The accurate simulation of wetting–drying processes in floodplains and coastal zones is a challenge for hydrodynamic modelling, especially for long time simulations. Indeed, dedicated numerical procedures are generally time-consuming, instabilities can occur at the wet/dry front, rapid transition of wet/dry interface and mass conservation are not always ensured.We present the extension of an existing wetting–drying algorithm in two space dimensions and its application to a real case. The wetting–drying algorithm is implemented in Second-generation Louvain-la-Neuve Ice-ocean Model (www.slim-ocean.be), a discontinuous Galerkin finite element model solving the shallow water equations in a fully implicit way. This algorithm consists in applying a threshold value of fluid depth for a thin layer and a blending parameter in order to guarantee positive values of the water depth, while preserving local mass conservation and the well balanced property at wet/dry interfaces.The technique is first validated against standard analytical test cases (Balzano 1, Balzano 3 and Thacker test cases) and is subsquently applied in a realistic domain, the Tonle Sap Lake in the Mekong River Basin, where the water level can vary by about 10 m between the dry and the wet season.

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The Mekong river is one of the largest rivers in the world, which flows through six countries of Southeast Asia (China, Myanmar, Laos, Thailand, Cambodia and Vietnam). Its hydro-sedimentary regime is changing rapidly, as a consequence of a regional shift of land use (agriculture, road, etc.), damming, sand mining and climate changes, among others. This study assesses the behavior of particles transported in suspension in the Lower Mekong River (LMR), along approximately 1700 km from fluvial to estuarine environments. Suspended sediment properties were estimated, simultaneously with hydrodynamic conditions, during three field campaigns. In addition, further investigations were performed in the laboratory to assess the structures of particles (flocculated or not), their capacity to flocculate (and the impacts on siltation), under a wide range of sediment concentration (20–30,000 mg.L⁻¹). This study confirms that suspended sediment transported in the LMR are predominantly (75% by volume) flocculi (or freshly eroded soils aggregates), with median aggregated particle size in the range 10–20 μm and median settling velocity of the order of 0.01–0.1 mm s⁻¹. These flocculi are robust under the hydrodynamic conditions (turbulence and suspended sediment concentration – SSC) existing in the LMR. Laboratory investigations reveal the existence of a threshold sediment concentration (400 mg.L⁻¹), beyond which flocculation and sedimentation increase of orders of magnitudes. Thus, concentration that exceeds this threshold might promote the formation of so-called fluid mud layers. Because of the nonlinear response of flocculation and sedimentation with SSC and considering the ongoing changes at a regional scale in the LMR, higher occurrence of fluid mud layers in the fluvial upstream waterbodies might be anticipated, and a lower occurrence in estuaries and alongshore where the concentration decrease. The geomorphology could be impacted, with an over-siltation in dams and an exacerbated erosion of the muddy-mangrove coast.

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Conceptually, tidal rivers are seen as narrow channels along which the cross-section geometry remains constant and the bed is horizontal. As tidal waves propagate along such a channel, they decrease exponentially in height. The more rapid the decrease, the stronger the river flow. Near the coast, the tidally averaged width and depth change little throughout the year, even if the river discharge varies strongly between the seasons. However, further upstream, the water depth varies considerably with the river discharge. Recent observations from the Kapuas River, Indonesia, show that the water surface forms a backwater profile when the river flow is low. In this case, the depth converges, i.e. it gradually decreases between the river mouth and the point where the bed reaches sea level. This effect distinctly influences how tidal waves propagate up river so that their wave height does not decrease exponentially any more. We present a theoretical analysis of this phenomenon, which reveals several so far overlooked aspects of river tides. These aspects are particularly relevant to low river flow. Along the downstream part of the tidal river, depth convergence counteracts frictional damping so that the tidal range is higher than expected. Along the upstream parts of the tidal river, the low depth increases the damping so that the tide more rapidly attenuates. The point where the bed reaches sea level effectively limits the tidal intrusion, which carries over to the overtide and the subtidal water level set-up.@en

The natural modes of Ontario Lacus surface oscillations, the largest lake in Titan’s southern hemisphere, are simulated and analyzed as they are potentially of broad interest in a variety of dynamical researches. We found that tidal forces are too low in frequency to excite the (barotropic) normal modes. Broadband wind forcing likely spans the resonant frequencies. High wind speed, which could be encountered under episodic phenomena such as storms, would be required to significantly excite the normal modes. While the slower baroclinic normal modes could more easily be resonantly forced by the low-frequency tidal forces, addressing this issue demands unavailable information about the lake stratification.

