Huib J. de Vriend

Modelling shoreface profile evolution

Current knowledge of hydro-, sediment and morpho-dynamics in the shoreface environment is insufficient to undertake shoreface-profile evolution modelling on the basis of first physical principles. We propose a simple, panel-type model to map observed behaviour. The internal dynamics are determined by slope-dependent, wave-induced cross-shoreface transports, while the external driving factors are lateral sediment supply and sea-level rise. This model concept is tested with reasonable success against the observed behaviour of the Central Holland Coast, considering two hindcast periods, one covering the evolution over the last century, the other the Subboreal/Subatlantic evolution. A limitation of this model is that the cross-shoreface dynamics are solely steered by the variations of shoaling, short waves. Since a variety of other wave and current dynamics may be expected to be present in the coastal boundary layer, it may well be that the effects of the mechanisms and conditions which are not represented are hidden in the coefficients of the sediment-transport formula. This limits the accuracy of the coefficients as used, and our findings should be considered as an-order-of-magnitude estimate only. Indeed, behaviour-oriented modelling implies that generalization of results to arbitrary situations and conditions is not straightforward. Yet, we expect that some of the conclusions are more generally applicable. This concerns the substantiation of the assumption that the upper shoreface responds on a much smaller time scale than the lower shoreface, and the idea that the shoreface profile is not always and everywhere in equilibrium with its forcing. A worthwhile observation from the Holland Coast application is, that the bottom slope effect on the transport is only important at geological time scales. The profile evolution at the engineering time scales (say 10 to 100 years) is effectively quasi-static, in that there is no feedback between the long-term averaged transport and the state of the profile. This implies that at these smaller scales the profile changes can be predicted on the basis of a static sediment balance. This does not mean that the gravitational downslope transport is unimportant as a physical phenomenon in coastal profile evolution: It is only unimportant if a highly aggregated model like this is applied at relatively short time scales.

The generation of offshore tidal sand banks and sand waves

A simple morphological model is considered which describes the interaction between a tidal flow and an erodible bed in a shallow sea. The basic state of this model describes a spatially uniform tide over a flat bottom where the flow vector is represented as a tidal ellipse. The linear stability of this solution is analysed with respect to bed form perturbations. Results are presented for both a uni-directional and circular tide. In the former case the wave-length and the orientation of the fastest growing bed mode agree well with those of tidal sand banks. However, this model only predicts the growth of large-scale sand ridges. With a simplified numerical model we tentatively show that the effects of secondary currents on the sediment transport trigger the formation of instabilities at an essentially smaller scale, viz, sand waves. Another limitation of a model with uni-directional tides is that no selective modes found are the first to become unstable if the model parameters are varied. In the case of a circular tide, critical model parameters are found below which the basic state is stable. We conclude that this provides a starting point for the development of a weakly non-linear analysis, which will yield information on the amplitude behaviour of marginally growing bed forms.

Modeling of channel patterns in short tidal basins

We model branching channel patterns in short tidal basins with two methods. A theoretical stability analysis leads to a relationship between the number of channels and physical parameters of the tidal system. The analysis reveals that width and spacing of the channels should decrease as the slope of the bottom profile and the Shields parameter increase and as the mean water depth decreases. In general, the channel depth should halve at every bifurcation. These theoretical results agree well with the field data from the Dutch Wadden Sea. A numerical model based on Delft3D, a software system of WL/Delft Hydraulics, is used to simulate the time evolution of a channel network in a geometrically simplified basin of similar dimensions as the Wadden Sea basins. The resulting channel network displays a three-times branching behavior, similar to the three- to four-times branching patterns observed in the Wadden Sea. The simulated channel pattern satisfies the relation derived from the theoretical analysis. The results of this pattern analysis provide for additional validation of two-dimensional/three-dimensional process-based morphodynamic models of tidal basins.

Modelling sand wave migration in shallow shelf seas

Sand waves form a prominent regular pattern in the offshore seabed of sandy shallow seas. The positions of sand-wave crests and troughs slowly change in time. Sand waves are usually assumed to migrate in the direction of the residual current. This paper considers the physical mechanisms that may cause sand waves to migrate and methods to quantify the associated migration rates. We carried out a theoretical study based on the assumption that sand waves evolve as free instabilities of the system. A linear stability analysis was then performed on a 2DV morphological model describing the interaction between the vertically varying water motion and an erodible bed in a shallow sea. Here, we disrupted the basic tidal symmetry by choosing a combination of a steady current (M0) and a sinusoidal tidal motion (M2) as the basic flow. We allowed for two different physical mechanisms to generate the steady current: a sea surface wind stress and a pressure gradient. The results show that similar sand waves develop for both flow conditions and that these sand waves migrate slowly in the direction of the residual flow. The rates of migration and wavelengths found in this work agree with theoretical and empirical values reported in the literature.

