B.C. van Prooijen

A stochastic formulation for erosion of cohesive sediments

The linear formulation for erosion E = M(?b??c), often applied in engineering applications, has two properties, which do not always comply with field and laboratory observations, they are as follows: (1) The erosion rate is zero below the critical bed shear stress ?c and increases linearly with bed shear stress ?b, when exceeding the critical bed shear stress; incipient motion (?b

A conceptual framework for shear flow–induced erosion of soft cohesive sediment beds

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Observations and modeling of steep-beach grain-size variability

?c) is poorly represented. (2) The erosion rate is constant in time for constant values of M and ?c, whereas observations often suggest time dependency. In this paper we analyze the process of incipient motion and time dependency by using a stochastic forcing (bed shear stress) and a stochastic bed strength (critical bed shear stress). It is well known that the bed shear stress is not constant but varies due to turbulence. This stochastic nature of the turbulent motion is accounted for by a probability density distribution for the bed shear stress, which is based on the formulation of Hofland and Battjes (2006). This distribution is implemented in the linear erosion formulation. An analytical solution for the erosion rate is obtained, which only depends on the mean bed shear stress. A parametrization is made for efficient application in numerical models. The sediment in the bed is considered to be nonuniform. Therefore, it is subdivided into several classes, distinguished by the critical bed shear stress and not necessarily by the grain size. The variability of the critical bed shear stress is treated in a discritized way. Sediment balance equations are solved for each class. Considering different classes, the total erosion rate becomes time dependent, as the erosion depends on the availability of sediment. The model is applied to two annular flume data sets, Jacobs (2009) and Amos et al. (1992a). The results show that with a proper choice of the required parameters, the time dependence of the erosion rate and the concentration can be reproduced. We conclude that the occurrence of incipient motion can be explained from a stochastic forcing. Time?varying erosion rates can be explained from a stochastic bed strength distribution or from a vertical gradient in bed strength. The latter is, however, not likely and not measurable in the top layers of dense consolidated cohesive sediment beds.

Do intertidal flats ever reach equilibrium

This paper proposes a conceptual framework for erosion of cohesive sediment beds. We focus on cohesive beds, distinguishing between floc erosion, surface erosion, and mass erosion. By (our) definition, surface erosion is a drained soil mechanical process, whereas mass erosion occurs under undrained conditions. The eroding shear stress is modeled through a probability density function. This yields a continuous description of floc erosion and surface erosion as a function of mean bed shear stress. Furthermore, we assume a distribution for the bed strength. The mean values of the bed strength are derived from soil mechanical theory, assuming that the surface erosion rate is limited by the swelling rate from the undrained shear strength in the bed to its drained value at its surface. The rate of erosion then relates to the undrained shear strength of the soil, and its consolidation (swelling) coefficient. The critical shear stress for erosion is slightly larger than the true cohesion of the bed, i.e., the drained strength, and follows a power law relation with the plasticity index. The conceptual framework proposed herein has been validated against a limited number of experimental data, and has a series of advantages above other methods of direct measuring erodibility, as it is inexpensive and can be used to attain space-covering information on the sediment bed. Moreover, the use of bulk soil mechanical parameters accounts implicitly for the effects of organic material, though the role of, e.g., macrophytobenthos mats and/or bioturbation is difficult to capture a priori.

Movement of tidal watersheds in the Wadden Sea and its consequences on the morphological development

Novel observations of surface grain-size distributions are used in combination with intra-wave modeling to examine the processes responsible for the sorting of sediment grains on a relatively steep beach (slope?=?1:7.5). The field observations of the mean grain size collected with a digital camera system at consecutive low and high tides for a 2 week period show significant temporal and spatial variation. This variation is reproduced by the modeling approach when the surf zone flow-circulation is relatively weak, showing coarse grain sizes at the location of the shore break and finer sediment onshore and offshore of the shore break. The model results suggest that grain size sorting is dominated by the wave-breaking-related suspended sediment transport which removes finer sediment from the shore break and transports it both on-shore and offshore. The transport capacity of wave-breaking-related suspended sediment is controlled by the sediment response time scale in the advection-diffusion equation, where small (large) values promote onshore (offshore) transport. Comparisons with the observed beach profile evolution suggest a relatively short time scale for the suspended sediment response which could be explained by the vigorous breaking of the waves at the shore break.

