Maximal Kinematical Invariance Group of Fluid Dynamics and Applications
The maximal kinematical invariance group of the Euler equations of fluid dynamics for the standard polytropic exponent is larger than the Galilei group. Specifically, the inversion transformation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline...
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MDPI AG
2022-06-01
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| Online Access: | https://www.mdpi.com/2218-1997/8/6/319 |
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| author | V. V. Sreedhar Amitabh Virmani |
| author_facet | V. V. Sreedhar Amitabh Virmani |
| author_sort | V. V. Sreedhar |
| collection | DOAJ |
| description | The maximal kinematical invariance group of the Euler equations of fluid dynamics for the standard polytropic exponent is larger than the Galilei group. Specifically, the inversion transformation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mo>Σ</mo><mo>:</mo><mi>t</mi><mo>→</mo><mo>−</mo><mn>1</mn><mo>/</mo><mi>t</mi><mo>,</mo><mspace width="0.166667em"></mspace><mover accent="true"><mi>x</mi><mo>→</mo></mover><mo>→</mo><mover accent="true"><mi>x</mi><mo>→</mo></mover><mo>/</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> leaves the Euler equation’s invariant. This duality has been used to explain the striking similarities observed in simulations of the supernova explosions and laboratory implosions induced in plasma by intense lasers. The inversion symmetry extends to discontinuous fluid flows as well. In this contribution, we provide a concise review of these ideas and discuss some applications. We also explicitly work out the implosion dual of the Sedov’s explosion solution. |
| first_indexed | 2024-03-09T22:18:00Z |
| format | Article |
| id | doaj.art-2dffac31176d4ff299e13ba960d8d815 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T22:18:00Z |
| publishDate | 2022-06-01 |
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| record_format | Article |
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| spelling | doaj.art-2dffac31176d4ff299e13ba960d8d8152023-11-23T19:19:13ZengMDPI AGUniverse2218-19972022-06-018631910.3390/universe8060319Maximal Kinematical Invariance Group of Fluid Dynamics and ApplicationsV. V. Sreedhar0Amitabh Virmani1Chennai Mathematical Institute, H1 SIPCOT IT Park, Kelambakkam, Chennai 603103, IndiaChennai Mathematical Institute, H1 SIPCOT IT Park, Kelambakkam, Chennai 603103, IndiaThe maximal kinematical invariance group of the Euler equations of fluid dynamics for the standard polytropic exponent is larger than the Galilei group. Specifically, the inversion transformation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mo>Σ</mo><mo>:</mo><mi>t</mi><mo>→</mo><mo>−</mo><mn>1</mn><mo>/</mo><mi>t</mi><mo>,</mo><mspace width="0.166667em"></mspace><mover accent="true"><mi>x</mi><mo>→</mo></mover><mo>→</mo><mover accent="true"><mi>x</mi><mo>→</mo></mover><mo>/</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> leaves the Euler equation’s invariant. This duality has been used to explain the striking similarities observed in simulations of the supernova explosions and laboratory implosions induced in plasma by intense lasers. The inversion symmetry extends to discontinuous fluid flows as well. In this contribution, we provide a concise review of these ideas and discuss some applications. We also explicitly work out the implosion dual of the Sedov’s explosion solution.https://www.mdpi.com/2218-1997/8/6/319fluid dynamicssymmetriesshock conditions |
| spellingShingle | V. V. Sreedhar Amitabh Virmani Maximal Kinematical Invariance Group of Fluid Dynamics and Applications Universe fluid dynamics symmetries shock conditions |
| title | Maximal Kinematical Invariance Group of Fluid Dynamics and Applications |
| title_full | Maximal Kinematical Invariance Group of Fluid Dynamics and Applications |
| title_fullStr | Maximal Kinematical Invariance Group of Fluid Dynamics and Applications |
| title_full_unstemmed | Maximal Kinematical Invariance Group of Fluid Dynamics and Applications |
| title_short | Maximal Kinematical Invariance Group of Fluid Dynamics and Applications |
| title_sort | maximal kinematical invariance group of fluid dynamics and applications |
| topic | fluid dynamics symmetries shock conditions |
| url | https://www.mdpi.com/2218-1997/8/6/319 |
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