Glyph‐Based Multi‐Scale Visualization of Spatial Turbulent Multi‐Physics Statistics

Abstract Many scientific and engineering problems involving multi‐physics span a wide range of scales. Understanding the interactions across these scales is essential for fully comprehending such complex problems. However, visualizing multivariate, multi‐scale data within an integrated view where correlations across space, scales and fields are easily perceived remains challenging. To address this, we introduce a novel local spatial statistical visualization of flow fields across multiple fields and turbulence scales. Our method leverages the curvelet transform for scale decomposition of fields of interest, a level‐set‐restricted centroidal Voronoi tessellation to partition the spatial domain into local regions for statistical aggregation, and a set of glyph designs that combines information across scales and fields into a single, or reduced set of perceivable visual representations. Each glyph represents data aggregated within a Voronoi region and is positioned at the Voronoi site for direct visualization in a 3D view centred around flow features of interest. We implement and integrate our method into an interactive visualization system where the glyph‐based technique operates in tandem with linked 3D spatial views and 2D statistical views, supporting a holistic analysis. We demonstrate with case studies visualizing turbulent combustion data—multi‐scalar compressible flows—and turbulent incompressible channel flow data. This new capability enables scientists to better understand the interactions between multiple fields and length scales in turbulent flows.