BAROTROPIC PROCESSES OF SEDIMENT TRANSPORT IN TIDAL BASINS: A 1D MODEL FOR THE WADDEN SEA

Various studies have identified a strong relation between the hydrodynamic forces and the equilibrium profile for intertidal flats. A thorough understanding of the interplay between the hydrodynamic forces and the morphology, however, concerns more than the equilibrium state alone. We study the basic processes and feedback mechanisms underlying the long-term behavior of the intertidal system, restricting ourselves to unvegetated intertidal flats that are controlled by cross-shore tidal currents and wind waves and applying a 1-D cross-shore morphodynamic model. The results indicate that by an adjustment of the profile slope and shape, an initial imbalance between deposition and erosion is minimized within a few decades. What follows is a state of long-term seaward progradation or landward retreat of the intertidal flat, in which the cross-shore profile shape is largely maintained and the imbalance between deposition and erosion is not further reduced. These long-term trends can be explained by positive feedbacks from the morphology onto the hydrodynamic forces over the flat: initial accretion (erosion) decreases (increases) the shear stresses over the flat, which induces further accretion (erosion). This implies that a static equilibrium state cannot exist; the flat either builds out or retreats. The modeled behavior is in accordance with observations in the Yangtze Estuary. To treat these unbalanced systems with a one-dimensional numerical model, we propose a moving (Lagrangian) framework in which a stable cross-sectional shape and progradation speed can be derived for growing tidal flats, as a function of the wave climate and the sediment concentration in deeper water.

Simulating the large-scale spatial sand-mud distribution in a schematized process-based tidal inlet system model

Abstract The Wadden Sea consists of a series of tidal lagoons which are connected to the North Sea by tidal inlets. Boundaries of each lagoon are the mainland coast, the barrier islands on both sides of the tidal inlet, and the tidal watersheds behind the two barrier islands. Behind each Wadden Island there is a tidal watershed separating two adjacent tidal lagoons. The locations of the tidal watersheds in the Wadden Sea are not fixed. Especially after a human interference in one of the tidal lagoons, a tidal watershed can move and thereby influence the distribution of area between the lagoons. This appears to be important for the morphological development in not only the basin in which the interference takes place, but also in the adjacent basins. This paper describes theoretical analyses and numerical modelling aimed at improving the insights into the location of the tidal watersheds, their movements, and the impact of the movements of tidal watersheds on the morphological development of a multi-basin system like the Wadden Sea.

Human impacts on morphodynamic thresholds in estuarine systems

Morphodynamic research is crucial for preserving the Wadden Sea’s unique environment. Its morphological evolution is governed by several sediment transport mechanisms, but a ranking of their relative long-term impact has not yet been established. 3D process-based models are not feasible for such purpose, while idealized models suffer from oversimplifications. In order to bridge the two, we propose an intermediate approach that is particularly suited to investigate the barotropic mechanisms recognized in literature as possibly dominant. The residual fluxes of non-cohesive sediment in the Vlie basin are simulated over a semidiurnal timescale. Different conditions are mimicked by varying settling velocities and critical bed-shear stresses. Results suggest a possible state of grain-size-selective residual transport, on which the bed resistance to erosion has only little influence. Under an average wind condition, tidal asymmetry is recognized as the main sediment transport mechanism.

Bed shear stress estimation on an open intertidal flat using in situ measurements

Tidal basins, as found in the Dutch Wadden Sea, are characterized by strong spatial variations in bathymetry and sediment distribution. In this contribution, the aim is at simulating the spatial sand-mud distribution of a tidal basin. Predicting this spatial distribution is however complicated, due to the non-linear interactions between tides, waves, sediment transport, morphology and biology. To reduce complexity, while increasing physical understanding, an idealized schematization of the Amelander inlet system is considered. Delft3D is applied with a recently developed bed module, containing various sediment layers, combined with formulations for both cohesive and non-cohesive sediment mixtures. Starting with uniform mud content in the spatial domain, the development of the sediment distribution is simulated. Realistic sand-mud patterns are found, with accumulation of mud on the tidal flats. The schematization is further used to determine the sensitivity of the sand-mud patterns to changes in tide, while assessing the influence of tidal dominance on the large-scale sand-mud patterns. The patterns are enhanced/diminished under the influence of higher/lower tides.