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Hydrodynamic modelling is an important tool for the development of tidal stream energy projects. Many hydrodynamic models incorporate the effect of tidal turbines through an enhanced bottom drag. In this paper we show that although for coarse grid resolutions (kilometre scale) the resulting force exerted on the flow agrees well with the theoretical value, the force starts decreasing with decreasing grid sizes when these become smaller than the length scale of the wake recovery. This is because the assumption that the upstream velocity can be approximated by the local model velocity, is no longer valid. Using linear momentum actuator disc theory however, we derive a relationship between these two velocities and formulate a correction to the enhanced bottom drag formulation that consistently applies a force that remains close to the theoretical value, for all grid sizes down to the turbine scale. In addition, a better understanding of the relation between the model, upstream, and actual turbine velocity, as predicted by actuator disc theory, leads to an improved estimate of the usefully extractable energy. We show how the corrections can be applied (demonstrated here for the models MIKE 21 and Fluidity) by a simple modification of the drag coefficient. [ABSTRACT FROM AUTHOR]

Coastal zones are vulnerable to both erosion and flood risk, which can be assessed using coupled hydro-morphodynamic models. However, the use of such models as decision support tools suffers from a high degree of uncertainty, due to both incomplete knowledge and natural variability in the system. In this work, we show for the first time how the multilevel Monte Carlo method (MLMC) can be applied in hydro-morphodynamic coastal ocean modelling, here using the popular model XBeach, to quantify uncertainty by computing statistics of key output variables given uncertain input parameters. MLMC accelerates the Monte Carlo approach through the use of a hierarchy of models with different levels of resolution. Several theoretical and real-world coastal zone case studies are considered here, for which output variables that are key to the assessment of flood and erosion risk, such as wave run-up height and total eroded volume, are estimated. We show that MLMC can significantly reduce computational cost, resulting in speed up factors of 40 or greater compared to a standard Monte Carlo approach, whilst keeping the same level of accuracy. Furthermore, a sophisticated ensemble generating technique is used to estimate the cumulative distribution of output variables from the MLMC output. This allows for the probability of a variable exceeding a certain value to be estimated, such as the probability of a wave run-up height exceeding the height of a seawall. This is a valuable capability that can be used to inform decision-making under uncertainty. • First use of MLMC (multilevel Monte Carlo) with a coupled hydro-morphodynamic model. • Large drop in computational cost for same accuracy using MLMC instead of Monte Carlo. • Determine the distribution of variables of interest in coastal zone cases using MLMC. [ABSTRACT FROM AUTHOR]

Abstract Turbulence-resolving simulations of wind turbine wakes are presented using a high-order flow solver combined with both a standard and a novel dynamic implicit spectral vanishing viscosity (iSVV and dynamic iSVV) model to account for subgrid-scale (SGS) stresses. The numerical solutions are compared against wind tunnel measurements, which include mean velocity and turbulent intensity profiles, as well as integral rotor quantities such as power and thrust coefficients. For the standard (also termed static) case the magnitude of the spectral vanishing viscosity is selected via a heuristic analysis of the wake statistics, while in the case of the dynamic model the magnitude is adjusted both in space and time at each time step. The study focuses on examining the ability of the two approaches, standard (static) and dynamic, to accurately capture the wake features, both qualitatively and quantitatively. The results suggest that the static method can become over-dissipative when the magnitude of the spectral viscosity is increased, while the dynamic approach which adjusts the magnitude of dissipation locally is shown to be more appropriate for a non-homogeneous flow such that of a wind turbine wake. • Investigation of the ability of SVV-LES techniques to provide high-fidelity solutions for wind turbine wakes. • Introduction of a novel implicit dynamic SVV technique. • Sensitivity analysis of the SVV magnitude in both the static and dynamic SVV methods for wind turbine wakes. [ABSTRACT FROM AUTHOR]

Highlights • We describe new optimisation approaches for improving the operational design of tidal power plants. • We demonstrate the value of flexible operation in maximising income from the Day Ahead energy market. • An income-based optimisation for a tidal lagoon case led to a 23% improvement in energy market income. • Tidal range power plants can have a short-term storage capability for generation during high-demand periods. Abstract Tidal range renewable power plants have the capacity to deliver predictable energy to the electricity grid, subject to the known variability of the tides. Tidal power plants inherently feature advantages that characterise hydro-power more generally, including a lifetime exceeding alternative renewable energy technologies and relatively low Operation & Maintenance costs. Nevertheless, the technology is typically inhibited by the significant upfront investment associated with capital costs. A key aspect that makes the technology stand out relative to other renewable options is the partial flexibility it possesses over the timing of power generation. In this study we provide details on a design methodology targeted at the optimisation of the temporal operation of a tidal range energy structure, specifically the Swansea Bay tidal lagoon that has been proposed within the Bristol Channel, UK. Apart from concentrating on the classical incentive of maximising energy, we formulate an objective functional in a manner that promotes the maximisation of income for the scheme from the Day-Ahead energy market. Simulation results demonstrate that there are opportunities to exploit the predictability of the tides and flexibility over the precise timing of power generation to incur a noticeable reduction in the subsidy costs that are often negotiated with regulators and governments. Additionally, we suggest that this approach should enable tidal range energy to play a more active role in ensuring security of supply in the UK. This is accentuated by the income-based optimisation controls that deliver on average more power over periods when demand is higher. For the Swansea Bay tidal lagoon case study a 23% increase is observed in the income obtained following the optimisation of its operation compared to a non-adaptive operation. Similarly, a 10% increase relative to an energy-maximisation approach over a year's operation suggests that simply maximising energy generation in a setting where power prices vary may not be an optimal strategy. [ABSTRACT FROM AUTHOR]

