Depth-averaged Velocity Research Articles

Application of Image Technique to Obtain Surface Velocity and Bed Elevation in Open-Channel Flow

The frequency of droughts and floods is increasing due to the extreme climate. Therefore, water resource planning, allocation, and disaster prevention have become increasingly important. One of the most important kinds of hydrological data in water resources planning and management is discharge. The general way to measure the water depth and discharge is to use the Acoustic Doppler Current Profiler (ADCP), a semi-intrusive instrument. This method would involve many human resources and pose severe hazards by floods and extreme events. In recent years, it has become mainstream to measure hydrological data with nonintrusive methods such as the Large-Scale Particle Image Velocimetry (LSPIV), which is used to measure the surface velocity of rivers and estimate the discharge. However, the unknown water depth is an obstacle for this technique. In this study, a method combined with LSPIV to estimate the bathymetry was proposed. The experiments combining the LSPIV technique and the continuity equation to obtain the bed elevation were conducted in a 27 m long and 1 m wide flume. The flow conditions in the experiments were ensured to be within uniform and subcritical flow, and thermoplastic rubber particles were used as the tracking particles for the velocity measurement. The two-dimensional bathymetry was estimated from the depth-averaged velocity and the continuity equation with the leapfrog scheme in a predefined grid under the constraints of Courant–Friedrichs–Lewy (CFL). The LSPIV results were verified using Acoustic Doppler Velocimetry (ADV) measurements, and the bed elevation data of this study were verified using conventional point gauge measurements. The results indicate that the proposed method effectively estimated the variation of the bed elevation, especially in the shallow water level, with an average accuracy of 90.8%. The experimental results also showed that it is feasible to combine the nonintrusive imaging technique with the numerical calculation in solving the water depth and bed elevation.

Formation of dry granular fronts and watery tails in debris flows

Debris flows are particle–fluid mixtures that pose a significant hazard to many communities throughout the world. Bouldery debris flows are often characterised by a deep dry granular flow front, which is followed by a progressively thinner and increasingly watery tail. The formation of highly destructive bouldery wave fronts is usually attributed to particle-size segregation. However, the moving-bed flume experiments of Davies (N. Z. J. Hydrol., vol. 29, 1990, pp. 18–46) show that discrete surges with dry fronts and watery tails also form in monodisperse particle–fluid mixtures. These observations motivate the development of a new depth-averaged mixture theory for debris flows, which explicitly takes account of the differing granular and phreatic surfaces, velocity shear, and relative motion between grains and fluid to explain these phenomena. The theory consists of four coupled conservation laws that describe the spatial and temporal evolution of the grain and water thicknesses and depth-averaged velocities. This system enables travelling wave solutions to be constructed that consist of (i) a large amplitude dry flow front that smoothly transitions to (ii) an undersaturated body, (iii) an oversaturated region and then (iv) a pure water tail. It is shown that these solutions are in good quantitative agreement with Davies’ experiments at high bed speeds and slope inclinations. At lower bed speeds and inclinations, the theory produces travelling wave solutions that connect to a steady-uniform upstream flow, and may or may not have a bulbous flow front, consistent with Davies’ observations.

Studies on navigational depth of a shipping channel using numerical modelling and bathymetric analysis in the Hooghly estuary, India

ABSTRACT Availability of navigational draft along the shipping channel is essential for effective freight transport of any port for its economic sustenance. Rangafala channel is one of the main channels leading to Kolkata port. The primary objective of this research work is to find the critical and vulnerable positions in the navigation channel. A Cartesian grid-based, two-dimensional, depth-averaged, finite volume model has been developed using existing bathymetry, water level, sediment data, and appropriate boundary conditions in hydrodynamic and sediment transport modelling. The developed model is first calibrated using observed velocity data, and then, it has been validated with observed water level data at the Haldia gauge station. The validated model has been simulated for 6-month boundary values, and it has been experienced that the depth-averaged model velocity is relatively high throughout the channel. The hydrodynamic and sediment transport model results suggest that the channel remains self-maintained, and only a few locations experience little deposition. Eleven years of channel bathymetric data are used to complement the simulated model results. It is observed that the required draft for navigation has always been maintained along the Rangafala channel.

