Gradient Richardson Number Research Articles

Quantification of Mixing Depth Using the Gradient Richardson Number in Submerged Aquatic Vegetation Meadows

AbstractUpper layer thickness (mixing depth) is an essential parameter for estimating the dissolved inorganic carbon and carbon flux at the water surface based on their association with the vertical flux of dissolved inorganic carbon. Previous studies quantified the mixing depth without SAV meadow or penetration depth in the SAV meadow without stratification and wind stress. However, mixing depth related to interaction with submerged aquatic vegetations (SAVs), stratification, and wind stress has yet to be quantified in the previous studies. Our study is the first to quantify the theoretical mixing depth with SAVs according to wind stress, SAV height, and drag coefficient. Theoretical mixing depth was quantified from modeled vertical temperature profile, vertical profile of horizontal velocity, and gradient Richardson number (Rig,veg). We found that mixing depth at a Rig,veg of 100 demonstrated good agreement with numerical results on average, with the mixing depth estimated in this study (hU,this study) showing high applicability to observations at Komuke Lagoon. Moreover, hU,this study increased with the increasing wind stress and decreasing drag coefficient and SAV height. Further, we found that SAV meadows with stratification and wind stress could be divided into four hydrodynamic regimes: non‐vegetated layers, upper vegetated layers, thermoclines, and benthic boundary layers. Our findings help us estimate mixing depth or vertical flux without complicated numerical simulation and understand flow interaction with SAV, wind stress, and stratification.

Wind Shear Model Considering Atmospheric Stability to Improve Accuracy of Wind Resource Assessment

An accurate wind shear model is an important prerequisite in extrapolating the wind resource from lower heights to the increasing hub height of wind turbines. Based on the 1-year dataset (collected in 2014) consisting of 15-minute intervals collected at heights of 2, 10, 50, 100, and 150 m on an anemometer tower in northern China, the present study focuses on the time-varying relationship between the wind shear coefficient (WSC) and atmospheric stability and proposes a wind shear model considering atmospheric stability. Through the relationship between Monin–Obukhov (M-O) length and gradient Richardson number, the M-O length is directly calculated by wind data, and the WSC is calculated by combining the Panofsky and Dutton (PD) models, which enhances the engineering practicability of the model. Then, the performance of the model is quantified and compared with two alternative methods: the use of annual average WSC and the use of stability change WSC extrapolation. The analysis demonstrates that the proposed model outperforms the other approaches in terms of normal root mean square error (NRMSE) and normal bias (NB). More specifically, this method reduces the NRMSE and NB by 24–29% and 76–95%, respectively. Meanwhile, it reaches the highest extrapolation accuracy under unstable and stable atmospheric conditions. The results are verified using the Weibull distribution.

Evolution of small-scale turbulence at large Richardson numbers

Abstract. The theory of stratified turbulent flow developed earlier by the authors is applied to data from different areas of the ocean. It is shown that turbulence can be amplified and supported even at large gradient Richardson numbers. The cause of that is the exchange between kinetic and potential energies of turbulence. Using the profiles of Brunt–Väisälä frequency and vertical current shear given in Forryan et al. (2013), the profiles of the kinetic energy dissipation rate are calculated. The results are in reasonable agreement with the experimental data.