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Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.

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The tidal response of Titan's two largest northern seas, Ligeia Mare and Kraken Mare, is studied by means of a two-dimensional, depth-averaged, shallow water model, SLIM (http://www.climate.be/slim). Kraken Mare is formed of two basins, the northern one being assumed to be linked by a single strait, Trevize Fretum, to Ligeia Mare. The tidal motions tend to be independent of each other in each basin (i.e., Ligeia Mare, Kraken 1 and Kraken 2) which results in sharp transitions in the straits. Our results are overall rather similar to those of Tokano et al. (2014), suggesting that a 2D model such as SLIM is adequate for modelling Titan's tides and, since it is (presumably) less computationally demanding, may be better for sensitivity studies. For instance, the maximum tidal range in Kraken and Ligeia Maria respectively are 0.29 m and 0.14 m, which is within the range predicted by Lorenz et al. (2014) although smaller by 0.07 m and larger by 0.04 m than the estimates of Tokano et al. (2014) (but it occurs at the same location). The tidal currents are faster (by about one order of magnitude) in the straits linking those Maria than in the basins themselves (with a maximum of 0.36 m/s in the strait linking Kraken 1 and Kraken 2, Seldon Fretum). A decomposition of the tidal history into different harmonic components is carried out. Except in specific areas such as the straits and the amphidromic point(s), the main tidal component has a period of 1 Titan Day. We also briefly studied the eigenmodes of the northern seas whose period is close to the tidal period: such modes are very local. Indeed, their magnitude is significant (with respect to the magnitude of the modes elsewhere in the seas) in small bay(s) or near the islands of Kraken 2 and Ligeia Mare. They are not excited by the tides as they do not appear in the tidal motion.A sensitivity analysis to poorly constrained parameters (bottom friction coefficient, depth of Trevize Fretum and attenuation factor - the latter is briefly discussed with respect to the values of the Love numbers found in the literature) is also conducted. The model parameters are seen to have a significant impact on the liquid exchanges between the basins and, consequently, on the tidal range and phase, fluid velocity and location of amphidromic point(s).

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The analytical solution is derived for rotational frictional flow in a shallow layer of fluid in which the top and bottom Ekman layers join without leaving a frictionless interior.This vertical structure has significant implications for the horizontal flow. In particular, for a layer of water subjected to both a surface wind stress and bottom friction, the vorticity of the horizontal flow is a function not only of the curl of the wind stress (the classical result for deep water known as Ekman pumping) but also of its divergence. The importance of this divergence term peaks for a water depth around 3 times the Ekman layer thickness. This means that a curl-free but non-uniform wind stress on a shallow sea or lake can, through the dual action of rotation and friction, generate vorticity in the wind-driven currents. We also find that the reduction of three-dimensional dynamics to a two-dimensional model is more subtle than one could have anticipated and needs to be approached with utmost care. Taking the bottom stress as dependent solely on the depth-averaged flow, even with some veering, is not appropriate. The bottom stress ought to include a component proportional to the surface stress, which is negligible for large depths but increases with decreasing water depth.

