrift fur Geomorphologie 59(3): 377-391, 2015) postulated that the capacity of these basins to balance sea level rise by accumulation on intertidal flats seems positively related to mean tidal range. In the present study, morphodynamical simulations with a numerical model were performed for two tidal basins in the German Wadden Sea to verify the empirically established hypothesis. The following conclusions are established. Larger mean tidal range improves the capacity of Wadden Sea tidal basins to balance sea level rise. Wadden Sea intertidal flats are effective sediment sinks and seem quite resilient against (higher rates of) sea level rise. Finally, subtidal gullies may constitute a significant sediment source for accumulation on intertidal flats in response to sea level rise. With respect to the limited comparability of the two investigated tidal systems, morphodynamical modelling of all Wadden Sea tidal systems should be conducted.

High-resolution water column observations have been carried out in the Wadden Sea to understand suspended particulate matter (SPM) transport in well-mixed tidal channels. These observations include more than 4000 consecutive CTD, microstructure shear and turbidity profiles from a free-falling microstructure probe, as well as velocity data from an ADCP and SPM samples for calibration. A horizontal density gradient was established by a landward temperature gradient built up during an extraordinarily warm and calm spring season. Tidal averaging along σ-layers (relative depth) provides the first direct observations of along-channel estuarine circulation in the Wadden Sea, with net inflow near the bottom and outflow near the surface. Increased westerly (up-estuary) winds during the second part of the campaign weakened and eventually even reversed estuarine circulation and yielded a net barotropic eastward transport. SPM concentrations showed a strong quarter-diurnal signal with maxima near full flood and full ebb and were generally lower during the calm period and increased during the windy period, mainly due to wave-related resuspension over nearby intertidal flats. The sediment flux analysis was based on a decomposition of the vertically integrated SPM flux into a barotropic advective component, an estuarine circulation component and a tidal pumping component. As a result, tidal pumping (due to ebb-dominance weakly seaward) dominated the SPM flux during calm conditions, whereas barotropic advection dominated the strong landward SPM flux during the windy period. Along-channel estuarine circulation is found to be of minor importance for the net SPM transport in such well-mixed systems.

Results from measurements are presented that were collected during a full tidal cycle in the Ems estuary, involving two landers and an anchored research vessel. The conditions were characterized by very weak winds, no wave effects, and low river run-off, so that the state was close to tide-only. We find that the lateral (i.e., cross-slope) transport of water and suspended particulate matter (SPM) much of the time shows a vertically layered structure, which is however subject to sudden transitions. Moreover, even on the small spatial scale of these measurements (i.e., within a distance of 200 m), a strong lateral variability is observed in the circulation patterns. We analyze its dynamics by means of dimensionless parameters. In addition, near-bottom peaks in SPM concentration are observed, notably during early flood. However, these episodic events have little effect on the overall transport of SPM, which involves the whole water column: the measurements show a high vertically integrated SPM signal during late ebb, resulting in an ebb-dominance in the transport at this position in the tidal channel.

For more than a century, estuarine exchange flow has been quantified by means of the Knudsen relations which connect bulk quantities such as inflow and outflow volume fluxes and salinities. These relations are closely linked to estuarine mixing. The recently developed Total Exchange Flow (TEF) analysis framework, which uses salinity coordinates to calculate these bulk quantities, allows an exact formulation of the Knudsen relations in realistic cases. There are however numerical issues, since the original method does not converge to the TEF bulk values for an increasing number of salinity classes. In the present study, this problem is investigated and the method of dividing salinities, described by MacCready et al. (2018), is mathematically introduced. A challenging yet compact analytical scenario for a well-mixed estuarine exchange flow is investigated for both methods, showing the proper convergence of the dividing salinity method. Furthermore, the dividing salinity method is applied to model results of the Baltic Sea to demonstrate the analysis of realistic exchange flows and exchange flows with more than two layers.

Transport algorithms of numerical ocean circulation models are frequently exhibiting truncation errors leading to spurious diapycnal mixing of water masses. This chapter discusses methods that might be useful in diagnosing spurious diapycnal mixing and describes some approaches that might be helpful for its reduction. The first one is related to the use of the Arbitrary Lagrangian Eulerian (ALE) vertical coordinate which allows the implementation of vertically moving meshes that may partly follow the isopycnals even if the basic vertical coordinate differs from isopycnal. The second approach relies on modified advection schemes with the dissipative part of the transport operators directed isopycnally. Finally the third approach deals with new efficient and stable advection algorithms of arbitrary high order based on the WENO-ADER method, which can be applied to both structured and unstructured meshes. While practical benefits of using the reviewed approaches depend on applications, there are indications that equipping present state-of-the-art ocean circulation models with them would lead to reduced spurious transformations.

