Whole-field density measurements by digital image correlation, Identifying dominant flow features from very-sparse Lagrangian data: a multiscale recurrence network-based approach

Abstract

Whole-field density measurements by digital image correlation A novel application of Synthetic Schlieren in a laboratory set-up yields a quantitative measurement of the density field of two-dimensional, stratified or homogeneous, transparent fluids in a laboratory set-up using a single camera. This application obtains local values of the density without the need for tomographic reconstruction algorithms that require images taken from different directions through the fluid nor does the application require regularization. This is achieved by placing the camera at a large oblique angle with respect to the experimental set-up. This step is motivated by a fallacy observed when applying ray tracing in a classical configuration, in which the camera's optical axis is perpendicular to the flat surface of a fluid container. The application is illustrated by the optical determination of static density fields of linearly and nonlinearly stratified fluids, as well as of multi-layered fluids. The application is validated by comparing with density profiles obtained from probe measurements of conductivity and temperature. Our application yields similar density and density gradient profiles as the probe while also providing a whole field measurement without disturbing the fluid, and allowing the determination of dynamical density fields. Identifying dominant flow features from very-sparse Lagrangian data: a multiscale recurrence network-based approach 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.