Reynolds Number Effects in Data-driven Learning of Mori-Zwanzig Memory Operators for Lagrangian Particle Dynamics

The Lagrangian view of turbulence is pivotal to problems involving turbulent dispersion and mixing. Lagrangian data at progressively higher Taylor scale Reynolds numbers R_λ are becoming available from experiments and simulations. In parallel, the inherent cost and challenge of tracking fluid particles in a turbulent flow are partly driving the need for the development of reduced-order models. In this work, we harness data obtained from particle tracking in high-resolution direct numerical simulations and a recent data-driven technique based on the Mori-Zwanzig formalism to learn the memory-dependent interactions between resolved and unresolved dynamics for particle trajectories. Results show that the learned model captures the key physical mechanisms governing the turbulent advection of particles and reproduces long-term Lagrangian statistics given a short time history of the trajectories. As the R_λ increases, the dynamics of particle motion in a turbulent flow grow increasingly complex due to interactions over a wider range of spatial-temporal scales. For instance, Lagrangian intermittency, marked by intense acceleration fluctuations, becomes more pronounced at high R_λ. Here, we analyse the robustness and fidelity of the reduced-order model in regimes far beyond those previously considered, evaluating its performance and changes in the learned operators at increasingly large values of R_λ, up to R_λ~2500.