Highlights • A multi-layer non-hydrostatic coastal ocean model is developed using the discontinuous Galerkin finite element method. • The model is shown to predict nearshore dispersive wave processes accurately using only a small number of vertical layers. • Use of arbitrary unstructured meshes allows for non-uniform resolution and accurate representation of complex geometries. • Automated code generation techniques are employed promoting code efficiency, readability, extensibility and maintainability. Abstract A multi-layer non-hydrostatic version of the unstructured mesh, discontinuous Galerkin finite element based coastal ocean model, Thetis, is developed. This is accomplished using the PDE solver framework, Firedrake, which is used to automatically produce the code for the discretised model equations in a rapid and efficient manner. The motivation for this work is a need to accurately simulate dispersive nearshore free surface processes. In order to resolve both frequency dispersion and non-linear effects accurately, additional non-hydrostatic terms are included in the layer-integrated hydrostatic equations, producing a form similar to the layered non-linear shallow water equations, but with extra vertical velocities at the layer interfaces. An implementation process is adopted to easily handle the inter-layer connection, i.e. the governing equations are transformed into a depth-integrated system through the introduction of depth-averaged variables. The model is verified and validated through comparisons against several idealised and experimentally-based test cases. All the comparisons demonstrate good agreement, showing that the developed non-hydrostatic model has excellent capabilities in representing coastal wave phenomena including shoaling, refraction and diffraction of dispersive short waves, as well as propagation, run-up and inundation of non-linear tsunami waves. [ABSTRACT FROM AUTHOR]

Wind turbine wake modelling is of crucial importance to accurate resource assessment, to layout optimisation, and to the operational control of wind farms. This work proposes a surrogate model for the representation of wind turbine wakes based on a state-of-the-art graph representation learning method termed a graph neural network. The proposed end-to-end deep learning model operates directly on unstructured meshes and has been validated against high-fidelity data, demonstrating its ability to rapidly make accurate 3D flow field predictions for various inlet conditions and turbine yaw angles. The specific graph neural network model employed here is shown to generalise well to unseen data and is less sensitive to over-smoothing compared to common graph neural networks. A case study based upon a real world wind farm further demonstrates the capability of the proposed approach to predict farm scale power generation. Moreover, the proposed graph neural network framework is flexible and highly generic and as formulated here can be applied to any steady state computational fluid dynamics simulations on unstructured meshes. • A novel wind turbine wake model is developed based on graph representation learning. • The developed model can generate 3D wake field predictions rapidly and accurately. • The graph neural network employed is directly compatible with unstructured meshes. • The proposed model is validated on a real-scale wind farm. [ABSTRACT FROM AUTHOR]

Renewable energy is the cornerstone of preventing dangerous climate change whilst maintaining a robust energy supply. Tidal energy will arguably play a critical role in the renewable energy portfolio as it is both predictable and reliable, and can be put in place across the globe. However, installation may impact the local and regional ecology via changes in tidal dynamics, sediment transport pathways or bathymetric changes. In order to mitigate these effects, tidal energy devices need to be modelled, to predict hydrodynamic changes. Robust mesh generation is a fundamental component required for developing simulations with high accuracy. However, mesh generation for coastal domains can be an elaborate procedure. Here, we describe an approach combining mesh generators with Geographical Information Systems. We demonstrate robustness and efficiency by constructing a mesh with which to examine the potential environmental impact of a tidal turbine farm installation in the Orkney Islands. The mesh is then used with two well-validated ocean models, to compare their flow predictions with and without a turbine array. The results demonstrate that it is possible to create an easy-to-use tool to generate high-quality meshes for combined coastal engineering, here tidal turbines, and coastal ocean simulations. [ABSTRACT FROM AUTHOR]

Tidal power lagoons have the potential to provide a reliable and long-term source of renewable power. The implementation of tidal lagoons will impact the tidal conditions and hydrodynamics of the surrounding coastal system. Impact assessments in the academic literature have generally investigated working proposals from industry of various shapes and sizes. As such, differences between the impacts arising from considered power plants in varying sites are in part influenced by the individual scheme characteristics, potentially masking the influence of site-specific factors. In this study, scheme design consistency is maintained, providing a basis to focus solely on the merits of the selected locations with regards to any associated impacts. The simulated tidal power lagoons are located in the Bristol Channel and Irish Sea, two distinct but tidally connected regions on the British coastline with contrasting marine environment characteristics. Results indicate that the more constrained geometry of the Bristol Channel contributes to higher individual and cumulative impacts than potential developments in the Irish Sea. This is in part facilitated by the higher degree of blockage introduced by tidal lagoon developments in the Bristol Channel. Furthermore, far-field impacts are found to be less pronounced compared to predictions reported in tidal barrage modelling studies. • Consistent tidal lagoon design highlights influence of marine environment on impacts. • Impacts resulting from developments in Bristol Channel and Irish Sea combine linearly. • Cumulative impacts in the Bristol Channel notable in whole region. • Impacts of Irish Sea tidal lagoons more localised than in the Bristol Channel. [ABSTRACT FROM AUTHOR]

