Suzanne J.M.H. Hulscher

Tidal‐induced large‐scale regular bed form patterns in a three‐dimensional shallow water model

The three-dimensional model presented in this paper is used to study how tidal currents form wave-like bottom patterns. Inclusion of vertical flow structure turns out to be necessary to describe the formation, or absence, of all known large-scale regular bottom features. The tide and topography are treated as a coupled system, and the potential free instabilities in this system are investigated. A linear stability analysis is used to study the dynamics of bed forms. This yields information on the role of physical mechanisms; such information cannot be obtained by direct numerical nonlinear simulation. The basic state represents a horizontal elliptical flow, veering in vertical direction, over a flat bottom. It is shown that in such a system, modes can grow which have characteristics of both tidal sand banks and sand waves. The model predictions are compared with observations and show good agreement.

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.

Analytical solution of the depth-averaged flow velocity in case of submerged rigid cylindrical vegetation

A new model for the depth-averaged velocity for flow in presence of submerged vegetation is developed. The model is based on a two-layer approach, where flow above and through the vegetation layer is described separately. Vegetation is treated as a homogeneous field of identical cylindrical stems, and the flow field is considered stationary and uniform. It is demonstrated that scaling considerations of the bulk flow field can be used to avoid complications associated with smaller scale flow processes and that still the behavior of depth-averaged flow over vegetation is described accurately. The derived scaling expression of the average flow field is simple in form, it follows fundamental laws of fluid flow, and it shows very good agreement with laboratory flume experiments. The new model can be used for quick evaluation of a river’s hydraulic response in cases where vegetated floodplains are inundated.

Quantification of variability in bedform geometry

We analyze the variability in bedform geometry in laboratory and field studies. Even under controlled steady flow conditions in laboratory flumes, bedforms are irregular in size, shape, and spacing, also in case of well-sorted sediment. Our purpose is to quantify the variability in bedform geometry. We use a bedform tracking tool to determine the geometric variables of the bedforms from measured bed elevation profiles. For each flume and field data set, we analyze variability in (1) bedform height, (2) bedform length, (3) crest elevation, (4) trough elevation, and (5) slope of the bedform lee face. Each of these stochastic variables is best described by a positively skewed probability density function such as the Weibull distribution. We find that, except for the lee face slope, the standard deviation of the geometric variable scales with its mean value as long as the ratio of width to hydraulic radius is sufficiently large. If the ratio of width to hydraulic radius is smaller than about ten, variability in bedform geometry is reduced. An exponential function is then proposed for the coefficients of variation of the five variables to get an estimate of variability in bedform geometry. We show that mean lee face slopes in flumes are significantly steeper than those in the field. The 95% and 98% values of the geometric variables appear to scale with their standard deviation. The above described simple relationships enable us to integrate variability in bedform geometry into engineering studies and models in a convenient way.

Comparison between predicted and observed sand waves and sand banks in the North Sea

For the first time a prediction model of regular morphological patterns on the seabed was tested against observations of sand wave and sand bank occurrence in the entire North Sea. The model, which originates from first physical principles, predicts this occurrence via two dimensionless parameters on the basis of the water depth, the tidal velocity amplitude, the level of zero intercept above the seabed (z0), and a viscosity variation parameter alt epsilon. The latter two quantities were varied in a number of predictions for the entire North Sea, whereas for the first two, local values were used. The range of realistic values of alt epsilon and z0 was large enough to let these two parameters distinguish between the possible (combinations of) bed forms, as is shown in the shallower southern bight of the North Sea. The results were more sensitive to variations in z0 than in alt epsilon. A slightly more detailed approach focused on sand waves only in the southern North Sea and estimated local values for z0 using depth information. Quantification of the results showed that the model was able to predict the contours of the sand wave patches, but it could not account for the absence of the bed features within this area. The type of bed deposit partly explains the smaller-scale variation. The work confirms the validity of the theoretical bed form prediction model and verifies the hypothesis that the large-scale seabed features are formed as free instabilities of tide-topography interactions.

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.

The cross-sectional shape of tidal sandbanks: modeling and observations

To improve our understanding of tidal sandbank dynamics, we have developed a nonlinear morphodynamic model. A crucial property of the model is that it fully resolves the dynamics on the fast (tidal) timescale, allowing for asymmetric tidal flow with an M0, M2, and M4 component. This approach, extending earlier research on the formation of tidal sandbanks, leads to equilibrium profiles. Their heights (60-90% of the water depth) and shapes are controlled by the mode of sediment transport and the hydrodynamic conditions. Bed load transport under symmetrical tidal conditions leads to high spiky banks. Several mechanisms tend to lower and smooth these profiles, such as the relaxation of suspended sediment, wind wave stirring, and tidal asymmetry. This last causes the profiles to be asymmetric, as well. The morphodynamic equilibrium expresses a tidally averaged balance between a destabilizing flux due to fluid drag and the downslope transport induced by both tidal flow and wind wave stirring. The modeled profiles are in fair agreement with observations from the North Sea.

Regeneration of sand waves after dredging

Sand waves are large bed waves on the seabed, being a few metres high and lying hundreds of metres apart. In some cases, these sand waves occur in navigation channels. If these sand waves reduce the water depth to an unacceptable level and hinder navigation, they need to be dredged. It has been observed in the Bisanseto Channel in Japan that the sand waves tend to regain their shape after dredging. In this paper, we address modelling of this regeneration of sand waves, aiming to predict this process. For this purpose, we combine a very simple, yet effective, amplitude-evolution model based on the Landau equation, with measurements in the Bisanseto Channel. The model parameters are tuned to the measured data using a genetic algorithm, a stochastic optimization routine. The results are good. The tuned model accurately reproduces the measured growth of the sand waves. The differences between the measured weave heights and the model results are smaller than the measurement noise. Furthermore, the resulting parameters are surprisingly consistent, given the large variations in the sediment characteristics, the water depth and the flow field. This approach was tested on its predictive capacity using a synthetic test case. The model was tuned based on constructed predredging data and the amplitude evolution as measured for over 2 years. After tuning, the predictions were accurate for about 10 years. Thus, it is shown that the approach could be a useful tool in the optimization of dredging strategies in case of dredging of sand waves.

Linear instability mechanisms for sand wave formation

A height- and flow-dependent model for turbulent viscosity is employed to explain the generation of sand waves in tidal seas. This new model resolves the problem of excitation of very long waves in sand wave formation, because it leads to damping of the long waves and gives a finite separation between the most excited mode and the zero mode. For parameters within their physically realistic ranges, a linear analysis of the resulting system yields a first excited mode whose wavelength is similar to the characteristic wavelength of sand waves observed in nature. The physical mechanism of sand wave formation as predicted by the new model is explained in detail. The dispersion relation obtained can be the starting point for a weakly nonlinear analysis of the system.

Simulating and understanding sand wave variation: A case study of the Golden Gate sand waves

In this paper we present a detailed comparison between measured features of the Golden Gate sand wave field and the results of a nonlinear sand wave model. Because the Golden Gate sand waves exhibit large variation in their characteristics and in their environmental physics, this area gives us the opportunity to study sand wave variation between locations, within one well-measured, large area. The nonlinear model used in this paper is presently the only tool that provides information on the nonlinear evolution of large-amplitude sand waves. The model is used to increase our understanding of the coupling between the variability in environmental conditions and the sand wave characteristics. Results show that the model is able to describe the variation in the Golden Gate sand waves well when both the local oscillating tidal current and the residual current are taken into account. Current and water depth seem to be the most important factors influencing sand wave characteristics. The simulation results give further confidence in the underlying model hypothesis and assumptions.