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Tides are important in various ways, e.g., by affecting navigation and coastal safety and by acting as a driver for sediment transport and seabed dynamics. To explain spatial patterns of tidal phase and range, observed in coastal seas around the world, we present an idealised process-based model. It solves the depth-averaged linearised shallow water equations, including the Coriolis effect and bottom friction, on schematised geometries with rectilinear coastlines and stepwise topographic variations. Based on an extended Klein-Gordon equation (accounting for bottom friction), Kelvin and Poincaré modes are identified as the fundamental wave solutions in a channel of uniform width and depth. We analyse their spatial structures and dynamic properties, addressing the roles of bottom friction and transverse topographic steps. The solution for a semi-enclosed basin, including topographic steps, is then obtained as a superposition of these wave modes, by applying a collocation technique. As an example, we present solutions that grossly explain the amphidromic system of the Gulf of California. Finally, we discuss the modelling approach and address the links with morphodynamics and climate change.

Research content This poster presents selected findings from the article Unsteady linearisation of bed shear stress for idealised storm surge modelling of 2021 for the participants in the NCK Days 2022, the yearly get-together of the Netherlands Centre for Coastal Research. The summary underlying the poster is available from the event's Book of Abstracts both as web page and as PDF document. The poster is open-access under a Creative Commons Attribution 4.0 International. Document design: structure and styling The conference organisers required the production of a paper-based poster in A0 format with portrait orientation. The document has been designed in A4 format, as available from the copy shared in this website. A resolution of 1200 dpi produced sharp enough images when printing in A0 size a document in PDF format. The whole document has been composed as a three-column table of a Google Doc document, with row-wise column merges which produce a well-marked layout consisting of stacked rows. In order to favour speed-reading, two font types and sizes produce a contrast between headings and narrative. Likewise, the text blocks are made of short and clearly spaced paragraphs, easy to point to and scan. The font size in the text body was readable when printed in A0 and, in retrospect for the specific venue the poster has been presented in, could still have been reduced to the same effect. Test prints confirmed that an additional margin would have been present around the page. The poster promotes a study published in a journal article, whereby the methods and results on display are already established. The audience is assumed to have been attracted by the poster title, thus to have been moved by an affinity for the topical area and to nurse a potential curiosity about reading the article in depth. As a result, the slant of this poster is intendedly descriptive, if not unimaginative; visuals are not especially meant or positioned to catch the eye. Document design: narrative and presentation The findings selected for the poster are those encapsulating the novelties of the article most compactly. This content selection provides maximum integration between narrative and scientific advances within the limited space of the document and of the interactions in a poster session. The table cells organise information progressively more detailed in the reading direction, broadly following a general-to-specific or abstraction-to-implementation order. During a poster session, the poster presenter could illustrate the content either in a bottom-up fashion starting from the results, supported by cartoons and graphs; or top-down, starting from the generalities presented as textual narrative. Outside the poster session, interested passerbys may find essential guidance into the topic scanning the poster in normal reading direction. Document design: on-line dissemination Hyperlinks to further resources, aimed at the digital poster version, are in blue. The DOI of this document has been reserved upon creating an unpublished Zenodo entry while drafting the poster. The DOI is shown in the poster so as to inform the viewers of the possibility to download the document after the conference. The poster has been uploaded ahead of the event and embargoed until the planned day of the off-line presentation. The publication date is the date of the poster session. Description authored by Giordano Lipari, {"references":["Roos PC, Lipari G, Pitzalis C, Reef KRG, Campmans GHP, Hulscher SJMH. Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling. Journal of Marine Science and Engineering. 2021; 9(11):1160. https://doi.org/10.3390/jmse9111160"]}

We investigate the influence of wind waves and wind-driven flow on sand wave dynamics using a two-model approach. Using a linear stability analysis, we find that waves decrease sand wave growth and wind causes sand wave migration. Combining linear stability analysis with a typical North Sea wave and wind climate explains variability in sand wave migration rates. Using a nonlinear sand wave model we show that waves reduce sand wave height and wind causes sand wave asymmetry as well as migration.