The effect of tides on internal variability in the Bohai and Yellow Sea

The hydrodynamics of marginal seas exhibit internal variability unprovoked by external forcing. To date, the role of tides in reducing this “noise” has not been evaluated. We investigated the effect of tides on internal variability in the Bohai and Yellow Sea. To do so, we conducted three ensembles of numerical experiments using the three-dimensional Finite-Volume Coastal Ocean Model (FVCOM) with tidal forcing, with “half-tidal” forcing, and without tidal forcing, while everything else was unchanged, and determined the intensity of the signal-to-noise ratio (hereinafter referred to as the S/N ratio), with the “signal” represented by the variance of the coherent variations of the different simulations subject to the same atmospheric variability and the noise represented by the intra-ensemble variance. The S/N ratio was determined for depth-averaged velocities, surface temperature, and surface salinity. The first result was that in all three ensembles, noise emerged but with different intensities. In the ensemble with tidal forcing, unprovoked variability emerged primarily at smaller scales. When the tides were weakened or turned off, the S/N ratios were reduced, more so in the Yellow Sea than in the Bohai. The increase in the S/N ratio was largest for large scales and for depth-averaged velocity. The reduction in tidal forcing resulted in an approximately 30% increase in S/N ratios in the Bohai at large scales. Thus, the absence of tidal forcing favored the emergence of increased unprovoked variability at large and medium scales but not at small scales. A hypothesis for explaining this scale-selective effect of tides, based on the stochastic climate model, is suggested.

Modeling of streamflow in a 30 km long reach spanning 5 years using OpenFOAM 5.x

Abstract. Developing accurate and efficient modeling techniques for streamflow at the tens-of-kilometers spatial scale and multi-year temporal scale is critical for evaluating and predicting the impact of climate- and human-induced discharge variations on river hydrodynamics. However, achieving such a goal is challenging because of limited surveys of streambed hydraulic roughness, uncertain boundary condition specifications, and high computational costs. We demonstrate that accurate and efficient three-dimensional (3-D) hydrodynamic modeling of natural rivers at 30 km and 5-year scales is feasible using the following three techniques within OpenFOAM, an open-source computational fluid dynamics platform: (1) generating a distributed hydraulic roughness field for the streambed by integrating water-stage observation data, a rough wall theory, and a local roughness optimization and adjustment strategy; (2) prescribing the boundary condition for the inflow and outflow by integrating precomputed results of a one-dimensional (1-D) hydraulic model with the 3-D model; and (3) reducing computational time using multiple parallel runs constrained by 1-D inflow and outflow boundary conditions. Streamflow modeling for a 30 km long reach in the Columbia River (CR) over 58 months can be achieved in less than 6 d using 1.1 million CPU hours. The mean error between the modeled and the observed water stages for our simulated CR reach ranges from −16 to 9 cm (equivalent to approximately ±7 % relative to the average water depth) at seven locations during most of the years between 2011 and 2019. We can reproduce the velocity distribution measured by the acoustic Doppler current profiler (ADCP). The correlation coefficients of the depth-averaged velocity between the model and ADCP measurements are in the range between 0.71 and 0.83 at 75 % of the survey cross sections. With the validated model, we further show that the relative importance of dynamic pressure versus hydrostatic pressure varies with discharge variations and topography heterogeneity. Given the model's high accuracy and computational efficiency, the model framework provides a generic approach to evaluate and predict the impacts of climate- and human-induced discharge variations on river hydrodynamics at tens-of-kilometers and decadal scales.

