ITP: Streamlines, Streaklines, and Pathlines

Now that we have discussed how one can mathematically describe flow fields (Eulerian versus Lagrangian) as well as reference frames for balances (system versus control volume), it is important to think of visualization of flows. (We already covered (briefly) fluid property fields and showed that for scalar properties, contour plots are sufficient up to 2D).

Three well-accepted flow "visualizers" are the following:

DEFINITION

A Streamline is a line that is tangent to the instantaneous velocity field. Imagine "connecting the dots" from a vector field plot of the velocity profile.

DEFINITION

A Pathline is a line that is traced out by "watching" the flow of a particular fluid element. Imagine a long-time exposure image of a firefly's motion.

DEFINITION

A Streakline is a line that is generated by "tagging" particles that have visited a particular location. Imagine injecting a continuous stream of dye into a flowing fluid.

There are a couple of interesting things to note regarding these lines:

OUTCOME:

Identify and differentiate between streaklines, streamlines, and pathlines

TEST YOURSELF

Determine when these three types of lines are the same; when are they different? (HINT: what would need to be true about the underlying flow, for the firefly to "change its mind", or our ink streams to follow different trajectories from each other?)

It is interesting to visualize how/why these lines are different using an example.

EXAMPLE

Given a time-dependent velocity field such as $v_x = sin(t)$ and $v_y = 1$ it is instructive to look at how each of these visualization lines look/evolve: