The collapse dynamics and runout of columns of elongated grains in two dimensions are numerically investigated in dry and immersed conditions, by means of an unresolved finite elements/discrete elements model. The elongated grains are modeled as rigid aggregates of disks. The column aspect ratio is systematically varied from 0.125 to 16 in order to span short and tall columns. To analyze the effect of the initial grain orientation, columns with an initial grain orientation that is either random or aligned with a given direction are both considered. Collapse dynamics, both in dry and immersed cases, are found analogous to that previously observed for circular grain columns, particularly with respect to the power law dependency for the runout as a function of the column aspect ratio. The effect of the fluid mainly results in a decrease of the runout distance. Interestingly, the collapse dynamics and runout are not significantly affected by the initial orientation of the grains, except maybe in the extreme case where the grains are all horizontally oriented, which geometrically prevents the collapse. Finally, a scaling based on the front propagation energy is proposed allowing one to unify the runout of short to tall and dry to immersed columns in a single description, regardless of the initial grain orientation.@en

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 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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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 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 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

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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A discontinuous Galerkin nonhydrostatic atmospheric model is used for two-dimensional and threedimensional simulations. There is a wide range of timescales to be dealt with. To do so, two different implicit/explicit time discretizations are implemented. A stabilization, based upon a reduced-order discretization of the gravity term, is introduced to ensure the balance between pressure and gravity effects. While not affecting significantly the convergence properties of the scheme, this approach allows the simulation of anisotropic flows without generating spurious oscillations, as it happens for a classical discontinuous Galerkin discretization. This approach is shown to be less diffusive than usual spatial filters. A stability analysis demonstrates that the use of this modified scheme discards the instability associated with the usual discretization. Validation against analytical solutions is performed, confirming the good convergence and stability properties of the scheme. Numerical results demonstrate the attractivity of the discontinuous Galerkin method with implicit/explicit time integration for large-scale atmospheric flows.@en

Understanding the transport and fate of suspended sediment exported by rivers is crucial for the management of sensitive marine ecosystems. Sediment transport and fate can vary considerably depending on the geophysical characteristics of the coastal environment. Fine sediment transport was studied in a setting in between “open” (uninterrupted coasts) and “semi-enclosed” (bays) coastal systems, namely a “semi-open” system of shallow coastal water with long (∼20 km) stretches of open coasts separated by capes and headlands. The case study was the large, seasonal, Burdekin River that discharges to a wide continental shelf containing headlands and shallow embayments adjacent to the Great Barrier Reef, Australia. A new three-dimensional fine sediment module for the unstructured-mesh SLIM 3D hydrodynamic model was developed. The model was successfully validated against available field data. The results were compared to previous studies on the Burdekin River sediment transport and differences were analysed. Wind direction and speed during river floods largely control the dynamics and the fate of the fine sediment. Most (67% for 2007) of the riverine fine sediment load is deposited near the river mouth; the remaining sediment is transported further afield in a riverine freshwater plume; that sediment can reach sensitive marine ecosystems and should be a priority for management. During the rest of the year, when the river flow has ceased, wind-driven resuspension events redistribute the deposited sediment within embayments but generate negligible longshore transport. This study suggests that semi-open systems trap most of the riverine fine sediment, somewhat like semi-enclosed systems.@en