Observations from the field show that the spatial distribution of benthic organisms is strongly correlated to the morphological structure of tidal sand waves. In particular the troughs of sand waves are typified by a large benthic community, in contrast to the crest. In this paper, we present an idealised process-based model to study these patterns of biota and sand waves. Our model results agree with the observations that these phase-related patterns can arise on the seabed. Moreover, we show that local topography disturbances may lead to spatial patterns of both sand waves and biomass.

Tidal sandwaves form a prominent bed pattern in shallow sandy shelf seas. Here the class of idealised process-based models, aimed at obtaining generic insight in sandwave dynamics, is reviewed. Since many model studies focus on the instability underlying sandwave formation, first an outline of linear stability analysis is given. Then, an overview of model results is presented, highlighting two ongoing research projects (SMARTSEA and SANDBOX) and followed by suggestions for future research.

Flow velocity measurements in rivers and coastal areas are often collected at cross-sections where velocity is measured at multiple locations and over certain period of time. Subsequent data processing often involves temporal averaging and spatial smoothing of the raw velocity data. This process of spatial smoothing and temporal averaging is motivated by spatial and temporal behavior we expect to be present in the data, such as coherent velocity patterns at the scale of the water depth and temporal coherence at the scale of for instance tides. The process of smoothing and averaging, however, is often arbitrary, and the consequences of averaging windows in space and time on the resulting velocity patterns are often obscure. In this contribution we investigate a method based on spectral analysis to analyze the spatial patterns in a cross-section. This allows to identify the dominant spatial patterns that are present in the velocity data leading to a more grounded choice for spatial smoothing. Furthermore, the choice of basis function allows to include some physically based constraints such as no-slip at the bed and banks. The method consists of computing the components and location of the velocities measured in a cross-section. These locations are transformed to a normalized coordinate system. For each velocity component a set of basis function is selected and higher order function are progressively included and fitted to all the velocity data measured at a cross-section. The process is repeated until there is no spatial structure in the residuals. The method is applied to velocity measurements collected in a sharp bend. The analysis allows to identify dominant spatial patterns present in the data and results in continuous functions that describe the velocity field in detail, and that meet the requirement of no slip at the boundaries. Future work will extend the analysis to include different of basis functions, to include more physical constraints, such as continuity.

The nonlinear nature of bottom friction in shallow flow complicates its analysis, particularly in idealised models. For tidal flows, Lorentz’ linearisation has been widely applied, using an energy criterion to specify the friction coefficient. Here we propose an extension of this approach to storm surges, leading to a friction coefficient that may gradually vary over a storm event. The derivation is provided along with first results for a single channel.

In order to quantify the effects of mutual feedbacks between geomorphology and benthic activity, we present a twoway coupled idealised sand wave model. This model allows for an extensive parameter analysis and gives insight in the effects of different time scales. Our analysis shows that the behaviour of the coupled system is essentially different from that of an abiotic system. Where in the latter, the basic state (flat bed) is essentially static, in the former, biomass may show growth (or decay). In turn, this affects hydro- and sediment dynamics, such that the basic state can be considered dynamic.

Barrier coasts display a chain of islands, separated by tidal inlets that connect a back-barrier basin to a sea or ocean. Observations show that barrier island length generally decreases for increasing tidal range and increasing basin area. However, this has neither been reproduced in model studies nor explained from the underlying physics. This is the aim of our study. Here we simulate barrier coast dynamics by combining a widely used empirical relationship for inlet dynamics with a process-based model of the tidal hydrodynamics. Our model results show stable inlet systems with more than one inlet open that support the observed qualitative relationships and fit in existing barrier coast classifications. To explain this, we identify a competition between a destabilizing mechanism (bottom friction in inlets, tending to reduce the number of open inlets) and a stabilizing one (spatially varying pressure gradients over the inlets, tending to keep the inlets open).

