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For tidal-stream energy to become a competitive renewable energy source, clustering multiple turbines into arrays is paramount. Array optimisation is thus critical for achieving maximum power performance and reducing cost of energy. However, ascertaining an optimal array layout is a complex problem, subject to specific site hydrodynamics and multiple inter-disciplinary constraints. In this work, we present a novel optimisation approach that combines an analytical-based wake model, FLORIS, with an ocean model, Thetis. The approach is demonstrated through applications of increasing complexity. By utilising the method of analytical wake superposition, the addition or alteration of turbine position does not require re-calculation of the entire flow field, thus allowing the use of simple heuristic techniques to perform optimisation at a fraction of the computational cost of more sophisticated methods. Using a custom condition-based placement algorithm, this methodology is applied to the Pentland Firth for arrays with turbines of $$3.05\,\hbox {m}/\hbox {s}$$ 3.05 m / s rated speed, demonstrating practical implications whilst considering the temporal variability of the tide. For a 24-turbine array case, micro-siting using this technique delivered an array 15.8% more productive on average than a staggered layout, despite flow speeds regularly exceeding the rated value. Performance was evaluated through assessment of the optimised layout within the ocean model that treats turbines through a discrete turbine representation. Used iteratively, this methodology could deliver improved array configurations in a manner that accounts for local hydrodynamic effects.

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.

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., 20 pages, 12 figures

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.

When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high fidelity models being more expensive than low fidelity ones. However, when assessing uncertainty, we can use a multifidelity approach to take advantage of the accuracy of high fidelity models and the computational efficiency of low fidelity models. Here, we apply the multilevel multifidelity Monte Carlo method (MLMF) to quantify uncertainty by computing statistical estimators of key output variables with respect to uncertain inputs, using the high fidelity hydrodynamic model XBeach and the lower fidelity coastal flooding model SFINCS. The multilevel aspect opens up the further advantageous possibility of applying each of these models at multiple resolutions. This work represents the first application of MLMF in the coastal zone and one of its first applications in any field. For both idealised and real-world test cases, MLMF can significantly reduce computational cost for the same accuracy compared to both the standard Monte Carlo method and to a multilevel approach utilising only a single model (the multilevel Monte Carlo method). In particular, here we demonstrate using the case of Myrtle Beach, USA, that this improvement in computational efficiency allows in-depth uncertainty analysis to be conducted in the case of real-world coastal environments – a task that would previously have been practically unfeasible. Moreover, for the first time, we show how an inverse transform sampling technique can be used to accurately estimate the cumulative distribution function (CDF) of variables from the MLMF outputs. MLMF based estimates of the expectations and the CDFs of the variables of interest are of significant value to decision makers when assessing risk.

Numerical modelling frequently involves a diagnostic quantity of interest (QoI) - often of greater importance than the PDE solution - which we seek to accurately approximate. In the case of coastal ocean modelling the power output of a tidal turbine farm is one such example. Goal-oriented error estimation and mesh adaptation can be used to provide meshes which are well-suited to achieving this goal, using fewer computational resources than required by other methods, such as uniform refinement. A mixed discontinuous/continuous Galerkin approach is applied to solve the nonlinear shallow water equations within the Thetis coastal ocean finite element model. An implementation of goal-oriented mesh adaptation is outlined, including an error estimate which takes account of the discontinuities in the discrete solution and a method for approximating the adjoint error. Results are presented for simulations of two model tidal farm configurations. Convergence analysis indicates that the anisotropic goal-oriented adaptation strategy yields meshes which permit accurate QoI estimation using fewer computational resources than uniform refinement.

The Maldives face the threat of tsunamis from a multitude of sources. However, the limited availability of critical data, such as bathymetry (a recurrent problem for many island nations), has meant that the impact of these threats has not been studied at an island scale. Studies of tsunami propagation at the island scale but across multiple Atolls is also a challenging task due to the large domain and high resolution required for modelling. Here we use a high resolution bathymetry dataset of the Maldives archipelago, and corresponding high numerical model resolution, to carry out a scenario-based tsunami hazard assessment for the entire Maldives archipelago to investigate the potential impact of plausible far-field tsunamis across the Indian Ocean at the island scale. The results indicate that the bathymetry of the Atolls, which are characterized by very steep boundaries offshore, is extremely efficient in absorbing and redirecting incoming tsunami waves. Results also highlight the importance that local effects have in modulating tsunami amplitude nearshore, including the location of the Atoll in question, the location of a given island within the Atoll, and the distance of that island to the reef, as well as a variety of other factors. We also find that the refraction and diffraction of tsunami waves within individual Atolls contribute to the maximum tsunami amplitude patterns observed across the islands in the Atolls. The findings from this study contribute to a better understanding of tsunamis across complex Atoll systems, and will help decision and policy makers in the Maldives asses the potential impact of tsunamis across individual islands. An online tool is provided which presents users with a simple interface allowing the wider community to browse the simulation results presented here and assess the potential impact of tsunamis at the local scale.