This work proposes a novel data-driven model capable of providing accurate predictions for the power generation of all wind turbines in wind farms of arbitrary layout, yaw angle configurations and wind conditions. The proposed model functions by encoding a wind farm into a fully connected graph and processing the graph representation through a graph transformer. The resultant graph transformer surrogate demonstrates robust generalisation capabilities and effectively uncovers latent structural patterns embedded within the graph representation of wind farms. The versatility of the proposed approach extends to the optimisation of yaw angle configurations through the application of genetic algorithms. This evolutionary optimisation strategy facilitated by the graph transformer surrogate achieves prediction accuracy levels comparable to industrially standard wind farm simulation tools, with a relative accuracy of more than 99% in identifying optimal yaw angle configurations of previously unseen wind farm layouts. An additional advantage lies in the significant reduction in computational costs, positioning the proposed methodology as a compelling tool for efficient and accurate wind farm optimisation. • A novel wind farm scale model is developed based on graph transformers. • Graph transformers can identify wake interactions within wind farms and accurately predict wind farm power. • The developed model generalises to diverse wind farm layouts and yaw angle configurations. • The proposed model achieves more than 99% accuracy when used as a surrogate for PyWake in yaw angle optimisation. [ABSTRACT FROM AUTHOR]

Abstract: Tsunamis are frequent events in modern marine environments but evidence of their passing in subtidal ancient epicontinental sea deposits is elusive. It has been suggested that this is due to mis-identification or poor preservation potential. Herein a numerical modelling approach is used to show that tsunami propagation in one large ancient epicontinental sea was hindered by the damping effect of shallow bathymetries and reflection, refraction and diffraction from emergent landmasses. The Imperial College Ocean Model (ICOM) is used for this study and is first validated against data from the Sumatra–Andaman Tsunami of December 2004. A palaeobathymetric dataset is then presented for the Hettangian (Lower Jurassic) Laurasian Seaway with idealised tsunami sources situated on the continental shelf and within the adjacent oceanic basin. Results show that tsunamis forced from within ocean basins adjacent to the epicontinental sea are rapidly attenuated over the continental slope and fail to propagate great distances onto the shelf. Similarly, the sedimentological effect of tsunamis forced from within the epicontinental sea is also restricted. It is concluded that tsunami deposits in ancient epicontinental seas are most likely to occur in relative proximity to the source region and this must contribute to their scarcity in the geological record. [Copyright &y& Elsevier]

Numerical storm surge models are essential to forecasting coastal flood hazard and informing the design of coastal defences. However, such models rely on a variety of inputs, many of which carry uncertainty. An awareness and understanding of the sensitivity of model outputs with respect to those uncertain inputs is therefore essential when interpreting model results. Here, we use an unstructured-mesh numerical coastal ocean model, Thetis , and its adjoint, to perform a sensitivity analysis for a hindcast of the 5th/6th December 2013 North Sea surge event, with respect to the bottom friction coefficient, bathymetry and wind stress forcing. The results reveal spatial and temporal patterns of sensitivity, providing physical insight into the mechanisms of surge generation and propagation. For example, the sensitivity of the skew surge to the bathymetry reveals the protective effect of a sand bank off the UK east coast. The results can also be used to propagate uncertainties through the numerical model; based on estimates of model input uncertainties, we estimate that modelled skew surges carry uncertainties of around 5 cm and 15 cm due to bathymetry and bottom friction, respectively. While these uncertainties are small compared with the typical spread in an ensemble storm surge forecast due to uncertain meteorological inputs, the adjoint-derived model sensitivities can nevertheless be used to inform future model calibration and data acquisition efforts in order to reduce uncertainty. Our results demonstrate the power of adjoint methods to gain insight into a storm surge model, providing information complementary to traditional ensemble uncertainty quantification methods. • We calibrate an unstructured-mesh finite element storm surge model of the North Sea • We use an adjoint approach to perform sensitivity analysis for modelled skew surges • We compare spatial and temporal patterns of sensitivity with respect to three inputs • We demonstrate the physical insight available through numerical adjoint methods. [ABSTRACT FROM AUTHOR]

