A pathline (Figures 1) is the continuous (usually smooth) trajectory of a single particle under investigation over time that shows the particle's temporal-spatial behavior governed by the underlying flow. A timeline (Figure 2) is a time-varying curve (not necessarily smooth) that connects a set of particles simultaneously released along an initial line (i.e., rake line, usually perpendicular to the local flow direction). Analogous to a rope released in and then warped by the flow, a timeline reveals the change in the direction orthogonal to the flow and hence is well suited for showing flow convergence and divergence. A streakline (Figure 3) is also a time-varying curve (the smoothness depends on the particle release interval) that connects a sequence of particles successively released from a fixed position to depict the change of the flow direction over time. A streakline emulates how a block of dye, released at a specified position in the flow, propagates to make a visual pattern. Animated streaklines (5.49M) are often used for unsteady flow visualization. Pathlines and streaklines are identical to streamlines in a steady flow, but different from one another in an unsteady flow (Figure 4).

Figure 1. Seeder-based pathlines.
Figure 2. The evolution of a timeline (left) and four timelines of a 2D time-verying flow (right).
Figure 3. 20 streaklines of a 2D time-varying flow.
Figure 4. The relationship between pathlines, timelines, and streaklines (© Zhanping Liu).
Flow Visualization
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