Shock at very large mach number in simple gases: A physicist approach
- 1 June 1987
- journal article
- research article
- Published by Taylor & Francis in Transport Theory and Statistical Physics
- Vol. 16 (4-6) , 727-734
- https://doi.org/10.1080/00411458708204311
Abstract
The inviscid equations for compressible flows predict the occurence of singularities after a finite time for a large class of smooth initial data[1]. Based upon the hyperbolic nature of these equations, the method of characteristics allows a detailed study of this phenomenon in one spatial dimension. Qualitatively speaking, the formation of discontinuities is related to the fact that perturbations with a larger amplitude move faster and pile up on lower amplitude perturbations. Thus, smooth initial data may produce after a finite time infinitely sharp density and/or velocity variations. This violates a basic assumptions of continuous hydrodynamics: any field as the mass density or the fluid velocity must be almost constant on molecular scales, that is on a mean free path in gases which I shall consider from now on.Keywords
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