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This work proposes to analyze the time-dependent characteristics of the physical attributes measured along pathlines derived from unsteady flows, which can be represented as a series of time activity curves (TAC). A new TAC-based unsteady flow visualization and analysis framework is proposed. The center of this framework is a new event-based distance metric (EDM) that compares the similarity of two TACs, from which a new spatio-temporal, hierarchical clustering of pathlines based on their physical attributes and an attribute-based pathline exploration are proposed. These techniques are integrated into a visual analytics system, which has been applied to a number of unsteady flow in 2D and 3D to demonstrate its utility. 

Abstract Most existing unsteady flow visualization techniques concentrate on the depiction of geometric patterns in flow, assuming the geometry information provides sufficient representation of the underlying physical characteristics, which is not always the case. To address this challenge, this work proposes to analyse the time‐dependent characteristics of the physical attributes measured along pathlines which can be represented as a series of time activity curves (TAC). We demonstrate that the temporal trends of these TACs can convey the relation between pathlines and certain well‐known flow features (e.g. vortices and shearing layers), which enables us to select pathlines that can effectively represent the physical characteristics of interest and their temporal behaviour in the unsteady flow. Inspired by this observation, a new TAC‐based unsteady flow visualization and analysis framework is proposed. The centre of this framework is a new similarity measure that compares the similarity of two TACs, from which a new spatio‐temporal, hierarchical clustering that classifies pathlines based on their physical attributes, and a TAC‐based pathline exploration and selection strategy are proposed. A visual analytic system incorporating the TAC‐based pathline clustering and exploration is developed, which also provides new visualizations to support the user exploration of unsteady flow using TACs. This visual analytic system is applied to a number of unsteady flow in 2D and 3D to demonstrate its utility. The new system successfully reveals the detailed structure of vortices, the relation between shear layer and vortex formation, and vortex breakdown, which are difficult to convey with conventional methods.