Abstract
Realistic fluid flow problems often require that Lagrangian tracers are deployed in a sparse or very-sparse manner, such as for oceanic and atmospheric flows where large-scale motion needs characterisation. Data sparsity represents a significant issue in Lagrangian analysis, especially for data-driven methods that rely heavily on large datasets. We propose a multiscale spatial recurrence network (MSRN) methodology for characterising very-sparse Lagrangian data, which exploits individual tracks and a spatial recurrence criterion to identify the spatio-temporal complexity of tracer trajectories. The MSRN is an unsupervised modelling framework that does not require a priori parameter setting, and—through the quantification of persistent link activation at specific trajectory intervals—can reveal the presence of dominant looping scales in a variety of salient fluid flows. This new paradigm is shown to be successful for the study of Lagrangian tracers seeded in complex (realistic) flows, including unsteady and advection-dominated problems. This makes MSRNs an effective and versatile tool to characterise sensor trajectories in key problems such as environmental processes critical to understanding and mitigating climate change.