Flow Characteristics Investigation On Trapezoidal Weir Using FLOW 3D

Weir is a building that is formed to change the nature of river flow to accommodate irrigation needs. The main purpose of a weir is to raise the river water level, drain the channel through the intake channel, allow water to be tapped, control all flow, etc. If a flow experiences a large shock, it will cause a hydraulic jump resulting in a transition of flow from supercritical to subcritical. The analysis can be performed, it was done using the Computational Fluids Dynamics (CFD) software, FLOW-3D. To model the 3-D weir used in this FLOW-3d, AutoCAD is used and finally, Flow Sight will be used to display visualization results such as graphics and videos. This paper investigates the Froude number and depth-averaged velocity on the trapezoidal weir. Moreover, the numerical modelling of trapezoidal weirs has been compared with the experimental result and numerical modelling of other types of weirs. The results show that the Froude number is proportional to the average velocity of this depth because the Froude number increases with the increase in the average velocity. There is a difference with the flow that flows after the weir, in a trapezoidal weir the Froude number decrease slightly but after that, it increases again downstream.

Macrocystis pyrifera forest development shapes the physical environment through current velocity reduction

Marine forests of the giant kelp Macrocystis pyrifera create biogenic habitat spanning the water column, within which hydrodynamic conditions can differ strongly from those outside. Such flow alteration has implications for physical, chemical, and ecological processes across multiple spatial scales. At the forest-wide scale, M. pyrifera has been shown to decrease alongshore current velocities, but relatively little is known about how the attenuation of such currents evolves as new kelp forests emerge and mature. Here, we quantified alongshore current velocities outside and within a temperate rocky reef environment that twice underwent a transition from a barren state to one in which a thick surface canopy was present. We identified a threshold density during forest emergence at which much of the attenuation of alongshore depth-averaged velocity occurs—3 stipes m-2 with a surface canopy present. Incremental increases in damping occur as the forest matures, highlighting that relatively young, thin forests can induce substantially reduced flows. Additionally, the presence of a young forest’s subsurface canopy and its subsequent increase in height create a seasonally changing profile of varying velocities through the water column. These results indicate greater complexity in how canopy-forming kelp influence nearshore flow properties than has often been recognized. Importantly, emerging forests can alter the nearshore environment through modulation of current speeds shortly following initial recruitment, with consequences for the transport of larvae, nutrients, and sediment throughout the forest and adjacent habitats.

Prediction of river discharges at confluences based on Entropy theory and surface-velocity measurements

Hydrodynamic features of the confluence zone of large rivers are complicated because of their three-dimensional flow structure. The confluence between the Rio Negro and the Rio Solimões, characterised by black and white waters, respectively, ranks among the largest river junctions on Earth. An Entropy-based investigation was carried out to assess the discharge and analyse the 2D structure of velocity distribution for large river flows relying on monitoring of near-surface velocity only. The estimated flow data where compared with in-situ ADCP data gathered across some transects of the Negro and Solimões rivers during both low and relatively high flow conditions. Results are illustrated through some transects at the confluence zone, upstream and downstream of the zone and in the Careiro Channel. Comparisons highlight that the Entropy-based flow velocity in terms of depth-averaged velocity, cross-sectional mean flow velocity and vertical velocity distributions, starting from the measured surface velocity, is in agreement with those determined by the ADCP measurements, with an error in mean flow velocity and discharge lower than 15%. The research highlights the potential of the Entropy method to estimate the discharge and velocity in very large rivers just relying on near-surface velocities monitoring.

Sensitivity of Surface Currents to Bathymetry in a Partially Mixed Estuary with Applications to Inverse Modeling

Abstract An inversion technique was tested for estimating bathymetry from observations of surface currents in a partially mixed estuary, the mouth of the Columbia River (MCR). The methodology uses an iterative ensemble-based assimilation scheme, which is found to have good skill for recovering bathymetry from observations distributed in space and time. However, the inversion skill is highly dependent on the tidal phase, location of the observations, and flow-dependent estuary dynamics. Inversion skill was found to degrade during periods of higher river discharge (up to ∼12 000 m3), or low tidal amplitude, while inversion of depth-averaged velocities instead of surface velocities caused increased skill throughout the domain. These results point to dynamical limits on inversion skill, caused by changes in estuary dynamics that affect the sensitivity of surface velocities to bathymetry. An adjoint sensitivity analysis is used to visualize these effects and is combined with data-denial experiments to explore the flow-dependent inversion skill.

