Maximal Kinematical Invariance Group of Fluid Dynamics and Applications

Abstract

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 (Σ:t→−1/t,x→→x→/t) 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.

Keywords

• fluid dynamics
• symmetries
• shock conditions