Streamlines, streaklines, and pathlines

Field lines in a fluid flow

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, we have that: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 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. Timelines are the lines formed by a set of fluid particles that were marked at a previous instant in time, creating a line or a curve that is displaced in time as the particles move.

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