Estimating Water Transport from Short-Term Vessel-Based and Long-Term Bottom-Mounted Acoustic Doppler Current Profiler Measurements in an Arctic Lagoon Connected to the Beaufort Sea.

Acoustic Doppler current profilers (ADCP) are quasi-remote sensing instruments widely used in oceanography to measure velocity profiles continuously. One of the applications is the quantification of land–ocean exchange, which plays a key role in the global cycling of water, heat, and materials. This exchange mostly occurs through estuaries, lagoons, and bays. Studies on the subject thus require that observations of total volume or mass transport can be achieved. Alternatively, numerical modeling is needed for the computation of transport, which, however, also requires that the model is validated properly. Since flows across an estuary, lagoon, or bay are usually non-uniform and point measurements will not be sufficient, continuous measurements across a transect are desired but cannot be performed in the long run due to budget constraints. In this paper, we use a combination of short-term transect-based measurements from a vessel-mounted ADCP and relatively long-term point measurements from a moored ADCP at the bottom to obtain regression coefficients between the transport from the vessel-based observations and the depth-averaged velocity from the bottom-based observations. The method is applied to an Arctic lagoon by using an ADCP mounted on a buoyant platform towed by a small inflatable vessel and another ADCP mounted on a bottom deployed metal frame. The vessel-based measurements were performed continuously for nearly 5 h, which was sufficient to derive a linear regression between the datasets with an R2-value of 0.89. The regression coefficients were in turn applied to the entire time for the moored instrument measurements, which are used in the interpretation of the subtidal transport variations.

Effect of Clearwater Scour on the Flow Field at a Single Bendway Weir: Two-Dimensional Numerical Modeling Supported by Flume Data

This study used two-dimensional (2D or depth-average) numerical modeling to examine the effects of clearwater scour on the flow field at a single bendway weir (BW) set at angles of 30°, 60°, and 90° pointing into the approach flow. The flow field was characterized in terms of depth-average velocity (location and magnitude) through the contraction formed around the BW and was supported by data and observations obtained from large and small flumes. In addition, a three-dimensional (3D) model was used to assess when a 2D model is of design use and when it is not. The 2D modeling showed that, when the ratio of flow depth (about four BW lengths upstream) to BW height (Y∶H) equaled 2.0, the differences (pre- and post-scour) in depth-average velocity magnitude and location of flow around the BW were fairly negligible for all orientations of the BW. However, when Y∶H equaled 1.25, the effects of the scour on the flow field were more prominent. Similar results were obtained for all three orientations of the BW. The value of Vmax obtained with the 2D model was closer to that measured in the large flume when Y∶H decreased from 2.0 to 1.25. This was due to the shallower flow’s greater effect in directing the flow around the BW than occurred for the deeper flow, in which flow had a larger vertical component of velocity when passing over the top of the BW. The practical implications of using a 2D model versus a 3D model were briefly assessed, and 2D models were found to be suitable for designing BWs to manage thalweg position but inadequate for estimating near-bank velocities.