Ice base slope effects on the turbulent ice shelf-ocean boundary current

Abstract Efforts to parameterize ice shelf basal melting within climate models are limited by an incomplete understanding of the influence of ice base slope on the turbulent ice shelf-ocean boundary current (ISOBC). Here we examine the relationship between ice base slope, boundary current dynamics, and melt rate using 3-D, turbulence-permitting large-eddy simulations (LES) of an idealized ice shelf-ocean boundary current forced solely by melt-induced buoyancy. The range of simulated slopes (3-10%) is appropriate to the grounding zone of small Antarctic ice shelves and to the flanks of relatively wide ice base channels, and the initial conditions are representative of warm-cavity ocean conditions. In line with previous studies, the simulations feature the development of an Ekman boundary layer adjacent to the ice, overlaying a broad pycnocline. The time-averaged flow within the pycnocline is in thermal wind balance, with a mean shear that is only weakly dependent on the ice base slope angle α, resulting in a mean gradient Richardson number 〈Rig〉 that decreases approximately linearly with sinα. Combining this inverse relationship with a linear approximation to the density profile, we derive formulations for the friction velocity, thermal forcing, and melt rate in terms of slope angle and total buoyancy input. This theory predicts that melt rate varies like the square root of slope, which is consistent with the LES results and differs from a previously proposed linear trend. The derived scalings provide a potential framework for incorporating slope-dependence into parameterizations of mixing and melting at the base of ice shelves.

Long-wave instabilities of sloping stratified exchange flows

We investigate the linear instability of two-layer stratified shear flows in a sloping two-dimensional channel, subject to non-zero longitudinal gravitational forces. We reveal three previously unknown instabilities, distinct from the well-known Kelvin–Helmholtz instability and Holmboe wave instability, in that they have longer wavelengths (of the order of 10 to $10^3$ shear-layer depths) and often slower growth rates. Importantly, they can grow in background flows with gradient Richardson number $\gg 1$ , which offers a new mechanism to sustain turbulence and mixing in strongly stratified flows. These instabilities are shown to be generic and relatively insensitive to Reynolds number, Prandtl number, base flow profile and boundary conditions. The nonlinear evolution of these instabilities is investigated through a forced direct numerical simulation, in which the background momentum and density are sustained. The growth of long unstable waves in background flows initially stable to short wave causes a decrease in the local gradient Richardson number. This leads to local nonlinear processes that result in small-scale overturns resembling Kelvin–Helmholtz billows. Our results establish a new energy exchange pathway, where the mean kinetic energy of a strongly stratified flow is extracted by primary unstable long waves and secondary short waves, and subsequently dissipated into internal energy.

High-Resolution Remote Sensing of the Gradient Richardson Number in a Megacity Boundary Layer

The Gradient Richardson Number (Ri) is an important parameter for appraising the stability and turbulence exchange at the atmospheric boundary layer (ABL). However, high-resolution measurements of Ri profiles are rarely reported, especially in megacities. In this study, a Doppler wind lidar and a microwave radiometer were simultaneously utilized to measure the 2 km Ri vertical profile in downtown Beijing. These measurements were verified to have high accuracy compared with observations from a 325 m meteorological tower, with root-mean-square errors (RMSEs) of less than 1.66 K, 7.9%, and 1.45 m/s for the temperature, relative humidity, and wind speed (WS) for all altitudes and corresponding Pearson correlation coefficients (R) of 0.97, 0.93, and 0.81. The inter-comparisons of different spatial (25 m, 50 m, 100 m) and temporal resolutions (1 min, 30 min, 1 h) form a 3 × 3 resolution matrix of Ri, in which the 1 h temporal resolution of Ri overestimates the intensity and active area of turbulence. The Ri value retrieved from the 100 m spatial resolution data overestimates these by half as it misidentifies the height of the stable area at the near surface. There are significant differences between the data with a 1 min temporal resolution and a 25 m spatial resolution (defined as the standard resolution of Ri), and the rest of the data in the resolution matrix (defined as data at other resolutions), with an RMSE > 1 and an R < 0.8. The difference between data at the standard resolution and data at other resolutions increases with elevations, which results from frequent weather processes or from water-vapor blocking at higher altitudes. The Ri profiles reveal that the atmospheric layer at altitudes from 100 m to 500 m in daytime is unstable, with Ri < 0, while it is neutral, with 0 < Ri < 0.25, at night-time from 200 m to 400 m. The atmosphere above the ABL in a megacity is rather stable, with Ri > 0.25, whereas below the ABL, it is neutral or unstable, which is due to drastic changes in the WS and temperature that are affected by the topography and surface friction.

