Streamlines, streaklines, and pathlines

Streamlines, streaklines and pathlines are <a href="/facts/Field_line/Nxr20d47">field lines</a> in a <a href="/facts/Fluid_flow/y7uzSCfg">fluid flow</a>.
They differ only when the flow changes with time, that is, when the flow is not <a href="/facts/Steady_flow/y7uzSCfg">steady</a>.

Considering a <a href="/facts/Velocity/Q3o1LVDe">velocity</a> <a href="/facts/Vector_field/ccFNuPPp">vector field</a> in <a href="/facts/Three-dimensional_space/KAqKWUbS">three-dimensional space</a> in the framework of <a href="/facts/Continuum_mechanics/vI7LpFDk">continuum mechanics</a>: 

<ul><li>Streamlines are a family of <a href="/facts/Curve/xBQ0pTBW">curves</a> whose <a href="/facts/Tangent/sF0jH3EI">tangent</a> vectors constitute the <a href="/facts/Velocity/Q3o1LVDe">velocity</a> vector field of the flow. These show the direction in which a massless <a href="/facts/Fluid_element/yk70LICD">fluid element</a> will travel at any point in time.</li>
<li>Streaklines are the <a href="/facts/Locus_(mathematics)/t4swdGJq">loci</a> of points of all the fluid particles that have passed continuously through a particular spatial point in the past. Dye steadily injected into the fluid at a fixed point (as in <a href="/facts/Dye_tracing/m0sB6HJs">dye tracing</a>) extends along a streakline.</li>
<li>Pathlines are the <a href="/facts/Trajectory/STNN33FK">trajectories</a> that individual fluid particles follow. These can be thought of as "recording" the path of a fluid element in the flow over a certain period. The direction the path takes will be determined by the streamlines of the fluid at each moment in time.</li></ul>
By definition, different streamlines at the same instant in a flow do not intersect, because a fluid particle cannot have two different velocities at the same point. Pathlines are allowed to intersect themselves or other pathlines (except the starting and end points of the different pathlines, which need to be distinct). Streaklines can also intersect themselves and other streaklines.
Streamlines provide a snapshot of some flowfield characteristics, whereas streaklines and pathlines depend on the full time-history of the flow. Often, sequences of streamlines or streaklines at different instants, presented either in a single image or with a videostream, may provide insight to the flow and its history.

If a line, curve or closed curve is used as start point for a continuous set of streamlines, the result is a <a href="/facts/Stream_surface/Np8NR3BQ">stream surface</a>. In the case of a closed curve in a steady flow, fluid that is inside a stream surface must remain forever within that same stream surface, because the streamlines are tangent to the flow velocity. A scalar function whose <a href="/facts/Contour_line/35Qten5r">contour lines</a> define the streamlines is known as the <a href="/facts/Stream_function/nEoYTGAl">stream function</a>.

Streamlines, streaklines, and pathlines open-in-new

Streamlines, streaklines, and pathlines