Streamlines are conceptual lines that are everywhere parallel to the flow at some instant (i.e., a snapshot). This is an Eulerian point of view. Fig. 17.32 shows an example of streamlines on a weather map. Streamlines never cross each other except where the speed is zero, and the wind never crosses streamlines. Streamlines can start and end anywhere, and can change with time. They are often not straight lines.
Streaklines are lines deposited in the flow during a time interval by continuous emission of a tracer from a fixed point. Examples can be seen in aerial photographs of smoke plumes emitted from smokestacks, or volcanic ash clouds.
Trajectories, also called path lines, trace the route traveled by an air parcel during a time interval. This is the Lagrangian point of view. For stationary (not changing with time) flow, streamlines, streaklines, and trajectories are identical.
For nonstationary flow (flow that changes with time), there can be significant differences between them. For example, suppose that initially the flow is steady and from the north. Later, the wind suddenly shifts to come from the west.
Fig. 17.33 shows the situation shortly after this wind shift. Streamlines (thin solid blue lines in this figure) are everywhere from the west in this example. The streakline caused by emission from a smokestack is the thick brown line. The green dashed line shows the path followed by one air parcel in the smoke plume.