Vertical sorting in bed forms: Flume experiments with a natural and a trimodal sediment mixture

Two sets of flume experiments were conducted to examine grain size selective transport and vertical sorting in conditions with migrating bed forms and bed load transport. In the two sets of experiments we used a sediment mixture from the river Rhine and a trimodal mixture, respectively. The vertical sorting profiles showed a downward coarsening trend within the bed forms, and in some experiments an essentially immobile coarse bed layer formed underneath the migrating bed forms. Three mechanisms contribute to the formation of such a coarse bed layer: (1) the avalanching process at the lee face, (2) conditions of partial transport in which a relatively large amount of coarse material does not participate in the transport process, and (3) the winnowing of fines from the trough surface and subsurface. The experiments show that vertical sorting fluxes not only occur through net degradation or aggradation but also through the migration of bed forms and through the variability in trough elevations. This is contradictory to the way vertical sorting processes are modeled in most existing sediment continuity models for nonuniform sediment. The present study is therefore also a plea for modifying existing sediment continuity models to account for vertical sorting processes other than through net aggradation or degradation.

SHEAR STRESSES AND MEAN FLOW IN SHOALING AND BREAKING WAVES

A special reflecting wall 12 m long and 2.1 m high was built off the beach at Reggio Calabria, and 30 wave gauges were assembled before the wall and were connected to an electronic station on land. It was possible to observe the reflection of wind waves generated by a very stable wind over a fetch of 10 Km. The experiment aimed to verify the general closed solution for the wave group mechanics (Boccotti, 1988, 1989), for the special case of the wave reflection.Significant features on Wadden Sea wave climate are evaluated in respect of the state of the art. Main emphasis was laid on an analysis of the governing boundary conditions of local wave climate in island sheltered Wadden Sea areas with extensions being sufficient for local wind wave growth. Explanatory for significant wave heights a reliable parametrization of local wave climate has been evaluated by using generally available data of water level and wind measurements.

A new type of sea bed waves

Sandy beds of shallow tidal seas often exhibit a range of rhythmic patterns, from small‐scale ripples a few metres long to large tidal sandbanks with a wavelength of kilometres. For example, on the access route to Rotterdam harbour ships cross a field of sandwaves. The crests of these sandwaves determine the effective navigation depth. To warrant navigability, the North Sea Directorate of the Netherlands Ministry of Transport, Public Works and Water Management continually monitors the bathymetry in the sandwave area, originally using echo sounding. Our analysis of these data has revealed a new rhythmic pattern, in addition to the well‐known sandwaves and tidal sandbanks. The wavelength of this new pattern, labelled here as long bedwaves, is three times the one of sandwaves, and the crest orientation is different. Interference of the three modes leads to the rather complex bathymetry revealed by echo soundings.

Vertical sorting and the morphodynamics of bed-form-dominated rivers: an equilibrium sorting model

A modeling framework is developed for taking into account the effects of sediment sorting in the morphodynamic modeling of bed-form-dominated rivers for the case of equilibrium or stationary conditions dominated by bed load transport. To this end, the Blom and Parker (2004) framework for sediment continuity is reduced to an equilibrium sorting model. The predicted equilibrium sorting profile is mainly determined by the probability density function (PDF) of bed form trough elevations and by a lee sorting function. The PDF of trough elevations needs to be known from either model predictions or measurements. A simple formulation for the lee sorting function is suggested, yet data on the avalanche mechanism down lee faces of dunes is required so as to improve the function and make it generic. The equilibrium sorting model is calibrated and verified using data from flume experiments. The agreement between the predicted and measured equilibrium sorting profiles is reasonable, although the model does not reproduce an observed coarse top layer. In a hydraulic-morphodynamic model this equilibrium sorting model may be applied instantaneously if the timescale of large-scale morphological changes is much larger than the ones of changes in vertical sorting and dune dimensions.

Sediment Exchange between a River and Its Groyne Fields: Mobile-Bed Experiment

Experiments have been carried out in a mobile-bed laboratory flume in order to study the sediment exchange process between the main channel and the groyne fields. The flume represented half the width of a schematized river reach with a series of groynes. The experiment was designed to represent typical dimensions of the Dutch River Waal at a geometrical scale of 1:100. The conditions were set to guarantee bed load as well as suspended load sediment transport. Conditions with submerged and emerged groynes were investigated. In addition to traditional measurements, viz., bed-level changes, suspended sediment concentrations, and flow velocities, bed-form propagation was measured in two dimensions using a the particle image velocimetry technique. The results were analyzed with focus on sediment exchange mechanisms and sediment transport patterns. The results demonstrate that under all flow conditions there is a net import of sediment into the groyne fields. The prevailing transport mechanisms vary with the fl...

Flow Details near River Groynes: Experimental Investigation

Experiments have been carried out in a fixed-bed flume for a schematized straight river reach with groynes on one side to study the dynamics of the flow near groynes. The flume had a geometrical scale of 1:40, based on typical dimensions of the Dutch River Waal. Both emergent and submerged groynes were studied. The measurements demonstrate the differences in the nature of the turbulence between submerged and emerged groynes stages; and provide insight into the flow pattern in the vicinity of groynes, the shape and the extent of the mixing layer at different flow stages, and the dynamic behavior of the velocity along the mixing layer between the main channel and the groyne fields. A parameterization of the turbulence characteristics of the flow near groynes is presented. Large-scale velocity fluctuations are found in all test cases, with timescales that vary with the flow stage. The large-scale u and v velocity fluctuations are in phase in the center of the mixing layer and out of phase for the points on the boundaries of the mixing layer.