Wind farm modelling is an area of rapidly increasing interest with numerous analytical and computational-based approaches developed to extend the margins of wind farm efficiency and maximise power production. In this work, we present the novel ML framework WakeNet, which reproduces generalised 2D turbine wake velocity fields at hub-height, with a mean accuracy of 99.8% compared to the solution calculated by the state-of-the-art wind farm modelling software FLORIS. As the generation of sufficient high-fidelity data for network training purposes can be cost-prohibitive, the utility of multi-fidelity transfer learning has also been investigated. Specifically, a network pre-trained on the low-fidelity Gaussian wake model is fine-tuned in order to obtain accurate wake results for the mid-fidelity Curl wake model. The overall performance of WakeNet is validated on various wake steering control and layout optimisation scenarios, obtaining at least 90% of the power gained by the FLORIS optimiser. Moreover, the Curl-based WakeNet provides similar power gains to FLORIS, two orders of magnitude faster. These promising results show that generalised wake modelling with ML tools can be accurate enough to contribute towards robust real-time active yaw and layout optimisation under uncertainty, while producing realistic optimised configurations at a fraction of the computational cost. • WakeNet produces generalised wakes 2 orders of magnitude faster than the Curl model. • The local turbulence and generated power can be approximated from 2D flow predictions. • Multi-fidelity transfer learning reduces the mid-fidelity data required for training. • WakeNet performs yaw and layout optimisation 2 orders of magnitude faster than FLORIS. • Deep Learning can produce fast realistic optimised wind farm configurations. [ABSTRACT FROM AUTHOR]

A σ -coordinate non-hydrostatic coastal ocean model is developed using the discontinuous Galerkin finite element method. With the selection of the low-order piecewise-constant P 0 DG and piecewise-linear P 1 DG discretisations in the vertical for the velocity and pressure fields, respectively, the proposed σ -coordinate model can naturally retain the wave dispersion characteristics of the widely-adopted multi-layer approach of Zijlema and Stelling (2005), which is demonstrated through both mathematical derivation and numerical tests. Under the finite element approach, higher-order vertical discretisation choices can also be readily made which can reduce the number of vertical layers required for the accurate representation of wave dispersion. The model is verified and validated through comparisons against a series of test cases with analytical solutions or experimental measurements. All the comparisons demonstrate good agreement, indicating that the proposed model can accurately represent dispersive barotropic surface waves with as few as one vertical layer, and can simulate baroclinic internal waves with reasonable accuracy using relatively coarse mesh resolution. It is also demonstrated that consistency in the coupling of barotropic and baroclinic flows can be properly ensured. • A σ -coordinate non-hydrostatic model is developed using the discontinuous Galerkin method. • The model can accurately represent dispersive barotropic surface waves with as few as one vertical layer. • The model can simulate baroclinic dynamics with reasonable accuracy using relatively coarse mesh resolution. • Theoretical links between the σ -formulation, the multi-layer approach and the ALE technique are established. [ABSTRACT FROM AUTHOR]

Tidal energy is one of the most predictable forms of renewable energy. Although there has been much commercial and R&D progress in tidal stream energy, tidal range is a more mature technology, with tidal range power plants having a history that extends back over 50 years. With the 2017 publication of the “Hendry Review” that examined the feasibility of tidal lagoon power plants in the UK, it is timely to review tidal range power plants. Here, we explain the main principles of tidal range power plants, and review two main research areas: the present and future tidal range resource, and the optimization of tidal range power plants. We also discuss how variability in the electricity generated from tidal range power plants could be partially offset by the development of multiple power plants (e.g. lagoons) that are complementary in phase, and by the provision of energy storage. Finally, we discuss the implications of the Hendry Review, and what this means for the future of tidal range power plants in the UK and internationally. [ABSTRACT FROM AUTHOR]

Tidal range power plants represent an attractive approach for the large-scale generation of electricity from the marine environment. Even though the tides and by extension the available energy resource are predictable, they are also variable in time. This variability poses a challenge regarding the optimal transient control of power plants. We consider simulation methods which include the main modes of operation of tidal power plants, along with algorithms to regulate the timing of these. This paper proposes a framework where simplified power plant operation models are coupled with gradient-based optimisation techniques to determine the optimal control strategy over multiple tidal cycles. The optimisation results inform coastal ocean simulations that include tidal power plants to gauge whether the benefits of an adaptive operation are preserved once their hydrodynamic impacts are also taken into consideration. The combined operation of two prospective tidal lagoon projects within the Bristol Channel and the Severn Estuary is used as an example to demonstrate the potential benefits of an energy maximisation optimisation approach. For the case studies considered, the inclusion of pumping and an adaptive operation is shown to deliver an overall increase in energy output of 20–40% compared to a conventional two-way uniform operation. The findings also demonstrate that smaller schemes stand to gain more from operational optimisation compared to designs of a larger scale. [ABSTRACT FROM AUTHOR]

Numerical studies of ice flow have consistently identified the grounding zone of outlet glaciers and ice streams (the region where ice starts to float) as crucial for predicting the rate of grounded ice loss to the ocean. Owing to the extreme environments and difficulty of access to ocean cavities beneath ice shelves, field observations are rare. Estimates of melt rates derived from satellites are also difficult to make near grounding zones with confidence. Therefore, numerical ocean models are important tools to investigate these critical and remote regions. The relative inflexibility of structured grid models means, however, that they can struggle to resolve these processes in irregular cavity geometries near grounding zones. To help solve this issue, we present a new nonhydrostatic unstructured mesh model for flow under ice shelves built using the Firedrake finite element framework. We demonstrate our ability to simulate full ice shelf cavity domains using the community standard ISOMIP+ Ocean0 test case and compare our results against those obtained with the popular MITgcm model. Good agreement is found between the two models, despite their use of different discretisation schemes and the sensitivity of the melt rate parameterisation to grid resolution. Verification tests based on the Method of Manufactured Solutions (MMS) show that the new model discretisation is sound and second-order accurate. A main driver behind using Firedrake is the availability of an automatically generated adjoint model. Our first adjoint calculations, of sensitivities of melt rate with respect to different inputs in an idealised grounding zone domain, are promising and point to the ability to address a number of important questions on ocean influence on ice shelf vulnerability in the future. • New model for ocean flow beneath ice shelves on flexible unstructured meshes. • 2nd-order accurate discretisation verified by Method of Manufactured Solution test. • Good agreement with MITgcm is found for the ISOMIP+ 3D test case. • Preliminary adjoint results show significant potential for ice-ocean applications. [ABSTRACT FROM AUTHOR]