River deltas and individual delta lobes frequently face reduction of sediment supply, either from the geologic process of river avulsion or, more recently, due to human activities such as river damming. Using a process-based shoreline evolution model, we investigate wave reworking of delta shorelines after fluvial input elimination. Model results suggest that littoral sediment transport can result in four characteristic modes of delta abandonment, ranging from diffusional smoothing of the delta (or delta lobe) to the development of recurved spits. A straightforward analysis of delta shape and wave characteristics provides a framework for predicting the mode of delta abandonment. The observed morphologies of historically abandoned delta lobes, including those of the Nile, Ebro, and Rhone rivers, fit within this framework. Our results provide quantitative insight into the potential evolution of active delta environments in light of future extreme reduction of fluvial sediment input.

The cross-sectional stability of double inlet systems is investigated using an exploratory model that combines Escoffier’s stability concept for the evolution of the inlet’s cross-sectional area with a two-dimensional, depth-averaged (2DH) hydrodynamic model for tidal flow. The model geometry consists of four rectangular compartments, each with a uniform depth, associated with the ocean, tidal inlets and basin. The water motion, forced by an incoming Kelvin wave at the ocean’s open boundary and satisfying the linear shallow water equations on the f -plane with linearised bottom friction, is in each compartment written as a superposition of eigenmodes, i.e. Kelvin and Poincaré waves. A collocation method is employed to satisfy boundary and matching conditions. The analysis of resulting equilibrium configurations is done using flow diagrams. Model results show that internally generated spatial variations in the water motion are essential for the existence of stable equilibria with two inlets open. In the hydrodynamic model used in the paper, both radiation damping into the ocean and basin depth effects result in these necessary spatial variations. Coriolis effects trigger an asymmetry in the stable equilibrium cross-sectional areas of the inlets. Furthermore, square basin geometries generally correspond to significantly larger equilibrium values of the inlet cross-sections. These model outcomes result from a competition between a destabilising (caused by inlet bottom friction) and a stabilising mechanism (caused by spatially varying local pressure gradients over the inlets).

This study focuses on the effects of changes in fluvial sediment supply on the plan-form shape of wave-dominated deltas. We apply a one-line numerical shoreline model to calculate shoreline evolution after (I) elimination and (II) time-periodic variation of fluvial input. Model results suggest four characteristic modes of wave-dominated delta development after abandonment. The abandonment mode is determined by the pre-abandonment downdrift shoreline characteristics and wave climate (which are, in turn, determined by previous delta evolution). For asymmetrical deltas experiencing shoreline instability on the downdrift flank, time-periodic variation in fluvial input influences the evolution of downdrift-migrating sandwaves. The frequency and magnitude of the riverine "forcing" can initiate a pattern that migrates away from the river mouth, interacting with the development of shoreline sandwaves. Model results suggest that long-period signals in fluvial delivery can be shredded by autogenic sand waves, whereas shorter-term riverine fluctuations can dominate the signal of the autogenic sandwaves. The insights provided by these exploratory numerical experiments provide a set of hypotheses that can be further tested using natural examples.

This study investigates the influence of basin geometry on the cross-sectional stability of double inlet systems. The inlet is in equilibrium when the amplitude of the inlet velocities equals the equilibrium velocity (~1 m s-1). This equilibrium is stable when after a perturbation the cross-sections of both inlets return to their original equilibrium value. The necessary amplitudes of the inlet velocities are obtained using an idealized 2DH hydrodynamic that calculates tidal elevation and flow in a geometry consisting of several adjacent rectangular compartments. Model results suggest that regardless of the inclusion or exclusion of bottom friction in the basin, stable equilibrium states exist. Qualitatively, the influence of basin geometry does not change the presence of stable equilibrium. Quantitatively, however, taking a basin surface area of 1200 km2, equilibrium values can differ up to a factor 2 depending on the geometry of the basin.

We investigate the effects of a mega-scale sand extraction trench (length ~200 km, width ~10 km, depth ~10 m, located in front of the Dutch coast) on tidal dynamics in the Southern North Sea. To this end, an idealized modeling approach is adopted, extending the classical problem of Kelvin wave reflection in rectangular semi-enclosed basins to account for lateral depth variations and the presence of a trench. The model results indicate changes in tidal range (zones of decrease and increase of the order of several cm), phase and currents (order cm/s) throughout the whole basin, which emphasizes the importance of a model domain on the scale of the basin. The changes in currents may structurally change sediment transport rates by several percents, which is relevant to coastal morphology. It is argued that this idealized model can be used to support a companion study carried out with a more detailed numerical engineering model. This is because of its ability to (1) provide insight into the physical mechanisms, (2) reveal the order of magnitude and area of influence of the effects and (3) allow for a quick sensitivity analysis with respect to trench geometry.

