Talk:Streamlines, streaklines, and pathlines

Merge
I think that in explaing one term it makes sense to explain the others, prehaps rename the article Streamlines, Streaklines and Pathlines? Already this article deals with all three so it would be much work. Rex the first 08:23, 20 April 2006 (UTC)

Differences?
The article states that streaklines are found by injecting smoke into a wind tunnel from one point. How is this different from streamlines? —Ben FrantzDale 02:22, 29 April 2007 (UTC)


 * Hmm, I am not an engineer so I do not know how streamlines are measured I can only say that injecting smoke from a point would measure the streaklines and not the streamlines (unless the flow was steady). If the flow changed direction (for example it was pointing up and it now points left) then the smoke would show the path that the flow did take in the past (streaklines), not the path parallel to the flow at a given instant (streamlines).   Rex the first  talk 21:04, 29 April 2007 (UTC)


 * OK, so for steady flow, streamlines are the same as streak lines?
 * Even in time-varying flow, it seems like you can use smoke or bubbles to find streamlines by basically using particle image velocimetry. That is, watch the particles for a moment and see where they traveled. —Ben FrantzDale 21:18, 29 April 2007 (UTC)


 * Yes, for steady flows they are the same (see the steady flow section). I know very little about how streamlines are actually measured.  For a quick glance at particle image velocimetry is seems like smoke is rarely used.  If you find out more please add it to this article.  There is a great historical tradition for using soot that I came across recently, see The discovery of the Mach reflection effect and its demonstration in an auditorium (not sure if you will be able to access this).  Rex the first  talk 13:48, 4 May 2007 (UTC)

Minor error: sentence about radius of curvature
I think there may be a minor error in the article (I believe that radius is a scalar and thus has no direction) : "The radius of curvature of the streamline is in the direction of decreasing radial pressure." Could someone knowledgeable in the subject correct it? Thanks much. Mark.camp (talk) 01:31, 12 February 2011 (UTC)


 * I have changed the sentence to "The center of curvature of the streamline lies in the direction of decreasing radial pressure." Dolphin  ( t ) 05:34, 12 February 2011 (UTC)


 * Thanks, Dolphin. That looks good.  Truth be told, on re-reading my post, I remembered that radius IS often treated as a vector!  But I still like your text, which treats it as a scalar, better.
 * Mark.camp (talk) 13:36, 18 February 2011 (UTC)

Form of the streamline equation
Why not give the streamlines as initial-value ODEs like the streaklines and pathlines? Also, it might be stressed that pathlines are spatiotemporal lines while streamlines are only spatial lines. — Preceding unsigned comment added by 62.16.179.14 (talk) 20:48, 7 August 2013 (UTC)

Assessment comment
Substituted at 21:59, 26 June 2016 (UTC)

Gif change
It might be easier to understand the concept if several pathlines were connected to the origin in the gif. This could demonstrate the generation of the streakline a little more clearly.

I cannot seem to run that code in maxima and don't have access to mathematica.

Regards.

213.55.176.226 (talk) 13:26, 24 June 2017 (UTC)

Self-intersection of streaklines
Contrary to what is written in the article, streaklines can self-intersect, and also intersect other streaklines. A simple example for this is the following flow field:

$$ \begin{align} u_1 &= -x_2 \\ u_2 &= x_1 + t \end{align}$$

which is a (counter-clockwise) rigid body rotation with a superposed constant horizontal translation. A streakline starting at $$\vec x=(-5,2)$$ will intersect itself twice. See also animation below which shows the pathlines of the emitted particles (emitted every 0.5 time units) and the streaklines. Both are analytical solutions.



Indeed, it is no problem for a marked particle to fly by its emission point again. If the flow field at the initial position has now changed, the streakline intersects itself from this point on.

There is also literature available that disputes this statement on theoretical grounds, e.g. Qinghai Zhang and Lingyun Ding (2019) Lagrangian Flux Calculation Through a Fixed Planar Curve for Scalar Conservation Laws, SIAM Journal on scientific computing (Volume 41, Issue 6).

I will submit a change request for the main page.

Turbulent4fun (talk) 19:29, 24 June 2022 (UTC)