Groundwater heat pump systems cause thermal anomalies in the aquifer that can impact upon downstream systems and reduce their efficiency. Therefore, it is important to optimally position the extraction and injection wells of such systems to avoid negative interactions and maximize the thermal potential of the aquifer. This paper presents a new method to determine optimal well layouts of groundwater heat pumps using the adjoint approach, which is an efficient way to solve the underlying PDE-constrained optimization problem. An integral part of the method is the numerical groundwater simulation, which here is based on the finite element method. In addition, a multi-start initialization strategy is introduced in an attempt to better reach the global optimum. The method is applied to a real case study with 10 groundwater heat pumps, i.e. 20 wells, and two optimization scenarios with different natural groundwater temperatures. In both scenarios, the optimization method successfully determines a well layout that maximizes groundwater temperatures at all extraction wells. Comparing the results from these scenarios demonstrates that hydro-geological conditions can have a significant impact on the optimal well layout. The proposed method is equally applicable to systems with multiple extraction and injection wells and can be extended to various other shallow geothermal applications, such as combined heating and cooling systems. • A new optimization method for well layouts of groundwater heat pumps is introduced. • The method is a gradient-based optimization that uses the adjoint approach. • The new method allows for continuous well locations and a large number of wells. • It can be used to find optimal well layouts of several neighboring or single systems. • A real case study with 10 systems is used to demonstrate the method's applicability. [ABSTRACT FROM AUTHOR]

Tsunami generated by submarine slides are arguably an under-considered risk in comparison to earthquake-generated tsunami. Numerical simulations of submarine slide-generated waves can be used to identify the important factors in determining wave characteristics. Here we use Fluidity, an open source finite element code, to simulate waves generated by deformable submarine slides. Fluidity uses flexible unstructured meshes combined with adaptivity which alters the mesh topology and resolution based on the simulation state, focussing or reducing resolution, when and where it is required. Fluidity also allows a number of different numerical approaches to be taken to simulate submarine slide deformation, free-surface representation, and wave generation within the same numerical framework. In this work we use a multi-material approach, considering either two materials (slide and water with a free surface) or three materials (slide, water and air), as well as a sediment model (sediment, water and free surface) approach. In all cases the slide is treated as a viscous fluid. Our results are shown to be consistent with laboratory experiments using a deformable submarine slide, and demonstrate good agreement when compared with other numerical models. The three different approaches for simulating submarine slide dynamics and tsunami wave generation produce similar waveforms and slide deformation geometries. However, each has its own merits depending on the application. Mesh adaptivity is shown to be able to reduce the computational cost without compromising the accuracy of results. [ABSTRACT FROM AUTHOR]

The development of reliable, sophisticated hydro-morphodynamic models is essential for protecting the coastal environment against hazards such as flooding and erosion. There exists a high degree of uncertainty associated with the application of these models, in part due to incomplete knowledge of various physical, empirical and numerical closure related parameters in both the hydrodynamic and morphodynamic solvers. This uncertainty can be addressed through the application of adjoint methods. These have the notable advantage that the number and/or dimension of the uncertain parameters has almost no effect on the computational cost associated with calculating the model sensitivities. Here, we develop the first freely available and fully flexible adjoint hydro-morphodynamic model framework. This flexibility is achieved through using the pyadjoint library, which allows us to assess the uncertainty of any parameter with respect to any model functional, without further code implementation. The model is developed within the coastal ocean model Thetis constructed using the finite element code-generation library Firedrake. We present examples of how this framework can perform sensitivity analysis, inversion and calibration for a range of uncertain parameters based on the final bedlevel. These results are verified using so-called dual-twin experiments, where the 'correct' parameter value is used in the generation of synthetic model test data, but is unknown to the model in subsequent testing. Moreover, we show that inversion and calibration with experimental data using our framework produces physically sensible optimum parameters and that these parameters always lead to more accurate results. In particular, we demonstrate how our adjoint framework can be applied to a tsunami-like event to invert for the tsunami wave from sediment deposits. • Development of first free and fully flexible adjoint hydro-morphodynamic framework. • Verification of adjoint capabilities using dual-twin experiments. • Application of adjoint methods to analyse sensitivity to spatially-varying parameters. • Use of adjoint methods to calibrate for several uncertain parameters in an experiment. • Inversion of a tsunami-like wave using final sediment deposits from experimental data. [ABSTRACT FROM AUTHOR]