Quantifying the contribution of external thermal energy and internal hydrodynamic processes to the water temperature of river-valley reservoirs

Hydropower plants utilize hydroelectric energy while also impacting the hydrodynamic and hydrothermal processes within river. To comprehend and address the environmental and ecological impacts of hydropower plants, it is crucial to quantify these processes. The study synthesizes methods for calculating reservoir heat transport and Richardson numbers, presenting a comprehensive framework for understanding the interaction of heat transport and hydrodynamic processes in reservoirs based on EFDC model simulations. It quantifies the external thermal and internal hydrodynamic effects on the water temperature evolution of a deep valley reservoir, using the Jinsha River Xiluodu Reservoir as a case study. Multi-interface heat transport calculations indicate that the Deep River Valley Reservoir is a hydrothermal body dominated by inflow and outflow. During the water temperature stratification period, the reservoir water temperature increases by 0.015 °C/day due to surface heat fluxes, incorporating hydraulic residence time, while the reservoir water temperature increases by 0.06 °C/day due to inflow heat fluxes. Furthermore, this study analyses the interrelationships between reservoir buoyancy and shear stress based on the gradient Richardson number, revealing the interaction between hydrodynamic and water temperature processes. This study not only provides a framework for understanding reservoir thermodynamics but also provides a theoretical basis for effective reservoir management and ecosystem assessment.

Processes of stratification and vertical turbulent mixing in a choked lagoon system

This work concentrates on the processes of stratification and turbulent mixing in a choked shallow lagoon, Xiaohai Lagoon, by using a three-dimensional hydrodynamic model. The model results were processed to derive buoyancy frequency, shear production, gradient Richardson number, and buoyancy flux during the tidal cycles. The parameters regarding stratification and turbulent mixing exhibited significant heterogeneity within the lagoon. Shear production primarily occurred in the downstream region with complex shoreline and bed morphology, whereas stratification was predominantly developed in the flat upstream region by tidal strain and baroclinic strain, especially during the ebb tide. The salinity mixing indicated by buoyancy flux was thus mainly confined during the ebbs in the downstream region and the middle-lower layer of the upstream region. In addition, the distribution of the gradient Richardson number indicated dominances of shear instability and buoyancy effects in the downstream and upstream regions, respectively. By simulating various combinations of river discharges and offshore tidal ranges, we examined the variations of stratification and turbulent mixing within the lagoon's parameter space. The results revealed the influence of the interaction between tidal and runoff forces through a modulation of the salinity interface's moving range. Further investigation of the buoyancy balance underlying the variation in stratification revealed the dominance of straining and mixing, while advection played a secondary role. Straining dominance appeared at locations with sufficient streamwise density gradients in the upstream region during the ebb. The contribution of advection was essential, as straining and mixing largely counteracted each other's effects through their persistent competition. A conceptual model for the stratification and mixing patterns in choked lagoons during the tidal cycle was then proposed. This conceptual model clarifies the process of the interaction between stratification and turbulent mixing in the distinctive hydrological and geomorphic environments of choked lagoons and could serve as a conference for investigating other lagoon systems in the world.

The Structure and Dynamics of an Estuarine Tidal Intrusion Front

AbstractTidal intrusion fronts are surface convergences that occur at constrictions in estuaries during the flood tide, separating incoming higher‐salinity water from lower‐salinity, stratified estuarine water. Previous observations of tidal intrusion fronts describe a V‐shaped planform, with the apex of the V pointing into the estuary, however the significance of this structure has not been previously explained. Observations near the mouth of the James River estuary during the flood tide reveal the development of a quasi‐steady, V‐shaped front. Considering a reference frame oriented normal to the front, the velocity and density structure are consistent with gravity‐current dynamics, but the oblique orientation of the front relative to the impinging flow indicates strong, along‐front shear, which results from vorticity produced by flow separation at the lateral boundaries as well as topographic torque from upstream. The combination of convergence and along‐front shear leads to enhanced mixing, as revealed by acoustic backscatter images of shear instability and persistent subcritical gradient Richardson number in the frontal zone. Oblique fronts such as this tidal intrusion front are common features of estuaries, and they play an important role in vertical exchange due to subduction and mixing of surface water.

