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File:Streaklines and pathlines animation.gif

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Streaklines_and_pathlines_animation.gif (500 × 514 pixels, file size: 1.32 MB, MIME type: image/gif, looped, 65 frames, 7.9 s)

Summary

Description
English: The plot shows fluid flow under the velocity field . The red dot represents a particle released from the origin at time , tracing out its pathline in red.
As it moves, it leaves behind a trail of blue ink (released from the origin), which starts on the pathline, but is carried up by the fluid flow.
The velocity is represented twice, with flow vectors, and the grey dashed streamlines, which connect the flow vectors.
Deutsch: Die Grafik zeigt Fluid-Strömung in einem Geschwindigkeitsfeld . Der rote Punkt wird zum Zeitpunkt im Ursprung ins Feld gesetzt und zeichnet eine rote Bahnlinie.
In seiner Bewegung hinterlässt er eine blaue Spur, die Streichlinie, die mit der Bahnlinie im Ursprung beginnt, aber die Punkte der Bahnlinie zeigt, wie sie von der Strömung des Fluids mitgenommen werden.
Die Geschwindigkeit wird zweifach dargestellt; mit Strömungs-Vektoren und mit grau gestrichelten Stromlinien, die die Strömungs-Vektoren verbinden.
Date
Source

Own work

 
This diagram was created with Mathematica.
Author Fi1Kaiv8
Other versions Streaklines and pathlines animation (low).gif

Source code

p = Join[{
   If[x < t, 1/3 x^3, 100],
   If[x < t, 1/2 t x^2 - 1/6 x^3, 100]},
  Table[1/2 (x^2) t + y0, {y0, -10, 40, 0.9}]];
Export["plot.gif",
Table[Plot[p, {x, 0, 10.6},
  PlotRange -> {0, 10.6},
  AspectRatio -> 1,
  PlotRangeClipping -> True,
  PlotStyle ->
   PadRight[{Directive[Thickness[Medium], Red],
     Directive[Thickness[Medium], Green]}, 60,
    Directive[Gray, Dashed]],
  Exclusions -> {t},
  ExclusionsStyle -> None,
  ImageSize -> 500,
  AxesLabel -> {x, y},
  Epilog ->
   {Line[Flatten[
      With[{\[Epsilon] = 0.025},
       Table[{{x - \[Epsilon]/Sqrt[1 + x^2 t^2],
          y - x t \[Epsilon]/Sqrt[1 + x^2 t^2]}, {x + \[Epsilon]/
            Sqrt[1 + x^2 t^2],
          y + x t \[Epsilon]/Sqrt[1 + x^2 t^2]}}, {x, 0.1, 4,
         0.1}, {y, 0.1, 4, 0.1}]]
      , 1]],
    PointSize[0.015], Red, Point[{t, 1/3 t^3}]}
  ], {t, 0, 1.6, 0.025}],
AnimationRepetitions -> Infinity,
"DisplayDurations" -> PadLeft[{1.5}, 65, 0.1]
]

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
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  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
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5 February 2009

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Date/TimeThumbnailDimensionsUserComment
current00:26, 6 February 2009Thumbnail for version as of 00:26, 6 February 2009500 × 514 (1.32 MB)Fi1Kaiv8{{Information |Description={{en|1=The plot shows fluid flow under the velocity field <math>\mathbf u(\mathbf x,t)=(1,yt)</math>. The red dot represents a particle released from the origin at time <math>t=0</math>, tracing out its ''pathline'' in red. As
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