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The Columbia River (CR) estuary is characterized by high river discharge and strong tides that generate high velocity flows and sharp density gradients. Its dynamics strongly affects the coastal ocean circulation. Tidal straining in turn modulates the stratification in the estuary. Simulating the hydrodynamics of the CR estuary and plume therefore requires a multi-scale model as both shelf and estuarine circulations are coupled. Such a model has to keep numerical dissipation as low as possible in order to correctly represent the plume propagation and the salinity intrusion in the estuary. Here, we show that the 3D baroclinic discontinuous Galerkin finite element model SLIM 3D is able to reproduce the main features of the CR estuary-to-ocean continuum. We introduce new vertical discretization and mode splitting that allow us to model a region characterized by complex bathymetry and sharp density and velocity gradients. Our model takes into account the major forcings, i.e. tides, surface wind stress and river discharge, on a single multi-scale grid. The simulation period covers the end of spring-early summer of 2006, a period of high river flow and strong changes in the wind regime. SLIM 3D is validated with in-situ data on the shelf and at multiple locations in the estuary and compared with an operational implementation of SELFE. The model skill in the estuary and on the shelf indicate that SLIM 3D is able to reproduce the key processes driving the river plume dynamics, such as the occurrence of bidirectional plumes or reversals of the inner shelf coastal currents.

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The discontinuous Galerkin (DG) finite element method is well suited for the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces.
The mesh vertical movement is determined by means of a conservative arbitrary Lagrangian–Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level.
The vertically adaptive mesh approach is implemented in the three-dimensional version of the geophysical and environmental flow Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM 3D; www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.@en

The Mekong river, located in Southeast Asia, is one of the largest rivers in the world. It is facing serious problems related to sediment transport, e.g. the reduction of sediment volume supply to the delta and estuary. This study focuses on the physical properties of suspended particles in the upstream fluvial section (Luang Prabang, Laos) and in the region of tidal influence (Song Hau estuary, Vietnam). These sites are respectively the upper and lower limits of the Lower Mekong River (LMR), which are experiencing contrasted transport modes. The main objective of this study is to quantify the proportion of inert sand and of cohesive particles in the water through comprehensive measurements of particle size, settling velocity and flocculation in the water column. Two field campaigns were undertaken in the summer monsoon season. The results point out the predominance of flocculi, with sizes of 18 ± 5 μm in the fluvial environment and 15 ± 5 μm in the estuary and the similarities in patterns, mixture of sand (12 ± 5 %) and mud (88 ± 5 %). They also provide a statistically representative set of suspended particle populations in the upstream and downstream regions that could be used for improving numerical models.

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The 2015/16 ENSO event increased the temperature of waters surrounding northeast Australia to above 30 °C, with large patches of water reaching 32 °C, for over two months, which led to severe bleaching of corals of the Northern Great Barrier Reef (NGBR). This study provides evidence gained from remote-sensing data, oceanographic data and oceanographic modeling, that three factors caused this excessive heating, namely: 1) the shutdown of the North Queensland Coastal Current, which would otherwise have flushed and cooled the Northern Coral Sea and the NGBR through tidal mixing 2) the advection of warm (>30 °C) water from the Gulf of Carpentaria eastward through Torres Strait and then southward over the NGBR continental shelf, and 3) presumably local solar heating. The eastward flux of this warm water through Torres Strait was driven by a mean sea level difference on either side of the strait that in turn was controlled by the wind, which also generated the southward advection of this warm water onto the NGBR shelf. On the NGBR shelf, the residence time of this warm water was longer inshore than offshore, and this may explain the observed cross-shelf gradient of coral bleaching intensity. The fate of the Great Barrier Reef is thus controlled by the oceanography of surrounding seas.

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The containment of genetically modified (GM) pollen is an issue of significant concern for many countries. For crops that are bee-pollinated, model predictions of outcrossing rates depend on the movement hypothesis used for the pollinators. Previous work studying pollen spread by honeybees, the most important pollinator worldwide, was based on the assumption that honeybee movement can be well approximated by Brownian motion. A number of recent studies, however, suggest that pollinating insects such as bees perform Lévy flights in their search for food. Such flight patterns yield much larger rates of spread, and so the Brownian motion assumption might significantly underestimate the risk associated with GM pollen outcrossing in conventional crops. In this work, we propose a mechanistic model for pollen dispersal in which the bees perform truncated Lévy flights. This assumption leads to a fractional-order diffusion model for pollen that can be tuned to model motion ranging from pure Brownian to pure Lévy. We parametrize our new model by taking the same pollen dispersal dataset used in Brownian motion modelling studies. By numerically solving the model equations, we show that the isolation distances required to keep outcrossing levels below a certain threshold are substantially increased by comparison with the original predictions, suggesting that isolation distances may need to be much larger than originally thought.@en