Constant stress layer characteristics in simulated stratified air flows: Implications for aeolian transport

Varying thermal atmospheric stability conditions and their effects on shearing flows has long been a subject of interest for researchers working in atmospheric science. The development of new instrument technologies now offers an opportunity to study flows with high spatial and temporal resolutions in wind tunnel atmospheric boundary layers. In the presented study, we use a laser Doppler anemometer within the Trent Environmental Wind Tunnel Laboratory to investigate the influence of thermal stratification on the constant stress layer. Analyses of the thermal stratification represented by the gradient Richardson number and the apparent von Kármán parameter, shear velocity, and the slope of the streamwise velocity profiles reveal strong linear relationships. An exponential relationship between thermal stability and the apparent roughness length is also revealed. Profiles of the streamwise and vertical velocity and turbulence intensity, as well as the dimensionless Reynolds stress, are influenced by the gradient Richardson number. These findings have implications for producing accurate models of sediment entrainment and transport by wind in non-neutral conditions.

Comparison of ADCP and ECCOv4r4 Currents in the Pacific Equatorial Undercurrent

Abstract The Pacific Equatorial Undercurrent (EUC) flows eastward across the Pacific at the equator in the thermocline. Its variability is related to El Niño. Moored acoustic Doppler current profiler (ADCP) measurements recorded at four widely separated sites along the equator in the EUC were compared to currents generated by version 4 release 4 of the Estimating the Circulation and Climate of the Ocean (ECCOv4r4) global model–data synthesis product. We are interested to learn how well ECCOv4r4 currents could complement sparse in situ current measurements. ADCP measurements were not assimilated in ECCOv4r4. Comparisons occurred at 5-m depth intervals at 165°E, 170°W, 140°W, and 110°W over time intervals of 10–14 years from 1995 to 2010. Hourly values of ECCOv4r4 and ADCP EUC core speeds were strongly correlated, similar for the EUC transport per unit width (TPUW). Correlations were substantially weaker at 110°W. Although we expected means and standard deviations of ECCOv4r4 currents to be smaller than ADCP values because of ECCOv4r4’s grid representation error, the large differences were unforeseen. The appearance of ECCOv4r4 diurnal-period current oscillations was surprising. As the EUC moved eastward from 170° to 140°W, the ECCOv4r4 TPUW exhibited a much smaller increase compared to the ADCP TPUW. A consequence of smaller ECCOv4r4 EUC core speeds was significantly fewer instances of gradient Richardson number (Ri) less than 1/4 above and below the depth of the core speed compared to Ri computed with ADCP observations. We present linear regression analyses to use monthly-mean ECCOv4r4 EUC core speeds and TPUWs as proxies for ADCP measurements. Significance Statement Hundreds of scientific papers have used ECCO data products generated with a continually evolving state-of-the-art ocean-model–data synthesis system. We ask, How representative is the latest version of ECCO equatorial ocean currents? We use independent in situ current measurements as the reference dataset to establish the accuracy of ECCO currents in the tropical Pacific. Attention is focused on the Pacific Equatorial Undercurrent (EUC) because it contributes to the formation of El Niño and La Niña events. ECCO EUC core speeds were smaller in magnitude and less variable in time compared to observations. As a consequence, ECCO currents generated smaller vertical mixing in the EUC compared to that inferred from current measurements. We developed a linear regression model to improve representation of monthly-mean ECCO currents.

