Streamlines, streaklines and pathlines are field lines in a fluid flow.They differ only when the flow changes with time, that is, when the flow is not steady.Considering a velocity vector field in three-dimensional space in the framework of continuum mechanics:
- Streamlines are a family of curves whose tangent vectors constitute the velocity vector field of the flow. These show the direction in which a massless fluid element will travel at any point in time.
- Streaklines are the loci 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 dye tracing) extends along a streakline.
- Pathlines are the trajectories 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.
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.