International audience; The state of the art of the numerics of hydrodynamic non-hydrostatic structured-grid coastal ocean models is reviewed here. First, some fundamental differences in the hydrodynamics of the coastal ocean, such as the large surface elevation variation compared to the mean water depth, are contrasted against large scale ocean dynamics. Then the hydrodynamic equations as they are used in coastal ocean models as well as in large scale ocean models are presented, including parameterisations for turbulent transports. As steps towards discretisation, coordinate transformations and vertical and horizontal discretisations based on a finite-volume approach are discussed with focus on the specific requirements for coastal ocean models. As in large scale ocean models, splitting of internal and external modes is essential also for coastal ocean models, but specific care is needed when wetting an drying of inter-tidal flats is included. As one obvious characteristics of coastal ocean models, open boundaries occur and need to be treated in a way that correct model forcing from outside is transmitted to the model domain without reflecting waves from the inside. Here, also new developments in two-way nesting are presented. Single processes such as internal inertia-gravity waves, advection and turbulence closure models are discussed with focus on the coastal scales. Some overview on existing hydrostatic structured-grid coastal ocean models is given, including their extensions towards non-hydrostatic models. Finally, an outlook on future perspectives is made.

In December 2014, an exceptional inflow event into the Baltic Sea was observed, a so-called Major Baltic Inflow (MBI). Such inflow events are important for the deep water ventilation in the Baltic Sea and typically occur every 3–10 years. Based on first observational data sets, this inflow had been ranked as the third largest since 100 years. With the help of a multinested modeling system, reaching from the North Atlantic (8 km resolution) to the Western Baltic Sea (600 m resolution, which is baroclinic eddy resolving), this event is reproduced in detail. The model gave a slightly lower salt transport of 3.8 Gt, compared to the observational estimate of four Gt. Moreover, by using passive tracers to mark the different inflowing water masses, including an age tracer, the inflowing water masses could be tracked and their paths and timing through the different basins could be reproduced and investigated. The analysis is supported by the recently developed Total Exchange Flow (TEF) to quantify the volume transport in different salinity classes. To account for uncertainties in the modeled velocity and tracer fields, a Monte Carlo Analysis (MCA) is applied to correct possible biases and errors. With the help of the MCA, 95% confidence intervals are computed for the transport estimates. Based on the MCA, the “best guess” of the volume transport is 291.0 ± 13.65 km3 and 3.89 ± 0.18 Gt for the total salt transport.

In this study, we present estuarine circulation driven by horizontal density gradients generated by spatially homogeneous surface buoyancy fluxes over sloping bathymetry as a dynamical feature in the coastal zone being potentially relevant for cross-coastal transports. A combination of downward buoyancy flux (net precipitation, net heating) together with tidal mixing may generate a classical estuarine circulation with landward near-bottom residual currents. The Wadden Sea of the south-eastern North Sea is a prototype for such a coastal regime. It is characterised by extensive inter-tidal flats along the coast separated from the open sea by barrier islands. Here, we present long-term observations from the Wadden Sea covering the years 2006–2011. We investigated the statistics of the density gradients. Typical values for the landward density gradient were ∂ x ρ≈−3⋅10−5 kg m−4 and maximum values were ∂ x ρ≈−6.5⋅10−5 kg m−4. The magnitude of the density gradient resulted from the magnitude of the salinity gradient, with some modifications by the positive (towards the coast, in spring) or negative (towards the sea, in autumn) temperature gradient. To explain the generation of estuarine circulation by the surface buoyancy flux, we construct an analytical model representing the geometry and dynamics of a Wadden Sea Basin. With downward buoyancy flux, a weak classical estuarine circulation due to gravitational forcing results, whereas upward buoyancy flux drives inverse estuarine circulation. Finally, a two-dimensional (vertical-longitudinal) numerical model was set up for the idealised geometry, including tidally asymmetric turbulent mixing. This results in significantly stronger estuarine circulation due to the presence of tidal straining. The model assesses the circulation due to neutral and upward surface buoyancy fluxes. We conclude that these mechanisms may be important in many coastal areas and may substantially contribute to coast-to-sea exchange in these areas.

This paper quantifies spurious dissipation and mixing of various advection schemes in idealised experiments of lateral shear and baroclinic instabilities in numerical simulations of a re-entrant Eady channel for configurations with large and small Rossby numbers. In addition, a two-dimensional barotropic shear instability test case is used to examine numerical dissipation of momentum advection in isolation, without any baroclinic effects. Effects of advection schemes on the evolution of background potential energy and the dynamics of the restratification process are analysed. The advection schemes for momentum and tracers are considered using several different methods including a recently developed local dissipation analysis. As highly accurate but computationally demanding schemes we apply WENO and MP5, and as more efficient lower-order total variation diminishing (TVD) schemes we use among others the SPL-max-View the MathML source13 and a third-order-upwind scheme. The analysis shows that the MP5 and SPL-max-View the MathML source13 schemes provide the most accurate results. Following our comprehensive analysis of computational costs, the MP5 scheme is approximately 2.3 times more expensive in our implementation. In contrast to the configuration with a small Rossby number, in which significant differences between schemes are apparent, the different advection schemes behave similarly for a larger Rossby number. Regions of high numerical dissipation are shown to be associated with low grid Reynolds numbers. The major outcome of the present study is that generally positive global numerical dissipation and positive background potential energy evolution delay the restratification process.