Development of multiphase solver for the modeling of turbidity currents (the case study of Dez Dam)

Dams in semi-arid regions, like Iran's Dez dam, are losing their capacity by sedimentation. Settling sediments reduces clear water, and hydropower plants' efficiency. Reservoir sedimentation relies on turbidity currents (TC). TC head velocity, and sediment content both affect particle tracking, and the removal from reservoirs. To comprehend the TC properties of Dez dam reservoir, large-scale TC modeling is required. To represent large-scale TC, a novel solver is developed. This solver couples a modified OpenFOAM® interFoam solver with the particle concentration transport equation. Two experimental tests, and Dez dam field data were verified and calibrated. The novel solution modeled these instances utilizing a two-dimensional vertical model (width averaged) with RANS turbulence closure, despite the fact that the Dez dam reservoir has a considerable size for numerical modeling. The solver simulated four Dez Dam reservoir scenarios with different water levels. Consequently, when the inlet water depth rose four times, the TC head velocity, and distance traveled by TC doubled. TC in Dez dam is a supercritical flow with the interface instabilities based on its local Richardson number, and gradient Richardson number. Furthermore, Kelvin-Helmholtz instabilities and recirculation vortex combine clear water with TC to reduce the particle concentration.

Intermittency and critical mixing in internally heated stratified channel flow

Through direct numerical simulations we investigate the effects of spatiotemporal intermittency as a result of stable stratification in surface heated stratified open channel flow. By adapting the density inversion criterion method of Portwood et al. [J. Fluid Mech., vol. 807, 2016, R2] for our flow, we demonstrate that the flow may be robustly separated into regions of active turbulence for which $Re_B \gtrsim {O}(10)$ and surrounding quiescent fluid, where $Re_B$ is the buoyancy Reynolds number. The intermittency in the flow spontaneously manifests as a deformed horizontal interface between the upper quiescent and lower turbulent flow, characterised by vigorous mixing from ‘overturning’ shear instabilities. The resulting vertical intermittency profile is accurately predicted by a local Monin–Obukhov length normalised by viscous wall units $\varLambda ^+$ such that the flow displays intermittency within the parameter range of $2.5 \lesssim \varLambda ^+ \lesssim 260$ . By considering conditional averages of the ‘turbulent’ and ‘quiescent’ flow separately, we find the ‘turbulent’ flow within this region to be described by constant critical gradient Richardson and turbulent Froude numbers of $Ri_{g,c} \approx 0.2$ and $Fr_c \approx 0.3$ . We find that the turbulent flow continues to display a $\varGamma \sim Fr^{-1}$ relationship when $Fr < Fr_c$ , whereas the quiescent flow shows no correlation between $\varGamma$ and $Fr$ , where $\varGamma$ is the flux coefficient. Hence, we demonstrate directly that for our flow, the emergence of an asymptotic ‘saturated’ $\varGamma$ regime in the limit of a low ‘global’ $Fr$ occurs due to intermittency and increasing contributions to measurements of $\varGamma$ from the quiescent flow.

Thermo-hydraulic characteristics of thermal interface induced by natural convection in water tank with internal heat source

Large-scale water tank or pool with internal heat source is common structures in solar energy and nuclear power. In this paper, a visible thermal interface is captured in the experiments in a square water tank with a horizontal heating rod, which is an interesting phenomenon hardly reported before. The direct shadowgraphy method is employed to record gray graphs of the forming process and flow regimes of the thermal interface. Corresponding transient numerical simulations with the large eddy simulation (LES) method are conducted to display detailed thermo-hydraulic characteristics of the thermal interface. Based on the temperature distribution and flow field, a natural convection circulation driven by buoyancy is formed above a stagnant zone, which is regarded as a two-layer stratified shear flow. The horizontal shear flow above the stagnant zone induces the visible thermal interface. Because the heat transfer mode switches from convection to conduction when crossing the interface, the sharp temperature gradient and density variation occur at the interface. The effect of the heat flux of the heating rod is investigated, and three different flow regimes of the thermal interface are observed under different heat loads. The stability of the flow regimes is analyzed by the gradient Richardson number, which is the ratio of the buoyancy to the turbulent shear. At low heat load, the thermal interface is destabilized because the turbulent shear overcomes the density barrier. As the heat loading increases, the buoyancy increasing rate exceeds the shear increasing rate, and the stronger potential barrier dominates the flow structure, which is beneficial to the interface stability.