International audience; 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.

When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high-fidelity models being more expensive than low-fidelity ones. However, when assessing uncertainty, we can use a multifidelity approach to take advantage of the accuracy of high-fidelity models and the computational efficiency of low-fidelity models. Here, we apply the multilevel multifidelity Monte Carlo method (MLMF) to quantify uncertainty by computing statistical estimators of key output variables with respect to uncertain input data, using the high-fidelity hydrodynamic model XBeach and the lower-fidelity coastal flooding model SFINCS (Super-Fast INundation of CoastS). The multilevel aspect opens up the further advantageous possibility of applying each of these models at multiple resolutions. This work represents the first application of MLMF in the coastal zone and one of its first applications in any field. For both idealised and real-world test cases, MLMF can significantly reduce computational cost for the same accuracy compared to both the standard Monte Carlo method and to a multilevel approach utilising only a single model (the multilevel Monte Carlo method). In particular, here we demonstrate using the case of Myrtle Beach, South Carolina, USA, that this improvement in computational efficiency allows for in-depth uncertainty analysis to be conducted in the case of real-world coastal environments – a task that would previously have been practically unfeasible. Moreover, for the first time, we show how an inverse transform sampling technique can be used to accurately estimate the cumulative distribution function (CDF) of variables from the MLMF outputs. MLMF-based estimates of the expectations and the CDFs of the variables of interest are of significant value to decision makers when assessing uncertainty in predictions.

Hydro-morphodynamic modelling is an important tool that can be used in the protection of coastal zones. The models can be required to resolve spatial scales ranging from sub-metre to hundreds of kilometres and are computationally expensive. In this work, we apply mesh movement methods to a depth-averaged hydro-morphodynamic model for the first time, in order to tackle both these issues. Mesh movement methods are particularly well-suited to coastal problems as they allow the mesh to move in response to evolving flow and morphology structures. This new capability is demonstrated using test cases that exhibit complex evolving bathymetries and have moving wet-dry interfaces. In order to be able to simulate sediment transport in wet-dry domains, a new conservative discretisation approach has been developed as part of this work, as well as a sediment slide mechanism. For all test cases, we demonstrate how mesh movement methods can be used to reduce discretisation error and computational cost. We also show that the optimum parameter choices in the mesh movement monitor functions are fairly predictable based upon the physical characteristics of the test case, facilitating the use of mesh movement methods on further problems.

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.