Interaction of tidal flow with a complex topography and bathymetry including headlands, islands, coral reefs and shoals create a rich submesoscale field of tidal jets, vortices, unsteady wakes, lee eddies and free shear layers, all of which impact marine ecology. A unique and detailed view of the submesoscale variability in a part of the Great Barrier Reef lagoon, Australia, that includes a number of small islands was obtained by using a “stereo” pair of 2-m-resolution visible-band images that were acquired just 54 s apart by the WorldView-3 satellite. Near-surface current and vorticity were extracted at a 50-m-resolution from those data using a cross-correlation technique and an optical-flow method, each yielding a similar result. The satellite-derived data are used to test the ability of the second-generation Louvain-la-Neuve ice-ocean model (SLIM), an unstructured-mesh, finite element model for geophysical and environmental flows, to reproduce the details of the currents in the region. The model succeeds in simulating the large-scale (> 1 km) current patterns, such as the main current and the width and magnitude of the jets developing in the gaps between the islands. Moreover, the order of magnitude of the vorticity and the occurrence of some vortices downstream of the islands are correctly reproduced. The smaller scales (< 500 m) are resolved by the model, although various discrepancies with the data are observed. The smallest scales (< 50 m) are unresolved by both the model- and image-derived velocity fields. This study shows that high-resolution models are able to a significant degree to simulate accurately the currents close to a rugged coast. Very-high-resolution satellite oceanography stereo images offer a new way to obtain snapshots of currents near a complex topography that has reefs, islands and shoals, and is a potential resource that could be more widely used to assess the predictive ability of coastal circulation models.

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Lagrangian forward and backward models are introduced into a coarse-grid ocean global circulation model to trace the ventilation routes of the deep North Pacific Ocean. The random walk aspect in the Lagrangian model is dictated by a rotated isopycnal diffusivity tensor in the circulation model, and the effect of diffusion is explicitly resolved by means of stochastic terms in the Lagrangian model. The analogy between the probability distribution of a Lagrangian model with Green's function of an Eulerian tracer transport equation is established. The estimated first- and last-passage time density of the deep North Pacific using both the Eulerian and the Lagrangian models ensured that the Lagrangian pathways and their ensemble statistics are consistent with the Eulerian tracer transport and its adjoint model. Moreover, the sample pathways of the ventilated mass fractions of the deep North Pacific particles to and from the ocean surface are studied.

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In the context of the emergence of extraterrestrial oceanography, we adapted an existing oceanographic model, SLIM (www.climate.be/slim), to the conditions of Titan, a moon of Saturn. The tidal response of the largest southern lake at Titan’s surface, namely Ontario Lacus, is simulated. SLIM solves the 2D, depth-averaged shallow water equations on an unstructured mesh using the discontinuous Galerkin finite element method, which allows for high spatial resolution wherever needed. The impact of the wind forcing, the bathymetry, and the bottom friction is also discussed. The predicted maximum tidal range is about 0.56 m in the southern part of the lake, which is more than twice as large as the previous estimates (see Tokano, Ocean Dyn 60:(4) 803–817
doi:10.1007/s10236-010-0285-3 2010). The patterns and magnitude of the current are also markedly different from those of previous studies: the tidal motion is not aligned with the major axis of the lake and the speed is larger
nearshore. Indeed, the main tidal component rotates clockwise in an exact period of one Titan day and the tidal currents can reach 0.046 ms−1 close to the shores depending on the geometry and the bathymetry. Except for these
specific nearshore regions, the current speed is less than 0.02 ms−1. Circular patterns can be observed offshore, their rotational direction and size varying along the day.@en

