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)
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Summary[edit]
DescriptionStreaklines and pathlines animation.gif |
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[edit]
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[edit]
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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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 00:26, 6 February 2009 | 500 × 514 (1.32 MB) | Fi1Kaiv8 (talk | contribs) | {{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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GIF file comment | Created by Wolfram Mathematica 6.0 |
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