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Abstract Tidal sandbanks are large-scale dynamic bed forms observed in shallow shelf seas. Their plan view evolution may display a single bank breaking into two or more banks, for which two mechanisms have been proposed in the literature. However, as both were based on interpretation of observations, generic support from a process-based modelling perspective is lacking so far. Here we present a new idealised process-based model study into the transient evolution of tidal sandbanks. Key elements are the inclusion of nonlinear dynamics for topographies that vary in both horizontal directions, and the focus on long-term evolution (centuries and longer). As a further novelty, the hydrodynamic solution, satisfying the nonlinear shallow water equations including bottom friction and the Coriolis effect, is obtained from a truncated expansion in the ratio of maximum bank elevation (w.r.t. mean depth) and mean water depth. Bed evolution follows from the tidally averaged bed load sediment transport, enhanced by depth-dependent wind-wave stirring. From our model results, we identify two paths of evolution, leading to either bank-breaking or an S-shape. Which of these paths occurs depends on initial topography, with bank orientation and bank length as major control parameters. The breaking and S-shape obtained in our model results show resemblance with banks observed in the North Sea. Highlights • A process-based model for the transient evolution of tidal sandbanks is presented. • Results show pattern expansion and evolution toward bank-breaking or an S-shape. • A regime diagram shows how this evolution depends on bank length and orientation. [ABSTRACT FROM AUTHOR]

Bathymetric resurveying in shallow seas is a costly process with limited resources, yet necessary for adequate nautical charts and therefore crucial for safe navigation. An important factor in an efficient resurvey policy is the type and size of sea floor dynamics. We propose four indicators, which we use in a procedure to recommend changes to the resurvey policies of the Belgian and Netherlands Continental Shelf (BNLCS). These shallow regions are characterised by a sandy sea floor covered with rhythmic patterns. The proposed indicators follow from the estimates for sea floor dynamics, as given by applying the statistical method of deformation analysis. We present a concept for the shallowest likely depth surface, on which we base two of the indicators. The other two indicators may act as a warning: they quantify the potentially missed dynamics, which makes the procedure more robust in case of complicated morphology. Finally, applying our procedure to the BNLCS, we show clear differences in recommended resurvey priority between the five analysed regions, which currently have equal resurvey frequencies. [ABSTRACT FROM AUTHOR]

Abstract: Long-term considerations of repeated and increasing sand extraction on the Netherlands Continental Shelf (North Sea) may lead to the creation of a mega-scale extraction trench in front of the Dutch coast (length hundreds of km, width over 10km, depth several m). We investigate the impact of such a huge topographic intervention on tidal dynamics, which is a key aspect in hydrodynamics, and indirectly also affecting morphodynamics and ecology. Because of the unprecedented extent of the extraction scenario, we follow a generic approach aimed at understanding the physical mechanisms behind the changes, the orders of magnitude and area of influence. Hence, rather than applying an existing numerical model, we develop an idealized model for tide propagation in semi-enclosed rectangular basins. The model geometry consists of three adjacent compartments with a realistic cross-basin depth profile, the trench being located in the second compartment, while assuming along-basin uniformity of depth within each compartment. The problem is forced by an incoming Kelvin wave. The solution in each compartment, satisfying the linear depth-averaged shallow water equations on the f plane including bottom friction, is written as the superposition of semi-numerically obtained wave solutions. A collocation technique is employed to satisfy no-normal flow across the basin''s closed end as well as continuity of elevation and flux across the interfaces between the compartments. The results indicate changes in tidal range, phase and currents throughout the whole basin, which shows the importance of a model domain on the scale of the basin. Changes in coastal tidal range show zones of decrease and increase (order cm). Changes in coastal shore-parallel tidal current amplitudes are of the order of cms−1. A sensitivity analysis for various trench geometries shows that the hydrodynamic impact generally increases with increasing extraction volume, being more sensitive to trench depth and width than trench length. The changes in tidal currents may structurally alter sediment transport rates with several percents. As the bathymetry and coastal morphology result from subtle balances in long-term sediment transport, the trench may indirectly affect various user functions and values (coastal safety, navigation, marine ecology, cables and pipelines) and, hence, be of concern to coastal management. [Copyright &y& Elsevier]

A new method to calculate flow in compound channels is proposed: the interacting divided channel method (IDCM), based on a new parametrization of the interface stress between adjacent flow compartments, typically between the main channel and floodplain of a two-stage channel. This expression is motivated by scaling arguments and allows for a simple analytical solution of the average flow velocities in different compartments. Good agreement is found between the analytical model results and laboratory data from the literature. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the hydrodynamic effects and morphodynamic impact of large-scale offshore sand extraction, for a variety of pit designs. We use a process-based idealized model for flow, sediment transport and bed evolution in a tide-dominated environment. Legislation and other practical considerations motivate our assumption that sandpits are both wide (horizontal dimensions of the order of kilometres) and shallow (the ratio of pit depth to water depth being small). This results in a semi-analytical tool that, unlike previous studies, enables a quick and extensive study into the effects of varying the physical characteristics as well as the pit design parameters. These parameters include pit length, width, and orientation with respect to the tide. The model results show that sandpits experience flow contraction, which is enhanced by friction–topography interactions and also affected by Coriolis effects. As a result, sandpits trigger the morphodynamic instability associated with the formation of large-scale bed features known as tidal sandbanks. It implies a gradual deepening and deformation of the pit itself, as well as the appearance of adjacent humps. The time scale of this behaviour is of the order of decades to centuries. A sensitivity analysis is then carried out to determine the effects of pit geometry on the model results. The morphodynamic response is found to be strongest for sandpits elongated in the preferred direction of sandbank formation (giving the largest area of morphodynamic influence), and weakest for pits perpendicular to this direction. The migration of the pit is shown not to depend on the pit geometry, but rather on the ambient flow conditions. [Copyright &y& Elsevier]

