Flow Patterns

• A streamline is a line everywhere tangent to the velocity vector at a given instant of time. (A streamline is an instantaneous pattern.) For example, consider simple shear flow between parallel plates. At some instant of time, a streamline can be drawn by connecting the velocity vector lines such that the streamline is everywhere parallel to the local velocity vector. In this example, streamlines are simply horizontal lines.
  
• A streakline is the locus of particles which have earlier passed through a prescribed point in space. (A streakline is an integrated pattern.) For example, consider simple shear flow between parallel plates. A streakline is formed by injecting dye into the fluid at a fixed point in space. As time marches on, the streakline gets longer and longer, and represents an integrated history of the dye streak. In this example, streaklines are simply horizontal lines.
  
• A pathline is the actual path traversed by a given (marked) fluid particle. (A pathline is an integrated pattern.) For example, consider simple shear flow between parallel plates. A pathline is the actual path traversed by a given (marked) fluid particle. A pathline represents an integrated history of where the fluid particle has been. In this example, pathlines are simply horizontal lines.
  
• A timeline is a set of fluid particles that form a line segment at a given instant of time. (A timeline is an integrated pattern.) For example, consider simple shear flow between parallel plates. A timeline follows the location of a line of fluid particles. A timeline represents an integrated flow pattern, since the time line continually distorts with time, as shown in the sketch. Notice the no-slip condition in action. The top of the time line moves with the top plate, i.e. at velocity V to the right. The bottom of the timeline, however, stays in the same location at all times, because the bottome plate is not moving.
  
• Note: For steady flow, streamlines, streaklines, and pathlines are all identical. However, for unsteady flow, these three flow patterns can be quite different.