A new method is proposed to calculate the cross-sectional flow field in compound channels for 1D flow models. The proposed method involves a new parameterization of the interface stress between adjacent compartments, typically between the main channel and floodplain of a two-stage channel. This expression, proportional to the difference in squared velocities allows for a simple calculation of the average flow velocities in different compartments. For two-stage channels good agreement is found between the model results and data from literature. Also, it is shown that the description of compartment-averaged velocities may be applied to flows in channel cross-sections with arbitrary geometry, thus providing a potentially useful improvement to 1D river flow models.

Offshore sandwaves are rhythmic bed patterns widely present in shallow shelf seas. Observations from the North Sea indicate a trend of coarser sediment with a higher sorting at sandwave crests. In this study, we present an extended model for sandwave dynamics that accounts for the presence and transport of non-uniform sediment. The extension involves an active layer as well as a fractional calculation of sediment transport, which includes hiding-exposure effects. Simulations of a growing sandwave for a bimodal mixture indicate a coarsening trend towards the crest, whereas in the sandwave troughs the sediment remains mixed. The model results show qualitative agreement with observations from various sites in the North Sea.

[1] Tidal sandbanks are large-scale bed features present in many shallow shelf seas. Here we investigate the effect of nonuniform sediment on their dynamics, with a particular aim to explain observed surficial grain size variations over tidal sandbanks from a process-based modeling perspective. To this end, we use a linear stability analysis that describes the positive feedback mechanism between hydrodynamics, sediment, and the seabed responsible for sandbank formation on a horizontal shelf. In this model the sediment transport and bed evolution modules are extended by introducing an active layer and a bimodal sediment mixture. We include a dynamic hiding/exposure description of sediment transport, enhancing the transport of coarse grains and inhibiting the transport of finer grains. The model results show that for symmetrical tidal conditions, coarse grains tend to accumulate at the bank crests. Moreover, the growth rates of the perturbations increase compared to the case of uniform sediment, while the preferred wavelength and bank orientation remain unchanged. For asymmetrical tidal conditions we find a spatial phase shift between topography and the mean grain size fraction, indicating an accumulation of coarse grains on the lee side of the bank. The model results qualitatively agree with observations from banks on the Belgian continental shelf.

This thesis aims at understanding the long-term morphodynamic e®ects of large-scale o®shore sand extraction, including the potential interaction with sandbank and sandwave dynamics. To that end, we follow an idealized processbased morphodynamic modelling approach, focusing on a tidally dominated o®shore environment where such patterns may exist. Regarding tidal sandbanks, we distinguish between a °at bed and one with sandbanks in morphodynamic equilibrium. On a smaller spatial scale, we investigate the potential interaction of sand extraction and sandwave formation.

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.

We extend the class of simple offshore models that describe large-scale bed evolution in shallow shelf seas. In such seas, shallow water flow interacts with the seabed through bed load and suspended load transport. For arbitrary topographies of small amplitude we derive general bed evolution equations. The initial topographic impulse response (initial sedimentation and erosion patterns around an isolated feature on a flat seabed) provides analytical expressions that provide insight into the inherent instability of the flat seabed, the Coriolis-induced preference for cyclonically oriented features, and bed load transport being a limiting case of suspended load transport. The general evolution equation can be used to describe sandbank formation, known as the result of self-organization. Examples of human intervention at the seabed include applications to a dredged channel and an offshore sandpit. An outlook toward future research is also presented.

We extend existing knowledge on theoretical growth characteristics of tidal sand banks by including asymmetrical tides with an M0, M2 and M4-constituent, thus allowing for migration. Furthermore, in the context of the continuously increasing demand on the Dutch sand market, we show that creating a large-scale offshore sand pit has long-term morphological implications, both for the pit itself and the surrounding area. The pit deepens, while around it a sand bank pattern emerges, spreading at a constant rate of the order of tens to hundred metres per year.