Thomas. A. A. Adcock

Extracting energy from a flow is a fundamental problem in fluid mechanics of significant practical engineering importance. To generate power from a flow, a resistance must be applied. Open questions remain on how to optimise this resistance, particularly for non-uniform flows. In this paper, we extend the multi-streamtube theory to address this gap. The extended theory allows for an arbitrary resistance distribution across an actuator strip (representing either a single turbine or an array of turbines) and is formulated as a power-coefficient maximisation problem to determine the optimal resistance distribution for both uniform and non-uniform flows. When the undisturbed kinetic energy flux projected onto the strip’s frontal area is used to normalise the extracted power, a uniform resistance maximises the resulting power coefficient for both uniform and non-uniform incoming flows. When the upstream kinetic energy flux of the flow through the strip is used for normalisation, the same optimisation result is obtained for uniform incoming flow, regardless of the assumed resistance distribution. However, for a non-uniform incoming flow, the optimal resistance distribution is non-uniform, with greater resistance applied in regions of higher velocity within the shear flow. This different optimisation result for non-uniform flow arises physically because the kinetic energy flux used in the second power-coefficient definition depends on the resistance applied across the strip, whereas the first does not. Two-dimensional direct numerical simulations are employed to examine the applicability and limitations of the multi-streamtube theory. The numerical and optimisation results together demonstrate that optimising the resistance distribution requires accounting not only for the non-uniformity of the incoming flow but also for the local flow variability around the strip.

The development of tidal stream energy sites is constrained by numerous practical, technical, and accessible constraints, including changes in the flow caused by the presence of the tidal farm. Large and complex sites are typically developed incrementally and may involve multiple developers. This regional modelling case study of the Pentland Firth, widely regarded as one of the most significant global locations for tidal energy extraction, investigates these dynamics. This study examines scenarios for the incremental development of the Pentland Firth, incorporating assumptions regarding tidal farm design. The analysis considers a range of configurations, including variations in turbine density and the incorporation of shipping lanes within designated lease areas. The study finds that there are interactions between individually developed tidal farms of the site, but they are moderate with the power in a given farm unlikely to vary by more than 20% (based on a positive interaction), as a result of the development of other farms in other parts of the Pentland Firth. To minimise such array interactions, it is recommended that site leasing be based on the allowable thrust applied to the flow rather than on projected power generation. Furthermore, the findings suggest that the maximum power generated from turbines in the Pentland Firth, averaged over time, is unlikely to exceed approximately 1 GW, broadly consistent with most estimates in the literature.

Forecast uncertainty is essential for operational decision-making in storm surge forecasting. Current probabilistic operational systems typically estimate uncertainty by ensembling deterministic numerical models forced by meteorological ensemble members. While this approach captures atmospheric uncertainty, it neglects uncertainty in the oceanic response and surge propagation, leading to forecasts that are commonly underdispersed.We present a framework that explicitly accounts for these missing sources of uncertainty, including those arising from waves and other coupled processes. Building on the deterministic tidal response method of Munk and Cartwright, we model storm surges as conditional time-invariant stochastic processes. These processes are defined by distributions over nonlinear impulse-response functions that map gravitational, meteorological, and other forcings to total sea level. The response distributions can be flexibly conditioned on recent observations, such as in-situ gauge data, while remaining robust when such data are unavailable.To learn these processes, we introduce Mixture Density Neural Processes (MDNPs), a Bayesian neural architecture that combines the expressiveness of neural networks with the stochastic function modeling capabilities of Gaussian processes. The models are trained on in-situ observational data at locations used for operational decision-making but, due to the conditional time-invariant formulation, do not require such data to generate subsequent forecasts.We demonstrate state-of-the-art performance against operational baselines from the UK, the Netherlands, and the United States. We further show how MDNPs can be coupled with traditional numerical models to improve both forecast accuracy and uncertainty calibration. Currently being trialed in UK and Dutch operational systems, the approach maintains high performance during extreme events, producing calibrated forecasts even for previously unseen peaks. We attribute this robustness on tail events to the impulse-response formulation and discuss the broader applicability of the framework to multiscale and compound coastal hazards.

This research examines in detail the complex nonlinear forces generated when steep waves interact with vertical cylindrical structures, such as those typically used as offshore wind turbine foundations. These interactions, particularly the nonlinear wave forces associated with the secondary load cycle, present unanswered questions about how they are triggered. Our experimental campaigns underscore the occurrence of the secondary load cycle. We also investigate how the vertical distributions of the scattering force, pressure field and wave field affect the nonlinear wave forces associated with the secondary load cycle phenomena. A phase-based harmonic separation method isolates harmonic components of the scattering force’s vertical distribution, pressure field and wave field. This approach facilitates the clear separation of individual harmonics by controlling the phase of incident waves, which offers new insights into the mechanisms of the secondary load cycle. Our findings highlight the importance of complex nonlinear wave–structure interactions in this context. In certain wave regimes, nonlinear forces are locally larger than the linear forces, highlighting the need to consider the secondary load cycle in structural design. In addition, a novel discovery emerges from our comparative analysis, whereby very high-frequency (over the fifth in harmonic and order) oscillations, strongly correlated to wave steepness, have the potential to play a role in structural fatigue. This new in-depth analysis provides a unique insight regarding the complex interplay between severe waves and typical cylindrical offshore structures, adding to our understanding of the secondary load cycle for applications related to offshore wind turbine foundations.

