Frequency synchronisation and modal mapping of wake dynamics to the performance of a vertical-axis turbine

The transition towards sustainable marine energy relies partly on efficient deployment of vertical-axis tidal turbines, yet their widespread application is constrained by the complex, unsteady fluid dynamics inherent in their operation. While vertical-axis turbines offer superior structural scalability, they experience intricate vortex shedding and wake-induced energy losses which can make performance difficult to predict accurately. We address this critical gap by establishing a novel, data-driven quantitative correlation between wake characteristics and hydrodynamic performance. A high-fidelity actuator line model within a large eddy simulation framework is used to simulate the three-dimensional dynamic response of a vertical-axis tidal turbine in unsteady flow. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) reveal that the wake is governed by prominent low-dimensional dynamics, with primary POD modes capturing over 60 percent sign 60 % $60\,%$ of the fluctuating energy. The dominant DMD mode corresponds to the fundamental blade rotation frequency, while a critical frequency shift in a secondary shedding mode ( italic St equals 1.477 St = 1.477 St = 1.477 ) is identified, elucidating the complex coupling between dynamic stall vortices and shear layer instabilities. By integrating reduced-order DMD-based modelling with a physics-inspired symbolic regression framework, we establish the first explicit mathematical mapping between pivotal modal descriptors (including energy fraction, decay rate and frequency) and the power coefficient upper C Subscript upper P C P C\!P . The resulting model demonstrates that power extraction at this optimal condition is governed primarily by frequency synchronisation among low-frequency coherent structures, achieving zero fitting error at the design point. These findings bridge the gap between instantaneous flow topologies and global performance metrics, and provide a rigorous physical foundation for real-time diagnostics and optimisation of tidal energy conversion systems.