Laboratory experiments and numerical simulations have shown that volcanic ash particles immersed in water can either settle slowly and individually, or rapidly and collectively as particle-laden plumes. The ratio of timescales for individual and collective settling, in the form of analytical expressions, provides a dimensionless quantitative measure of the tendency for such plumes to grow and persist which has important implications for determining particle residence times and deposition rates. However, existing measures in the literature assume that collective settling obeys Stokes' law and is therefore controlled by the balance between gravitational forces and viscous drag, despite plume development actually being controlled by the balance between gravitational forces and inertial drag even in the absence of turbulence during early times. This paper presents a new measure for plume onset which takes into account the inertial drag-controlled (rather than viscous drag-controlled) nature of plume growth and descent. A parameter study comprising a set of numerical simulations of small-scale volcanic ash particle settling experiments highlights the effectiveness of the new measure and, by comparison with an existing measure in the literature, also demonstrates that the timescale of collective settling is grossly under-estimated when assuming that plume development is slowed by viscous drag. Furthermore, the formulation of the new measure means that the tendency for plumes to form can be estimated from the thickness and concentration of the final deposit; the magnitude and duration of particle flux across the water's surface do not need to be known. The measure therefore permits the residence times of particles in a large body of water to be more accurately and practically determined, and allows the improved interpretation of layers of volcaniclastic material deposited at the seabed. [ABSTRACT FROM AUTHOR]

The ∼8.15 ka Storegga submarine slide was a large (∼3000 km 3 ), tsunamigenic slide off the coast of Norway. The resulting tsunami had run-up heights of around 10–20 m on the Norwegian coast, over 12 m in Shetland, 3–6 m on the Scottish mainland coast and reached as far as Greenland. Accurate numerical simulations of Storegga require high spatial resolution near the coasts, particularly near tsunami run-up observations, and also in the slide region. However, as the computational domain must span the whole of the Norwegian-Greenland sea, employing uniformly high spatial resolution is computationally prohibitive. To overcome this problem, we present a multiscale numerical model of the Storegga slide-generated tsunami where spatial resolution varies from 500 m to 50 km across the entire Norwegian-Greenland sea domain to optimally resolve the slide region, important coastlines and bathymetric changes. We compare results from our multiscale model to previous results using constant-resolution models and show that accounting for changes in bathymetry since 8.15 ka, neglected in previous numerical studies of the Storegga slide-tsunami, improves the agreement between the model and inferred run-up heights in specific locations, especially in the Shetlands, where maximum run-up height increased from 8 m (modern bathymetry) to 13 m (palaeobathymetry). By tracking the Storegga tsunami as far south as the southern North sea, we also found that wave heights were high enough to inundate Doggerland, an island in the southern North Sea prior to sea level rise over the last 8 ka. [ABSTRACT FROM AUTHOR]

This paper applies metric-based mesh adaptation methods to advection-dominated tracer transport modelling problems in two and three dimensions, using the finite element package Firedrake. In particular, the mesh adaptation methods considered are built upon goal-oriented estimates for the error incurred in evaluating a diagnostic quantity of interest (QoI). In the motivating example of modelling to support desalination plant outfall design, such a QoI could be the salinity at the plant inlet, which could be negatively impacted by the transport of brine from the plant's outfall. Four approaches are considered, one of which yields isotropic meshes. The focus on advection-dominated problems means that flows are often anisotropic; thus, three anisotropic approaches are also considered. Meshes resulting from each of the four approaches yield solutions to the tracer transport problem which give better approximations to QoI values than uniform meshing, for a given mesh size. The methodology is validated using an existing 2D tracer transport test case with a known analytical solution. Goal-oriented meshes for an idealised time-dependent desalination outfall scenario are also presented. • Derivation of a goal-oriented error estimate for tracer transport modelling. • Implementation and comparison of four goal-oriented mesh adaptation approaches. • Validation against an established test case with an analytical solution. • Application of goal-oriented adaptation to an idealised desalination outfall problem. [ABSTRACT FROM AUTHOR]

Tidal currents represent an attractive renewable energy source particularly because of their predictability. Prospective tidal stream development sites are often co-located in close proximity. Under such circumstances, in order to maximise the exploitation of the resource, multiple tidal stream turbine arrays working in tandem would be needed. In this paper, a continuous array optimisation approach based on the open source coastal ocean modelling framework Thetis is applied to derive optimal configurations for four turbine arrays around Zhoushan Islands, Zhejiang Province, China. Alternative optimisation scenarios are tested to investigate interactions between the turbine arrays and their hydrodynamic footprint. Results show that there are no obvious competition effects between these four arrays around Hulu and Taohua Island. However, significant interactions could arise among the three turbine arrays situated around Hulu Island, with a maximum decrease in average power of 42.2%. By optimising all turbine arrays simultaneously, the competition effects can be minimised and the cost of energy reduced as less turbines are required to deliver an equivalent energy output. As for the potential environmental impact, it is found that the turbine array around Taohua Island would affect a larger area than turbine arrays around Hulu Island. • Demonstrate superior hydrodynamic modelling of Thetis over OpenTidalFarm. • Present a tidal array optimisation approach around Zhoushan islands. • Investigate interactions between near-field/far-field tidal arrays. • Quantify hydrodynamic impact of tidal arrays around Hulu and Taohua islands. • Exhibit an optimisation methodology transferable to multi-array applications. [ABSTRACT FROM AUTHOR]

