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In this work, we assess global offshore wind energy resources, wake-induced losses, array layout optimisation potential and climate change impacts. We first map global offshore ambient wind resource from reanalysis data. We estimate wake-induced losses using an engineering wake model, revealing that locations with low (high) resource typically experience larger (smaller) percentage losses. However, we further find that the specific wind speed distribution is important, with narrower distributions generally leading to greater losses. This is due to the overlap between the wind speed distribution and the high-sensitivity region of the turbine thrust and power curves. Broadly, this leads to much stronger wake-induced losses in the tropics (which experience the trade winds) than mid-latitudes. However, the tropics also experience a narrower wind direction distribution; our results demonstrate that this leads to greater potential for mitigation of wake effects via layout optimisation. Finally, we assess projected changes in wind resource and wake losses due to climate change under a high-emission scenario. Many regions are projected to decrease in ambient wind resources, and furthermore these regions will typically experience greater wake-induced losses, exacerbating the climate impact. These results highlight the different challenges and opportunities associated with exploiting offshore wind resources across the globe.

Rapid deployment of offshore wind is expected within the coming decades to help meet climate goals. With offshore wind turbine lifetimes of 25-30 years, and new offshore leases spanning 60 years, it is vital to consider long-term changes in potential wind power resource at the farm planning stage. Such changes may arise from multiple sources, including climate change, and increasing wake-induced power losses. In this work, we investigate and compare these two sources of long-term change in wind power, for a case study consisting of 21 wind farms within the German Bight. Consistent with previous studies, we find a small but significant reduction in wind resource due to climate change by the end of the 21st century under the high-emission RCP8.5 scenario, compared with a historical period, with a mean power reduction (over an ensemble of seven climate models) of 2.1%. To assess the impact of wake-induced losses due to increasingly dense farm build-out, we model wakes within the German Bight region using an engineering wake model, under various stages of (planned) build-out corresponding to the years 2010-2027. By identifying clusters of wind farms, we decompose wake effects into long-range (inter-cluster), medium-range (intra-cluster) and short-range (intra-farm) effects. Inter-cluster wake-induced losses increase from 0 for the 2010 scenario to 2.5% for the 2027 scenario, with intra-cluster losses also increasing from 0 to 4.3%. Intra-farm losses are relatively constant, at around 13%. While the evolution of wake effects therefore outweighs the climate effect, and impacts over a shorter timescale, both factors are significant. We also find evidence of non-linear interactions between the climate and wake effects. Both climate change and evolving wake effects must therefore be considered within resource assessment and wind farm planning.

Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Amp\`ere PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. Our project page is at https://erizmr.github.io/UM2N/.