Michiel Knaapen

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.

Sand wave migration predictor based on shape information

[1] Migration of offshore seabed waves, which endangers the stability of pipelines and communication cables, is hard to measure. The migration rates are small compared to the measurement errors. Here, sandwave migration rates are determined from the change in the crest position deduced from long time series of bathymetric echo-sounding data. The crests are identified as local extremes in a bathymetric profile, after low-pass filtering. This approach is applied to both two-dimensional data and to profiles along pipelines. A consistent migration rate of several meters per year is found. A strong correlation between the sandwave shape and the migration rate is translated in a migration predictor. The predictor assumes that the sandwaves migrate in the direction of the steepest slope, following a quadratic relation with the asymmetry. Furthermore, it is included that longer waves travel faster but higher waves travel slower. The predictor is calibrated against data from nine areas and validated using three additional areas. An error analysis using markers shows that the error of the predictor is small compared to the noise in the individual crest position observations.

Mathematical modelling of sand wave migration and the interaction with pipelines

A new method is presented for identifying potential pipeline problems, such as hazardous exposures. This method comprises a newly developed sand wave amplitude and migration model, and an existing pipeline–seabed interaction model. The sand wave migration model is based on physical principles and tuned with field data through data assimilation techniques. Due to its physical basis, this method is trusted to be more reliable than other, mostly engineering-based methods. The model describes and predicts the dynamics of sand waves and provides the necessary bed level input for the pipeline–seabed interaction model. The method was tested by performing a hindcast on the basis of survey data for a specific submarine gas pipeline, diameter 0.4 m, on the Dutch continental shelf. Good agreement was found with the observed seabed–pipeline levels. The applicability of the method was investigated further through a number of test cases. The self-lowering of the pipeline, in response to exposures due to sand wave migration, can be predicted, both effectively and efficiently. This allows the use of the method as a tool for pipeline operation, maintenance and abandonment.

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.

Use of a genetic algorithm to improve predictions of alternate bar dynamics

Alternate bars may form in sandy beds of straight rivers and channels. These bars are characterized by the alternation of crests, all moving downstream at a speed of several meters per day. The aim of this paper is to predict the dynamics of alternate bars. To that end, we tested predictions of measured alternate bars in flume experiments, as derived from an amplitude evolution model. Weakly nonlinear stability analysis underlies this amplitude evolution model, so that it applies to situations in which the width-to-depth ratio is close to the critical ratio, above which alternate bars occur. The experiments have a width-to-depth ratio far above the critical value, well outside the range of formal validity of the model. While wavelengths and heights of the alternate bars are still well predicted, we found that the migration rate is not: the amplitude evolution model produces an underestimation of close to a factor of two. Therefore we took a slightly different approach. We tested the predictive capability for this amplitude evolution model by using a genetic algorithm to tune the model to bathymetric data. After tuning, the model is indeed able to predict the migration rate of the bars over periods that exceed the tuning period by far. Limits to the prediction time, i.e., failure of this method, could not be derived for the data sets used in this work.

Height and wavelength of alternate bars in rivers : modelling vs . laboratory experiments

Alternate bars are large wave patterns in sandy beds of rivers and channels. The crests and troughs alternate between the banks of the channel. These bars, which move downstream several meters per day, reduce the navigability of the river. Recent modelling of alternate bars has focused on stability analysis techniques. We think, that the resulting models can predict large rhythmic patterns in sandy beds, especially if the models can be combined with data-assimilation techniques. The results presented in this paper confirm this thought. We compared the wavelength and height of alternatejjars as predicted by the model of Schielen et al. [14], with the values measured in several flume experiments. Given realistic hydraulic conditions > 2*103, (R the width-to-depth ratio and Re the Reynolds number), the predictions are in good agreement with the measurements. In addition, the model predicts the bars measured in experiments with graded sediment. If < 2*103, the agreement between model results and measurements is lost. The wave height is clearly underestimated, and the standard deviation of the differences between predictions and measurements increases. This questions the usefulness of small flume experiments for morphodynamic problems.

Predicting the regeneration of sand waves after dredging: an amplitude evolution model tuned by a genetic algorithm

To optimise the dredging of sand waves in navigation channels, it is important to predict the regeneration of the sand waves. For this purpose, the authors combine a morphodynamic evolution model, based on the Landau equation, with data measured in a field experiment in the Bisanseto sea in Japan. A good agreement is found between the measurements and the model result. Therefore, the combination of the Landau model and a genetic algorithm, proves to be a useful tool for the maintenance of navigation channels through a sand wave field.