Fluid–structure interaction in a square array of submerged flexible stems

The evolution of flow structure is fundamental to establishing an accurate framework for predicting turbulent energy dissipation, momentum transfer, and sediment and nutrient transport within and above flexible stem arrays. The dynamics of flexible stems plays a crucial role in shaping these physical features. In this paper, direct numerical simulations are performed to examine flow through a three-dimensional square array of flexible stems, with explicit consideration of flexibility ( upper K K $K$ ) effects. The results provide a comprehensive characterisation of the coupled stem dynamics, flow distribution and vortex structures. Three distinct dynamical regimes are identified. For large upper K K $K$ , the stems behave as nearly rigid, causing the flow to accelerate through the gaps while attenuating behind the stems. At intermediate upper K K $K$ , a perfect lock-in occurs between the stem’s natural and oscillation frequencies, leading to large-amplitude vibrations and markedly altered flow characteristics. For small upper K K $K$ , the oscillation amplitude decreases but deformation increases, producing irregular stem dynamics and complex flow features. The flow dynamics underlying these regimes is systematically elucidated. Furthermore, energy dissipation and sediment transport effects are quantified through hydrodynamic drag, bed shear stress, and root mean square bed shear friction distributions. The array with intermediate upper K K $K$ exhibits the highest energy dissipation efficiency, surpassing even the rigid configuration. The bed shear stress reaches a peak at the upstream edge of the array, whereas stem oscillation redistributes the flow momentum towards the upper canopy and the overlying flow, reducing velocity fluctuations near the bed. Finally, the mechanisms governing the structural dynamics and hydrodynamic forces are discussed in detail. This study offers new physical insights into flow–structure interactions within flexible stem arrays, and proposes an optimised strategy for improving energy dissipation in coastal protection applications.