The design and operation of tidal stream energy farms will require the accurate prediction of tidal currents from field data. In the present paper we compare the performance of a physics based flow model, the traditional harmonic analysis method, and a newly developed code RTide. RTide is based on the Response Method proposed by Munk and Cartwright in the 1960s and uses machine learning to overcome the key disadvantages of their original approach. We use field data from the Meygen site in the Inner Sound of the Pentland Firth. We find RTide predictions based solely on the field data outperform both the flow model predictions and the currents predicted by harmonic analysis. Interestingly, feeding the physics-based flow model into RTide as an additional input does not outperform the predictions based on the field data alone. However, RTide can still be used as a correction tool to physics-based flow models.

As energy systems transition from centralised, dispatchable power produced by fossil fuel-based technologies, to de-centralised, intermittent renewables, the need for resilient energy system design is becoming ever-more pertinent. This challenge was brought to the forefront during the 2021-22 energy crisis, when the combination of unseasonally low wind resource, and high imported energy prices, resulted in significant increases in the cost of energy that were around an order of magnitude greater than the value of the loss in wind load [1]. It is estimated that by 2050, the UK will require up to 116 TWh/year and 502 TWh/year of electricity generated from solar PV and onshore/offshore wind respectively [2]. These projections show other renewables to play a very small part, contributing up to 15 TWh/year. Currently, solar PV, onshore/offshore wind and other renewables provide around 16 TWh/year, 96 TWh/year and 12 TWh/year respectively. Whilst solar and wind are critical as the primary suppliers of renewable energy now and in the future, their intermittency and weather-dependency inevitably bring system resilience risks that require mitigation. The research presented here investigates enhancement to resilient energy system design at times of high system stress, through the uptake of alternative renewable generation technology, focussing on tidal stream energy. Tidal stream provides a different offering to solar PV and wind, since its power generation is independent of weather, predictable far into the future, and reliable in providing power every day, albeit at different levels depending on the timing of spring-neap cycles. This research queries future energy scenarios that rely so heavily solar PV and wind, and so little on alternative, weather-independent technologies. Results are presented from a new energy system model (ESM). The ESM simulates the power flows between power generators, energy storage and load, with these system components linked by the transmission grid that connects 12 nodes across the UK electricity network. A range of tidal stream capacities are investigated, to establish the impact(s) of replacing a relatively small proportions of solar PV and onshore/offshore wind, acknowledging that solar PV and wind will always remain the primary sources of renewable power. The ESM solves the linear optimal power flow equations using the Gurobi solver, to minimise the cost of hourly dispatch over a full year, adopting a similar modelling framework to that set out by Pennock et al., (2023) [3]. The year 2022 was chosen to simulate the recent energy crisis, thereby stress testing the energy system during a period when known significant cost impacts were incurred as a result of high imported energy prices and low wind generation. References [1] UK Government, 2023, £40 billion spent protecting families and businesses from energy costs, Available online: https://www.gov.uk/government/news/40bn-spent-protecting-families-and-businesses-from-energy-costs [2] Energy System Operator, 2024, Future Energy Scenarios: Pathways at a Glance, Technical report [3] Pennock S et al., 2023, A modelling framework to quantify the power system benefits from ocean energy deployments, Applied Energy, 121413

Conservation laws play an important role in analysing physical systems and solving partial differential equations (PDEs). In this paper, we use associated conserved quantities (CQs) to construct a simple and robust way to approximate the interaction between surface solitary waves—a common nonlinear phenomenon in many research fields and engineering applications. One major constraint of such an approach is how many CQs are available from the governing equation. In this study, we start with the Korteweg–De Vries (KdV) equation, which has an infinite number of CQs. We show that these CQs can be used to predict soliton interaction accurately. The regularized long wave (RLW) equation—an equivalent reduction form to the KdV equation, however, has insufficient CQs to apply the approach. To address this problem, we use a new symbolic-based machine learning (ML) approach to search for any higher-order empirically CQs (e-CQs), which allow the proposed approach to be applied directly to the RLW equations and leverages the constraints on the number of CQs available. This opens a new opportunity for more complex systems governed by a variety range of PDEs to be modelled with such a CQ-based approach.

We present numerical simulations investigating the evolution of liquid droplets into baglike structures in turbulent airflows. The droplet bag breakup problem is of significance for many multiphase processes in scientific and engineering applications. Turbulent fluctuations are introduced synthetically into a mean flow, and the droplet is inserted when the air-phase turbulence reaches a statistically stationary state. The morphological evolution of the droplet under different turbulence configurations is retrieved and analyzed in comparison with laminar aerobreakup results. While the detailed evolution history of individual droplets varies widely between different realizations of the turbulent flow, common dynamic and morphological evolution patterns are observed. The presence of turbulence is found to enhance the drag coefficient of the droplet as it flattens. At late times, the droplet becomes tilted and increasingly corrugated under strong turbulence intensity. We quantify these phenomena and discuss their possible governing mechanisms associated with turbulence intermittency. Lastly, the influences of liquid-gas viscosity ratio are examined and the implications of air-phase turbulence on the later bag film breakup process are discussed.