Formation and transport of fluid mud triggered by typhoon events in front of the subaqueous Changjiang Delta

Fluid mud supported by waves can move downslope on a gentle slope under gravity to transport massive sediment across the continental shelf and cause significant geomorphological changes. In order to explore the formation and transportation of fluid mud under extreme conditions, we undertook in-situ measurements and observed fluid-mud-related processes triggered by a typhoon, Danas, in the subaqueous Changjiang Delta. Under the action of waves, firstly, the seabed was eroded slowly for ∼930 min caused by the wave-enhanced bed shear stress; next, rapid erosion occurred when the bed erodibility Me/ρB doubled the value during no waves. The great change in bed erodibility implied that bed liquefaction occurred due to waves. The fluid mud occurred concurrently with the strongest waves and went through five stages with an interval of 0.5–3.5 h between each stage in which waves weakened continuously. In addition, the five fluid mud stages all underwent three identical phases, i.e., formation, stabilization, and decay. In the formation and decay phases, the bottom friction force exceeded the buoyancy gravitational force, and the gradient Richardson number (Ri) was lower than the typical threshold of 0.25, indicating that fluid mud was unstable due to high turbulence energy enhanced by Kelvin-Helmholtz instabilities. During the stabilization phase, the buoyancy gravity force was almost balanced with the drag friction force, and Ri was close to or higher than 0.25, suggesting a laminar fluid mud status. Eventually, the fluid mud disappeared when significant wave height decreased to <1.39 m. Our observation results showed that bed erosion and liquefaction both contributed to the formation of the fluid mud, and the fluid mud played an important role in sediment transportation and bed landforms in subaqueous deltas during extreme events.

Some Further Aspects of Stable Boundary-Layer Simulation in a Stratified-Flow Wind Tunnel

It is demonstrated that the vertical profile of gradient Richardson number, Ri, can be shaped by control of the working-section inlet temperature profile. In previous work (Hancock and Hayden in Boundary-Layer Meteorol 168:20–57, 2018; 175:93–112, 2020; 180:5–26, 2021) the inlet temperature profile had been specified but without control of the profile of Ri in the developed-flow region of the working section. Control of the inlet temperature profile is provided by 15 inlet heaters (spread uniformly across the height of the working section), allowing control of the temperature gradient over the bulk of the boundary layer, and the overall temperature level above that of the surface. The bulk Richardson number for the 11 cases covers the range 0.01–0.17 (there is no overlying inversion). In the upper approx 2/3 of the boundary layer the Reynolds stresses and turbulent heat flux are controlled by the gradient in mean temperature, while in the lower approx 1/3 they are controlled both by this gradient and by the level above the surface temperature. In three examples, Ri is approximately constant at 0.07, 0.10 and 0.13 across the bulk of the layer. The previous observation of horizontally homogenous behaviour in the temperature profiles in the top approx 2/3 of the boundary layer but not in the lower approx 1/3 is repeated here, except when, tentatively, Ri does not exceed 0.05 over the bulk of the boundary layer. Favourable validation comparisons are made against two sets of local scaling systems and field data over the full depth of the boundary layer, over the range 0.006 le Ri le 0.3, or, in terms of height and local Obukhov length, 0.005 le z/L le 1.

Study of Some Stability Parameters in the Atmosphere of Oil Al-Dura Refinery, Southeast Baghdad

Wind and temperature measurements at an oil refinery site located southeast of Baghdad city at two levels, 15 and 30 m, are presented. Three schemes are used to determine different stability classifications: Monin-Obukhov length, gradient, and bulk Richardson numbers. Meanwhile, vertical changes in air temperature and wind shear are also computed. There were lapse rate and inversion cases during the nights and days while favorable wind shear was dominant. The variation of stability in each scheme is large, covering the entire range of stability for a given class. The results of stability schemes are compared to each other. The results show that the schemes based on gradient and bulk Richardson numbers reasonably compare them.

