Perceptual multivariate visualisation of volumetric Lagrangian fluid-flow processes

Lagrangian flow data in oceanography are highly complex, encompassing not only the underpinning Eulerian, advective, vectorial flow fields and the three-dimensional position coordinates of tracer particles but also supplementary trajectory information such as interaction radii of particles, lifecycle source-to-sink information and biochemical process data. Visualising all those data cooperatively in its three-dimensional context is a prime challenge, as it demands to present all relevant information to enable a contextual analysis of the flow process while preventing the most commonly-occurring perceptual issues of clutter, colourisation conflicts, artefacts and the lack of spatial references in fluid-flow applications. In this article, we present visualisation design approaches for 4D spatio-temporal data in their context and introduce a novel colour-mapping approach for 3D velocity tensors. The employed visualisation approach is evaluated towards perceptual adequacy and efficacy with respect to algebraic visualisation design and on an oceanographic case study. The technical and perceptual elements have further implications and applications for still-picture and animated volumetric visualisation design in related applications of the natural sciences, such as geological flow mapping.