Coherent motions to predict Lagrangian trajectories

Abstract: Accurate prediction of Lagrangian trajectories in turbulent flow remains challenging due to limited temporal information in transport functions. This paper shows that even with sparse temporal observations, there might be enough information from surrounding coherent motions, sharing the same dynamics, to provide highly probable trajectories. The proposed coherent predictor is derived from the concept of Lagrangian coherent structures (LCSs), which are advective transport barriers that govern the cohesive motion of neighbouring particles. Coherent trajectories are quantified using a local segmentation with the finite-time Lyapunov exponents (FTLE). The coherent predictor incorporates information from the particle's position history and neighbouring coherent velocity and acceleration into a novel generic energy function to predict its trajectory. We assess our proposed approach using both three-dimensional (3D) synthetic and experimental data of the wake behind a smooth cylinder and two-dimensional (2D) homogeneous isotropic turbulent (HIT) flow. The coherent predictor is deemed generic due to its consistent behaviour regardless of flow dimensions, Reynolds number, and flow topology. Our results demonstrate that the optimal parameters of the proposed energy function can be modelled based on measurement uncertainties, resulting in enhanced prediction accuracy and reduced uncertainty compared to current methods. We reveal direct signatures of flow topology, including the cylinder leading edge boundary layer, sideward shear layers, and vortex formation structures, on the prediction error map. These topologies, which are fundamental structures in fluid dynamics, are marked by high Lagrangian gradients and 3D directional motions. These findings on coherent predictions hold great potential for various Lagrangian analyses in turbulence.