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, multiscale 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 centered 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.

翻译：许多涉及多物理场的科学与工程问题跨越了广泛的空间尺度。理解这些尺度间的相互作用对于全面把握此类复杂问题至关重要。然而，在单一视图中对多变量、多尺度数据进行可视化，并使其在空间、尺度和物理场之间的关联易于被感知，仍然具有挑战性。为此，我们提出了一种新颖的、针对多物理场及湍流尺度的流场局部空间统计可视化方法。我们的方法利用曲波变换对目标物理场进行尺度分解，采用水平集约束的质心Voronoi图将空间域划分为用于统计聚合的局部区域，并设计了一套字形符号系统，将跨尺度与跨物理场的信息整合为单一或精简的可感知视觉表征。每个字形符号代表一个Voronoi区域内的聚合数据，并定位于Voronoi站点，以便在以关注的流动特征为中心的三维视图中直接可视化。我们将该方法实现并集成到一个交互式可视化系统中，其中基于字形符号的技术与关联的三维空间视图和二维统计视图协同工作，支持整体性分析。我们通过可视化湍流燃烧数据（多标量可压缩流动）和湍流不可压缩槽道流动数据的案例研究进行演示。这一新功能使科研人员能够更好地理解湍流中多物理场与多长度尺度之间的相互作用。