Offshore gasmining is an example of a human intervention with a morphological impact. On land, it is usually attended with a dish-like bed depression. We show that, if located at sea, such a bed depression can become morphodynamically active by triggering mechanisms related to tidal sand bank formation. To that end, a simple morphological model is considered which describes an erodible bed subject to a tidal wave in a shallow sea. The continuous subsidence is modelled by a sink term in the sediment balance. Then, a linear approximation is carried out to describe the bed evolution after the onset of subsidence. The results, presented in physical space, show that the subsidence triggers the formation of a sand bank pattern that gradually spreads around the centre of subsidence, at a rate that may go up to 160 m year−1, depending on the tidal transport rate and the tidal eccentricity. The dimension of the depression does not affect the spreading rate nor the orientation of the sand banks, but it does influence their spacing. The main conclusion is that the horizontal extent of the area influenced by the bed depression by far exceeds that of the direct subsidence, thus showing that bed depressions on land and at sea indeed behave in fundamentally different ways. The results suggest that nonlinear effects are worthwhile to be investigated in order to describe finite amplitude development of sand banks as well as the interaction between subsidence and bed forms. [Copyright &y& Elsevier]

The article presents the author's response to the criticism of their paper titled "Interacting Divided Channel Method for Compound Channel Flow," that was published in the August 2009 issue of the journal. They say that the discussers point out the numerical value of turbulent exchange factor as 0.16 but they have adopted the value of 0.020 from researchers S. Proust and colleagues. The authors say that the discussers have correctly identified inconsistencies in several equations.

We present an idealized network model for storm surges in the Wadden Sea, specifically including a time-dependent wind forcing (wind speed and direction). This extends the classical work by H.A. Lorentz who only considered the equilibrium response to a steady wind forcing. The solutions obtained in the frequency domain for the linearized shallow-water equations in a channel are combined in an algebraic system for the network. The velocity scale that is used for the linearized friction coefficient is determined iteratively. The hindcast of the storm surge of 5 December 2013 produces credible time-varying results. The effects of storm and basin parameters on the peak surge elevation are the subject of a sensitivity analysis. The formulation in the frequency domain reveals which modes in the external forcing lead to the largest surge response at coastal stations. There appears to be a minimum storm duration, of about 3-4 h, that is required for a surge to attain its maximum elevation. The influence of the water levels at the North Sea inlets on the Wadden Sea surges decreases towards the shore. In contrast, the wind shearing generates its largest response near the shore, where the fetch length is at its maximum. [ABSTRACT FROM AUTHOR]

We develop a three-dimensional idealized model that is specifically aimed at gaining insight in the physical mechanisms resulting in the formation of estuarine turbidity maxima in tidally dominated estuaries. First, the three-dimensional equations for water motion and suspended sediment concentration together with the so-called morphodynamic equilibrium condition, are scaled. Next, surface elevation, velocity and sediment concentration are expanded in a small parameter ϵ = A ¯ M 2 / H , where A ¯ M 2 is the mean amplitude of the M 2 tide and H is the mean water depth at the seaward side. This results in a system of equations at each order in this small parameter. This ordering allows solving for the vertical structure of the velocity and suspended sediment concentration, independently of the horizontal dimension. After obtaining these vertical structures, the horizontal dependencies of the physical variables follow from solving a two-dimensional elliptic partial differential equation for the surface elevation. The availability of fine sediments in the estuary follows from a two-dimensional elliptic partial differential equation which results from requiring the system to be in morphodynamic equilibrium, and prescribing the total amount of easily erodible sediments available in the estuary. These elliptic equations for the surface elevation and sediment availability are solved numerically using the finite element method with cubic polynomials as basis functions. As a first application, the model is applied to the Ems estuary using a simplified geometry and bathymetric profiles characteristic for the years 1980 and 2005. The availability of fine sediments and location of maximum concentration are investigated for different lateral depth profiles. In the first experiment, a uniform lateral depth is considered. In this case, both the sediment availability and suspended sediment concentration are, as expected, uniform in the lateral direction. In 1980, the sediment is mainly trapped near the entrance, while in 2005, the sediment is mostly trapped in the freshwater zone. In the next experiment, the lateral bathymetry is varied parabolically while keeping the mean depth unchanged. In this case, the fine sediment is mainly found at the shallow sides, but the maximum sediment concentration is found in the deeper channel where the bed shear stress is much larger than on the shoals. As a final experiment, a more realistic (but smoothed) geometry and bathymetry for the Ems estuary are considered, showing the possibilities of applying the newly developed model to complex geometries and bathymetries. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

This review highlights three morphodynamics modelling approaches, used for offshore marine aggregate extraction impact assessment. These approaches are based upon examples of (1) full process-based models; (2) idealised process- based models; and (3) conceptual models. Illustrated also is the way in which these models, applied for extractions on flat bed or sandbanks, can complement each other, towards the estimation of Coastal State Indicators (CSIs). This review leads to the conclusion that, for an optimal environment assessment, there are two main approaches: (1) either combine and couple the models, in order to simulate the full morphodynamics of the system over a long time-scale, taking into account also short-term events, or (2) use a set of existing models, knowing precisely their applicability to the CSI's and the reliability of their predictions, rather than using only the best model, available presently. [ABSTRACT FROM AUTHOR]