Spatial and temporal variation of salinity stratification in a tropical estuary

Longitudinal and vertical distribution of salinity field in the Vellar River Estuary (VRE) was investigated across the lower, mid and upper estuarine zone, monthly from January to December 2011. The hydrological survey of VRE revealed shallow bathymetry with a complex topography and a mean tidal amplitude of around 0.9 to 1 m. The depth-averaged tidal velocity had a magnitude that was observed with a maximum value of 0.56 m/s at the estuarine mouth and was indirectly proportional to the increasing distance from the mouth. The wind speed fluctuated from 1 to 4.1 km h-1 with a mean of 2.5±0.82 km h-1. The temperature ranged from 25.32 °C to 32.93 °C with a mean of 28.89±2.26 °C while salinity varied between 0 to 34 psu with a mean of 13±12.77 psu and negatively correlated with rainfall (r = -0.69; p = 0.04). A higher stratification number, i.e. ns ~ 1 at the lower estuarine zone indicated the formation of the salt wedge in the monsoon while during the rest of the year the estuarine water column was observed to be homogeneous. Wave height, tide and currents were estimated through 2D hydrodynamic models and they were significantly correlated with in-situ data. Recorded seasonal variation in salinity stratification of VRE from the present work reflected on shaping the primary governing factors on estuarine circulation at spatial and temporal scales.

An observational study of hydrodynamic impact on water mass transport due to tidal power generation

The world's largest Sihwa Tidal Power Plant (TPP), located on the west coast of Korea, was built in 2011 for the purpose of improving water quality and producing renewable energy. After several years of actual operation, most of the original purpose was achieved, but unexpected coastal environmental changes such as tidal flat damage and sediment accumulation also occurred. In this study, in order to understand the causes of these environmental changes, field observations were conducted near TPP, and spatial and temporal variability of flow structure and water exchange process were investigated. Three-dimensional velocity data were collected along the closed line surrounding the outside of the TPP for 11 h during spring tide and analyzed according to two discharge phases: power generation phase (PGP) and drainage phase (DP). The results show that the depth-averaged maximum current velocity was more than three times greater at DP than at PGP. Jet-like flow during DP caused very high horizontal shear, whereas vertical shear was relatively weak, indicating that the horizontal and vertical flow structures were very different. The most notable result is that the mass transport patterns between PGP and DP are significantly different, i.e., during PGP, mass transport is dominated on the left side of the TPP, whereas during DP, it occurs at the front of the TPP. This means that there is a strong spatiotemporal asymmetry between the inflow from the downstream (outside of the TPP) during PGP and the outflow from the upstream (inside of the TPP) during DP. These asymmetric processes can have a significant impact on the material exchange and sediment transport near the TPP. Since observational studies on TPP are extremely rare, this study is expected to contribute to future TPP related research, such as numerical modeling.

Effect of water depth on Kelvin–Helmholtz instability in a shallow water flow

It is well known that the interface between two regions of an incompressible ideal fluid flow moving in a relative motion is necessarily destabilized, regardless of the velocity difference’s strength. This phenomenon is the so-called Kelvin–Helmholtz instability. However, a large number of works demonstrated a surprising result that the instability is suppressed for shallow water flows; the interface is stabilized if the Froude number, defined by the velocity difference’s ratio to the gravity wave’s speed, is sufficiently large. In a limited way, these authors used the shallow water equations without the higher-order effect of the dispersive terms. Thus, this investigation aims at examining these higher-order dispersive effects to analyze the interface stability problem of tangential-velocity discontinuity in shallow water flows. In particular, we use the Green–Naghdi equations to introduce the dispersive terms related to the depth and the depth-averaged horizontal velocities of the fluid. We show that the interface stability depends on the Froude number (i.e., the velocity difference’s strength) and the water depth. A critical value of the Froude number to stabilize the interface is smaller than the case of no dispersive terms, and the flow in a deeper region is more stable than in a shallower one. We also consider the distribution of kinetic and potential energy to clarify a feature characteristic of a large class of instabilities in shallow water flow. The instability of flows is caused by the decrease in the kinetic energy during the perturbation of waves. This phenomenon is known as negative energy modes and plays a vital role in applying the model to industrial equipment. A conclusion is that the equipartition of energies occurs if and only if the velocity difference is zero and the water depth is shallow enough to ignore the dispersive terms.

