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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-06-01
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| Series: | Universe |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-1997/8/6/319 |
| Summary: | 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. |
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| ISSN: | 2218-1997 |