Turbulent Kinetic Energy Production in a Far‐Field River Plume Under Upwelling‐Favorable Winds

AbstractAn idealized three‐dimensional numerical model is used to investigate turbulent kinetic energy (TKE) production in a far‐field river plume under upwelling‐favorable winds. TKE production decreases over longer length scales as the river plume thickens. Maximum TKE production appears in the surface layer and is mainly generated by the alongshore component of the velocity shear. The large velocity shear and weak stratification in the surface layer result in a gradient Richardson number (Ri) of &lt;0.25, which corresponds to the locally high TKE production. We find that asymmetrical TKE production occurs at the two edges of the river plume, due to the opposite nonlinear interaction of the Ekman and geostrophic effects at the shoreward and seaward edges of the river plume. This asymmetrical TKE production combines with secondary upwelling circulation in the river plume under upwelling‐favorable winds, which may generate more intense biological activity at the shoreward edge of the river plume than at the seaward edge. Numerical model experiments are performed to examine the effects of wind, river discharge, and stratified conditions on TKE production in the river plume. Finally, we propose a conceptual model in which the depth‐averaged TKE production in the river plume is proportional to the alongshore wind stress () and inversely proportional to the cube of the surface boundary layer thickness (D3), which is consistent with the results of numerical experiments.

Circulation, stratification and salt dispersion in a former estuary after reintroducing seawater inflow

Around the world, estuaries have been partially or completely closed-off from the sea and their number may increase with rising sea levels. Concurrently, there is a trend to reintroduce seawater inflow into enclosed former estuaries for ecosystem improvement. This is also the case in the Haringvliet, a former estuary in the Rhine-Meuse Delta, closed-off in 1970 with floodgates blocking seawater inflow and regulating outflow. As the reintroduced salt water inflow can threaten fresh water intake, inflow, flushing and dispersion need to be well understood and carefully managed.Here we investigate stratification, flow circulation and salt transport in the Haringvliet by analyzing ADCP data collected in two former tidal channels, together with salinity time series and profiles. The profiles show that the incoming water reaches the deeper parts and that the system tends to be strongly stratified. Over time, the interface levels deepen in steps, mainly coinciding with floodgate discharge events, which are strongly correlated with the primary current velocities in the channels. However, even floodgate discharges for above average Rhine discharge conditions were insufficient to quickly flush or mix the salt out of the channels. This is consistent with calculated gradient Richardson numbers, which barely get in the range of critical values.For closed floodgates with no outward discharge, we found considerable depth-averaged upwind currents in the channels for axial winds. This reveals a dominant horizontal circulation, with downwind currents over the shallow parts and upwind currents over the deep parts of the system, explained by a local imbalance between the wind stress and pressure gradient force at both shoals and channels. This horizontal circulation is an important driver for inland salt transport, as increased salinity values were found at landward locations for seaward wind. This implies this is a condition with increased risks for fresh water availability. Analytical calculations confirmed the upwind currents in the channels can become sufficiently strong to transport salt mixed up at one side of the system to the other within the duration of a wind event. However, the current-related shear is likely not strong enough to induce interfacial mixing directly above the deep parts, and we hypothesize mixing mostly occurs when salt water reaches less deep areas after tilting of the pycnocline.The insights from this study are relevant for other formerly enclosed estuaries for which reintroduction of seawater inflow is considered, as well as presently open systems for which (partial) closure is discussed.

Turbulent Transport in a Stratified Shear Flow

Within the framework of the theory of unsteady turbulent flows in a stratified fluid, a new parameterization of the turbulent Prandtl number is proposed. The parameterization is included in the k-ε-closure and used within the three-dimensional model of thermohydrodynamics of an enclosed water body where density distribution includes pycnocline. This allows us to describe turbulence in a stratified shear flow without the restrictions associated with the gradient Richardson number and justify the choice of closure constants. Numerical experiments, where the downward penetration of turbulence was considered, confirm the advantage of the developed approach in describing the effects neglected in the classical closures.