Migration of buoyancy-controlled active particles in a laminar open-channel flow

The migration of active particles in a laminar open-channel flow is significant for many ecological and biological processes associated with ambient water, for example, the harmful algae blooms in the long-distance water conveyance project. This paper presents an analytical analysis of the migration of the buoyancy-controlled active particles in a laminar open-channel flow. The analytical solution of concentration distribution has also been derived for the active particle cloud in the laminar open-channel flow under the combined action of ambient flow and self-migration of active particles, by combing Chatwin’s long-time asymptotic expansion and central concentration moments. The analytical solution shows that the active particle cloud accumulates near the surface rather than uniform distribution in the cross-section even for the long-time evolution. The analytical solutions are also been rigorously derived to reflect the holistic characteristics of the active-particle cloud, including the total quantity over each streamline, moving velocity of mass center, longitudinal dispersivity, skewness, and kurtosis have been rigorously derived for an instantaneous point source in a laminar open-channel flow. It is found that the distribution of total active particles over each streamline, centroid motion, and longitudinal dispersion eventually reach a stable status with a necessary time dependent on the relative strength of the vertical migration velocity and the total vertical diffusion. However, the self-migration of active particles results in the deviation of the moving velocity of mass center from the depth-averaged flow velocity. The longitudinal dispersivity of the active particle cloud gradually increases to the peak and then decreases to a constant value, in contrast to the monotonous increase for the passive particle cloud. It is also found that the strong vertical self-migration can result in changes of skewness and kurtosis of concentration distribution: negative skewness and positive kurtosis during the initial stage. However, both of them gradually tend to zero for the long-time evolution of the active particle cloud.

Novel Method for the Estimation of Vertical Temperature Profiles Using a Coastal Acoustic Tomography System

Systems based on remote sensing technology, which use reciprocal acoustic signals to continuously monitor changes in the coastal oceanic environment, are referred to as coastal acoustic tomography (CAT) systems. These systems have been applied in regions in which heavy ship traffics, fishing and marine aquaculture activities make it difficult to establish in situ oceanic sensor moorings. Conventionally, CAT measurements were used to successfully produce horizontal maps of the depth-averaged current velocity and temperature in these coastal regions without attempting to produce a vertical temperature profile. This prompted us to propose a new method for vertical temperature profile estimation (VTPE) from CAT data using the available sea surface temperature (SST), near-bottom temperature (NBT), and water depth. The VTPE method was validated using data-assimilated and tide-included high-resolution ocean model outputs, including tide data, by comparing the estimated and simulated temperatures. Measurements were performed in the southern coastal region of Korea, where two CAT stations were moored to establish a continuous coastal ocean monitoring system. The validation results revealed that the algorithm performed well across all seasons. Sensitivity tests of the VTPE method with reasonable realistic random errors in the SST, NBT, and acoustic travel time measurements demonstrate that the method is applicable to CAT observation data because the monthly mean root-mean-squared difference (RMSD) for the vertical profiles for February, May, August, and November were 0.23, 0.30, 0.50, and 0.24°C, respectively. The VTPE method was applied to the CAT observation datasets acquired in February and August. The transceivers at the CAT stations were at depths 11 and 6 m on average. The RMSD between the estimated and observed temperatures in the middle layer (∼3 m depth) between two stations in February and August were 0.08 and 0.60°C, respectively, the accuracy of which is sufficient in largely time-varying coastal environments. We provide a novel method for continuous coastal subsurface environmental monitoring without interrupting maritime traffic, fishing, and marine aquaculture activities.

Impact of the porosity of an urban block on the flood risk assessment: A laboratory experiment