Large rivers often present a river–lake–delta system, with a wide range of temporal and spatial scales of the flow due to the combined effects of human activities and various natural factors, e.g., river discharge, tides, climatic variability, droughts, floods. Numerical models that allow for simulating the flow in these river–lake–delta systems are essential to study them and predict their evolution under the impact of various forcings. This is because they provide information that cannot be easily measured with sufficient temporal and spatial detail. In this study, we combine one-dimensional sectional-averaged (1D) and two-dimensional depth-averaged (2D) models, in the framework of the finite element model SLIM, to simulate the flow in the Mahakam river–lake–delta system (Indonesia). The 1D model representing the Mahakam River and four tributaries is coupled to the 2D unstructured mesh model implemented on the Mahakam Delta, the adjacent Makassar Strait, and three lakes in the central part of the river catchment. Using observations of water elevation at five stations, the bottom friction for river and tributaries, lakes, delta, and adjacent coastal zone is calibrated. Next, the model is validated using another period of observations of water elevation, flow velocity, and water discharge at various stations. Several criteria are implemented to assess the quality of the simulations, and a good agreement between simulations and observations is achieved in both calibration and validation stages. Different aspects of the flow, i.e., the division of water at two bifurcations in the delta, the effects of the lakes on the flow in the lower part of the system, the area of tidal propagation, are also quantified and discussed.

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SLIM is an unstructured mesh, finite element model of environmental and geophysical fluid flows, which is being improved to simulate fine-grained sediment transport in riverine and marine water systems. A 2D depth-averaged version of the model is applied to the Mahakam Delta (Borneo, Indonesia), the adjacent ocean, and three lakes in the central part of the Mahakam River catchment. The 2D code is coupled to a 1D section-averaged model for the Mahakam River and four tributaries. The coupled 2D/1D model is mainly aimed at simulating fine-grained sediment transport in the riverine and marine water continuum of the Mahakam River system. Using the observations of suspended sediment concentration (SSC) at five locations in the computational domain, the modelling parameters are first determined in a calibration step, for a given
period of time. A validation step is then performed using data related to another period of time. It is concluded that the coupled 2D/1D model
reproduces very well the observed suspended sediment distribution within the delta. The spatial distribution of sediment concentration in the delta
and its temporal variation are also discussed.@en

With the second largest outflow in the world and one of the widest hydrological basins, the Congo River is of a major importance both locally and globally. However, relatively few studies have been conducted on its hydrology, as compared to other great rivers such as the Amazon, Nile, Yangtze, or Mississippi. The goal of this study is therefore to help fill this gap and provide the first high-resolution simulation of the Congo river-estuary-coastal sea continuum. To this end, we are using a discontinuous-Galerkin finite element marine model that solves the two-dimensional depth-averaged shallow water equations on an unstructured mesh. To ensure a smooth transition from river to coastal sea, we have considered a model that encompasses both hydrological and coastal ocean processes. An important difficulty in setting up this model was to find data to parameterize and validate it, as it is a rather remote and understudied area. Therefore, an important effort in this study has been to establish a methodology to take advantage of all the data sources available including nautical charts that had to be digitalized. The model surface elevation has then been validated with respect to an altimetric database. Model results suggest the existence of gyres in the vicinity of the river mouth that have never been documented before. The effect of those gyres on the Congo River dynamics has been further investigated by simulating the transport of Lagrangian particles and computing the water age.@en

Transport timescales (TTS), namely residence time and exposure time, were computed for adjacent shallow meso-tidal tropical estuarines system using the Lagrangian model D-Waq Part coupled with the hydrodynamic model Delft3D-Flow, and the Constituent-oriented Age and Residence time Theory, CART. The main results are threefold: (a) The TTS differs more between releases at high or low tide than between those at spring and neap tides. The exposure time was also calculated and found to be larger than the residence time by a few days. (b) The exposure and residence times were used to evaluate the return coefficient (r) for different scenarios. As with residence and exposure times, the return coefficient was found to differ more between releases at high or low tide than between those at spring and neap tides. (c) For the Caravelas Estuary, where the river inflow was low (~4 m³ s^-1), the residence time was found to be much larger than for the Peruípe Estuary, where the river discharge was greater and nearly constant during the sampling period (~20 m³ s^-1). These results shows the importance of advection in decreasing TTS in the Peruípe Estuary compared to the Caravelas Estuary. The influence of the advection and dispersion agrees with previous simple estimates obtained using the newly modified Land Ocean Interaction Coastal Zone (LOICZ) model by Andutta et al. (2014).

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