Ancient shoreline–shelf depositional systems are influenced by an unusually wide array of geological, biological and hydrodynamic processes, with sediment transport and deposition primarily determined by the interaction of river, wave (including storm) and tidal processes, and changes in relative sea level. Understanding the impact of these processes on shoreline–shelf morphodynamics and stratigraphic preservation remains challenging. Numerical modelling integrated with traditional facies analysis provides an increasingly viable approach, with the potential to quantify, and thereby improve understanding of, the impact of these complex coastal sedimentary processes. An integrated approach is presented here that focuses on palaeotidal modelling to investigate the controls on ancient tides and their influence on sedimentary deposition and preservation – one of the three cornerstones of the ternary process classification scheme of shoreline-shelf systems. Numerical tidal modelling methodology is reviewed and illustrated in three palaeotidal model case studies of different scales and focus. The results are synthesised in the context of shoreline–shelf processes, including a critique and modification of the process-based classification scheme. The emphasis on tidal processes reflects their global importance throughout Earth's history. Ancient palaeotidal models are able to highlight and quantify the following four controls on tidal processes: (1) the physiography (shape and depth) of oceans (1000s km scale) determines the degree of tidal resonance; (2) the physiography of ocean connections to partly enclosed water bodies (100–1000s km scale) determines the regional-scale flux of tidal energy (inflow versus outflow); (3) the physiography of continental shelves influences shelf tidal resonance potential; and (4) tides in relatively local-scale embayments (typically 1–10s km scale) are influenced by the balance of tidal amplification due to funnelling, shoaling and resonance effects versus frictional damping. In deep time, palaeogeographic and palaeobathymetric uncertainty can be accounted for in palaeotidal models by performing sensitivity analyses to different scenarios, across this range of spatial scales. These tidal process controls are incorporated into an updated predictive decision tree for determining shoreline–shelf process regime in terms of the relative interaction of wave, fluvial and tidal processes. The predictive decision tree considers the effects of basin physiography, shelf width and shoreline morphology on wave, fluvial and tidal processes separately. Uncertainty and ambiguity in applying the widely used three-tier process classification scheme are reduced by using the decision tree in conjunction with a proposed two-tier classification of process regime that is limited to primary and secondary processes. This two-tier classification scheme is illustrated in the three case studies, showing how integration of numerical modelling with facies analysis of the preserved stratigraphic record improves confidence in prediction of tide-influenced shoreline-shelf process regimes. Wider application of this approach will further improve process-based classifications and predictions of modern and ancient shoreline–shelf systems. [ABSTRACT FROM AUTHOR]

Highlights: [•] Ocean circulation beneath ice shelves is simulated using an unstructured-mesh. [•] We represent a smoothly varying ice base in the presence of a vertical ice front. [•] We implemented ice shelf/ocean interaction in the context of finite-element method. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the reactivity during a transient of a layered MOX, and moderating lubricant (zinc stearate) mixing system which is used as part of fuel processing. The reactivity effects with increases in temperature and mixing (moderation) are investigated here. The transient and static simulations reveal that large increases in reactivity and temperature are possible. The nuclear criticality modelling of powders is performed using the Finite Element Transient Criticality (FETCH) code. This models criticality transients in spatial and temporal detail using a continuum multi-fluid model of the gas and solid-powder phases. The neutronics model in FETCH solves the neutron transport in full phase space. In this study a number of hypothetical criticality scenarios with the same generic mixing device and MOX powder are investigated in order to gain an understanding of the dynamics of powder criticality. An additive zinc stearate is also introduced. The zinc stearate, can act as a moderator and thus, on mixing, a ramp reactivity can be introduced. The mixing device is introduced into the simulations to help investigate this ramp reactivity. [Copyright &y& Elsevier]

• Variable friction based on seabed morphology aids hydrodynamic model calibration. • High mesh refinement required to capture small but influential bathymetric features. • Implications of these model configurations for tidal energy developments are discussed Representation of the marine environment is key for reliable coastal hydrodynamic models. This study investigates the implications of common depth-averaged model configuration choices in sufficiently characterising seabed geometry and roughness. In particular, applications requiring a high level of accuracy and/or exhibiting complex flow conditions may call for greater detail in marine environment representation than typically adopted in coastal models. Ramsey Sound, a macrotidal strait in Pembrokeshire, Wales, UK is considered as a case study. The site contains various steeply inclined bathymetric features, including a submerged pinnacle named Horse Rock and a rocky reef called "The Bitches". The available energy in Ramsey Sound's tidal currents has attracted attention from tidal energy developers. There is interest in accurately modelling the energetic hydrodynamics surrounding its pronounced bathymetry. The coastal flow solver Thetis is applied to simulate the flow conditions in Ramsey Sound. It is shown that notable prominent bathymetric features in the strait influence localised and, most importantly, regional hydrodynamic characteristics. "The Bitches" consistently accelerate flow in the strait while Horse Rock induces a notable wake structure and flow reversals. The model is calibrated against bed- and vessel-mounted Acoustic Doppler Current Profiler (ADCP) observations, by altering seabed roughness parameterisations. A spatially variable and locally scaled Manning coefficient based on diverse seabed classification observations is found to improve model performance in comparison to uniformly applied constants, the latter a more common approach. The local impact of altering the Manning coefficient configuration is found to be greatest during spring flood periods of high velocity currents. Meanwhile, the effect of coarsening the computational mesh around bathymetric features towards values more typically applied in coastal models is investigated. Results indicate severe misrepresentation of seabed geometry and subsequent wake hydrodynamics unless refined to a mesh element size that adequately represents Horse Rock and "The Bitches". [ABSTRACT FROM AUTHOR]

