File:Streaklines and pathlines animation.gif
Summary
The plot shows fluid flow under the velocity field <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d49ce691e076f1a90297ab4a1fed2b377418c7a4" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:15.988ex; height:2.843ex;" alt="{\displaystyle \mathbf {u} (\mathbf {x} ,t)=(1,xt)}">. The red dot represents a particle released from the origin at time <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43469ec032d858feae5aa87029e22eaaf0109e9c" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:5.132ex; height:2.176ex;" alt="{\displaystyle t=0}">, 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.
Licensing
Lua error in package.lua at line 80: module 'strict' not found.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 11:44, 7 January 2017 | | 500 × 514 (1.32 MB) | 127.0.0.1 (talk) | The plot shows fluid flow under the velocity field <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">x</mi></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mi>x</mi><mi>t</mi><mo stretchy="false">)</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \mathbf {u} (\mathbf {x} ,t)=(1,xt)}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d49ce691e076f1a90297ab4a1fed2b377418c7a4" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:15.988ex; height:2.843ex;" alt="{\displaystyle \mathbf {u} (\mathbf {x} ,t)=(1,xt)}"></span>. The red dot represents a particle released from the origin at time <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>t</mi><mo>=</mo><mn>0</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle t=0}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43469ec032d858feae5aa87029e22eaaf0109e9c" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:5.132ex; height:2.176ex;" alt="{\displaystyle t=0}"></span>, tracing out its <i>pathline</i> in red. <p>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. </p> The velocity is represented twice, with flow vectors, and the grey dashed <i>streamlines</i>, which connect the flow vectors. |
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