streakline

A streakline is the locus of points in a fluid that have previously passed through a fixed location, such as a point source, in the flow. It is commonly visualized by releasing a dye, smoke, or tracer at a line or point so that the moving fluid leaves a visible trail that records the history of the flow at that location.

In a time-dependent velocity field u(x,t), the trajectory of a fluid particle satisfies dx/dt = u(x,t). If a tracer is released from a fixed point a at times τ ≤ t, the streakline at time t is the set of positions x(t; τ, a) obtained for all release times τ. Equivalently, the streakline is the locus of all particles that have passed through a, up to the current time.

In steady flows, where u does not depend on time, streaklines coincide with streamlines and with pathlines. In unsteady flows, these three concepts generally differ: streamlines are instantaneous tangents to the velocity field; pathlines are the paths of individual particles; streaklines map the history of particles released from a fixed location.

Streaklines are widely used in experimental fluid dynamics to visualize complex flows, such as wakes, mixing regions, and boundary layers. Visualization methods include dye sheets or lines, smoke injection, or fluorescent particles, often captured with high-speed imaging and analyzed to infer flow structure.

Limitations include dependence on the release point, potential diffusion of tracers, and finite tracer concentration. The concept is also used in computational methods to analyze unsteady flows by tracking particle release histories.