Physical modelling of urban flooding usually considers that the flow is concentrated in the streets, assuming that urban blocks and individual buildings are non-porous structures. This assumption is open to criticism, as potential lateral flow exchanges through openings in the walls of an urban block (e.g. gates, windows and doors) are likely to modify the flow pattern in the block and adjacent streets. This paper reports an experimental study conducted on a 5.4 m long and 3.2 m wide physical model, representing a rectangular urban block and four surrounding streets. The focus of the study was on investigating the lateral flow exchange processes between the porous urban block and its adjacent streets during flooding, for a variable urban block porosity. Eight porosity values were studied, keeping the same boundary conditions. A porosity equals zero, i.e. a flow around a non-porous block, served as a reference flow situation. For each porosity value, the impact of the lateral flow exchanges on the spatial distribution of flow depth and velocity in the streets and within the block was assessed, as well as the risk to pedestrians. First, it was found that, in the streets surrounding the block, flow depth and depth-averaged velocity can vary by 12% and 70%, respectively, when modifying block porosity. Within the block, the most impacted flow parameter is the number and size of horizontal secondary flow cells. Second, noticeable differences in flow depth can be observed from either side of an opening between street and block. Third, when moving away from the block, flow parameters are little affected. Last, the risk to pedestrians, which is both related to local flow depth and velocity, is dependent on the block porosity value.

Method for predicting depth-averaged current velocities of underwater gliders based on data feature analysis

In this paper, the data feature of depth-averaged current velocities (DACVs) derived from underwater gliders is analyzed for the first time. Two features of DACVs have been proposed: one is the complex ingredients and small samples, and the other is the stationarity that occurs as the length of a DACV sequence increases. With these features in mind, a set of methods combining statistical analysis and machine learning are proposed to realize the prediction of DACVs. Four groups of DACV data of different gliders from sea trials in the South China Sea are used to verify the prediction method. Based on three general error criteria, the prediction performance of the proposed model is demonstrated. The persistence method is used as a comparison model. The results show that the prediction methods proposed in this paper are effective.

Estimating current-related bed shear stresses during flooding phase on intertidal flats from measured water depths

Current-related bed shear stress is vital for the prediction of the morphological evolution of intertidal flats. The present study develops a simple method to estimate the current-related bed shear stress during the flood phase on intertidal flats, which is based on the easy-to-measure water depth. To verify this simple method, comparisons were made to the current-related shear stress derived from both the LP and the TKE methods based on the measured velocities. The results show that the widely used approach on intertidal flats, which relates the current-related bed shear stress to the square of the depth-averaged velocity with a constant factor, underestimates the bed shear stress for water depths smaller than ca. 0.5 m when high sediment concentrations and significant bed-level changes however usually occur. For water depths smaller than approximately 0.5 m, the uniform horizontal velocity assumption in the vertical direction in the shallow water theory is inappropriate, and velocity shear must be considered. The current-related bed shear stresses could be estimated using the measured water depths during flood phase, even when the water depth is smaller than 0.5 m. The developed method also shows that the scale of current-related shear stress is u‾/h, not u‾2, at least with a water depth smaller than 0.5 m.

An integrated marine data collection for the German Bight – Part 2: Tides, salinity, and waves (1996–2015)

Abstract. Marine spatial planning requires reliable data for, e.g., the design of coastal structures, research, or sea level rise adaptation. This task is particularly ambiguous in the German Bight (North Sea, Europe) because a compromise must be found between economic interests and biodiversity since the environmental status is monitored closely by the European Union. For this reason, we have set up an open-access, integrated marine data collection for the period from 1996 to 2015. It provides bathymetry, surface sediments, tidal dynamics, salinity, and waves for the German Bight and is of interest to stakeholders in science, government, and the economy. This part of a two-part publication presents data from numerical hindcast simulations for sea surface elevation, depth-averaged current velocity, bottom shear stress, depth-averaged salinity, wave parameters, and wave spectra. As an improvement to existing data collections, our data represent the variability in the bathymetry by using annually updated model topographies. Moreover, we provide data at a high temporal and spatial resolution (Hagen et al., 2020b); i.e., numerical model results are gridded to 1000 m at 20 min intervals (https://doi.org/10.48437/02.2020.K2.7000.0004). Tidal characteristic values (Hagen et al., 2020a), such as tidal range or ebb current velocity, are computed based on numerical modeling results (https://doi.org/10.48437/02.2020.K2.7000.0003). Therefore, this integrated marine data collection supports the work of coastal stakeholders and scientists, which ranges from developing detailed coastal models to handling complex natural-habitat problems or designing coastal structures.