The development of morphodynamic models to simulate sediment transport accurately is a challenging process that is becoming ever more important because of our increasing exploitation of the coastal zone, as well as sea-level rise and the potential increase in strength and frequency of storms due to a changing climate. Morphodynamic models are highly complex given the non-linear and coupled nature of the sediment transport problem. Here we implement a new depth-averaged coupled hydrodynamic and sediment transport model within the coastal ocean model Thetis , built using the code generating framework Firedrake which facilitates code flexibility and optimisation benefits. To the best of our knowledge, this represents the first full morphodynamic model including both bedload and suspended sediment transport which uses a discontinuous Galerkin based finite element discretisation. We implement new functionalities within Thetis extending its existing capacity to model scalar transport to modelling suspended sediment transport, incorporating within Thetis options to model bedload transport and bedlevel changes. We apply our model to problems with non-cohesive sediment and account for effects of gravity and helical flow by adding slope gradient terms and parametrising secondary currents. For validation purposes and in demonstrating model capability, we present results from test cases of a migrating trench and a meandering channel comparing against experimental data and the widely-used model Telemac-Mascaret. • Implementation of a new morphodynamic model within a code generating framework. • Novel use of discontinuous Galerkin based finite element methods to solve this system. • Model simulates suspended and bedload transport with gravity and helical flow effects. • Successful validation evidence through standard trench migration and meander cases. [ABSTRACT FROM AUTHOR]

Large tsunamis can be generated by submarine slides, but these events are rare on human timescales and challenging to observe. Experiments and numerical modelling offer methods to understand the mechanisms by which they generate waves and what the potential hazard might be. However, to fully capture the complex waveform generated by a submarine slide, the slide dynamics must also be accurately modelled. It is computationally difficult to model both a three-dimensional submarine slide whilst simultaneously simulating oceanic-scale tsunamis. Past studies have either coupled localised models of the slide generation to oceanic-scale tsunami simulations or simplified the slide dynamics. Here, we present a new methodology of model coupling that generates the wave in the ocean-scale model via boundary-condition coupling of a two-dimensional dynamic slide simulation. We verify our coupling methodology by comparing model results to a previous simulation of a tsunamigenic slide in the Gulf of Mexico. We then examine the effect of slide deformation on the risk posed by hypothetical submarine slides around the UK. We show the deformable submarine slide simulations produce larger waves than the solid slide simulations due to the details of acceleration and velocity of the slide, although lateral spreading is not modelled. This work offers a new methodology for simulating oceanic-scale tsunamis caused by submarine slides using the output of a two-dimensional, multi-material simulation as input into a three-dimensional ocean model. This facilitates future exploration of the tsunami risk posed by tsunamigenic submarine slides that affect coastlines not normally prone to tsunamis. • Numerical modelling framework simulates tsunami waves generated by deformable submarine slides. • Predicted waves agree with numerical model for waves generated by submarine slide in Gulf of Mexico. • Used methodology to simulate waves from hypothetical submarine slides around the UK. • We show how slide speed, acceleration, deformation and direction affect the wave. [ABSTRACT FROM AUTHOR]

The unstructured mesh, discontinuous Galerkin finite element discretisation based coastal ocean model, Thetis , has been extended to include non-hydrostatic (buoyancy-driven and free surface) dynamics. Two alternative approaches to achieve this are described in this work. The first (a 3D based algorithm) makes use of prismatic element based meshes and uses a split-step pressure projection method for baroclinic and barotropic modes, while the second (a 2D based algorithm) adopts a novel multi-layer approach to convert a 3D problem into a combination of multiple 2D computations with only 2D triangle meshes required. Model development is carried out at high-level with the Firedrake library, using code generation techniques to automatically produce low-level code for the discretised model equations in an efficient and rapid manner. Through comparisons against several barotropic/baroclinic test cases where non-hydrostatic effects are important, the implemented approaches are verified and validated, and the proposed algorithms compared. Depending on whether the problems are dominated by dispersive, baroclinic or barotropic features, recommendation are given over the use of full 3D or multi-layer 2D based approaches to achieve optimal computational accuracy and efficiency. It is demonstrated that while in general the 2D approach is well-suited for barotropic problems and dispersive free surface waves, the 3D approach is more advantageous for simulating baroclinic buoyancy-driven flows due in part to the high vertical resolution typically required to represent the active tracer fields. • A non-hydrostatic discontinuous finite element coastal ocean model is presented. • Two non-hydrostatic extensions are compared showing respective advantages. • Both algorithms are validated using several barotropic/baroclinic test cases. • The model development is carried out using a code generation framework, Firedrake. • The model is able to provide accurate reproduction of surface and exchange flows. [ABSTRACT FROM AUTHOR]