D.C., J.M., P.T. and S.W. acknowledge the financial support of the Tidal Stream Industry Energiser project (TIGER), which is co-financed by the European Regional Development Fund through the Interreg France (Channel) England Programme. A.A. acknowledges the support of NERC through the Industrial Innovation fellowship grant no. NE/R013209/2. D.G., B.S., T.S., D.W., R.W. and B.W. acknowledge EPSRC for supporting part of this work through EP/S000747/1. G.H. and C.S. acknowledge support by the Scottish government-funded Marine Mammal Scientific Support Programme MMSS/002 with additional resources from the Natural Environment Research Council grant nos. NE/R014639/1 and NE/R015007/1. M.L. acknowledges the support of the Smart Efficient Energy Centre (SEEC) at Bangor University, part-funded by the European Regional Development Fund (ERDF), administered by the Welsh Government, and the EPSRC METRIC fellowship grant no. (EP/R034664/1). L.M. acknowledges the financial support of an EPSRC PhD studentship award, grant no. EP/R513052/1(18-22). J.McN. acknowledges the financial support of R.Willden’s EPSRC Advanced Fellowship grant no. EP/R007322/1. S.N. acknowledges the support of SEEC (Smart Efficient Energy Centre) at Bangor University, part-funded by the European Regional Development Fund (ERDF), administered by the Welsh Government. This review provides a critical, multi-faceted assessment of the practical contribution tidal stream energy can make to the UK and British Channel Islands future energy mix. Evidence is presented that broadly supports the latest national-scale practical resource estimate, of 34 TWh/year, equivalent to 11% of the UK’s current annual electricity demand. The size of the practical resource depends in part on the economic competitiveness of projects. In the UK, 124 MW of prospective tidal stream capacity is currently eligible to bid for subsidy support (MeyGen 1C, 80 MW; PTEC, 30 MW; and Morlais, 14 MW). It is estimated that the installation of this 124 MW would serve to drive down the levelized cost of energy (LCoE), through learning, from its current level of around 240 £/MWh to below 150 £/MWh, based on a mid-range technology learning rate of 17%. Doing so would make tidal stream cost competitive with technologies such as combined cycle gas turbines, biomass and anaerobic digestion. Installing this 124 MW by 2031 would put tidal stream on a trajectory to install the estimated 11.5 GW needed to generate 34 TWh/year by 2050. The cyclic, predictable nature of tidal stream power shows potential to provide additional, whole-system cost benefits. These include reductions in balancing expenditure that are not considered in conventional LCoE estimates. The practical resource is also dependent on environmental constraints. To date, no collisions between animals and turbines have been detected, and only small changes in habitat have been measured. The impacts of large arrays on stratification and predator–prey interaction are projected to be an order of magnitude less than those from climate change, highlighting opportunities for risk retirement. Ongoing field measurements will be important as arrays scale up, given the uncertainty in some environmental and ecological impact models. Based on the findings presented in this review, we recommend that an updated national-scale practical resource study is undertaken that implements high-fidelity, site-specific modelling, with improved model validation from the wide range of field measurements that are now available from the major sites. Quantifying the sensitivity of the practical resource to constraints will be important to establish opportunities for constraint retirement. Quantification of whole-system benefits is necessary to fully understand the value of tidal stream in the energy system. Publisher PDF

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.

Microbes play a primary role in aquatic ecosystems and biogeochemical cycles. Spatial patchiness is a critical factor underlying these activities, influencing biological productivity, nutrient cycling and dynamics across trophic levels. Incorporating spatial dynamics into microbial models is a long-standing challenge, particularly where small-scale turbulence is involved. Here, we combine a fully 3D direct numerical simulation of convective mixed layer turbulence, with an individual-based microbial model to test the key hypothesis that the coupling of gyrotactic motility and turbulence drives intense microscale patchiness. The fluid model simulates turbulent convection caused by heat loss through the fluid surface, for example during the night, during autumnal or winter cooling or during a cold-air outbreak. We find that under such conditions, turbulence-driven patchiness is depth-structured and requires high motility: Near the fluid surface, intense convective turbulence overpowers motility, homogenising motile and non-motile microbes approximately equally. At greater depth, in conditions analogous to a thermocline, highly motile microbes can be over twice as patch-concentrated as non-motile microbes, and can substantially amplify their swimming velocity by efficiently exploiting fast-moving packets of fluid. Our results substantiate the predictions of earlier studies, and demonstrate that turbulence-driven patchiness is not a ubiquitous consequence of motility but rather a delicate balance of motility and turbulent intensity.

This paper presents a methodology that uses site-specific topographic and cosmogenic 10Be data to perform multi-objective model optimisation of a coupled coastal evolution and cosmogenic radionuclide production model. Optimal parameter estimation of the coupled model minimises discrepancies between model simulations and measured data to reveal the most likely history of rock coast development. This new capability allows a time series of cliff retreat rates to be quantified for rock coast sites over millennial timescales. Without such methods, long-term cliff retreat cannot be understood well, as historical records only cover the past ∼150 years. This is the first study that has (1) applied a process-based coastal evolution model to quantify long-term cliff retreat rates for real rock coast sites and (2) coupled cosmogenic radionuclide analysis with a process-based model. The Dakota optimisation software toolkit is used as an interface between the coupled coastal evolution and cosmogenic radionuclide production model and optimisation libraries. This framework enables future applications of datasets associated with a range of rock coast settings to be explored. Process-based coastal evolution models simplify erosional processes and, as a result, often have equifinality properties, for example that similar topography develops via different evolutionary trajectories. Our results show that coupling modelled topography with modelled 10Be concentrations can reduce equifinality in model outputs. Furthermore, our results reveal that multi-objective optimisation is essential in limiting model equifinality caused by parameter correlation to constrain best-fit model results for real-world sites. Results from two UK sites indicate that the rates of cliff retreat over millennial timescales are primarily driven by the rates of relative sea level rise. These findings provide strong motivation for further studies that investigate the effect of past and future relative sea level rise on cliff retreat at other rock coast sites globally.