Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids
Abstract
The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one dimensional nonsteady isentropic motions of a fluid whose equation of state is of MieGruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented.
 Publication:

Ph.D. Thesis
 Pub Date:
 July 1976
 Bibcode:
 1976PhDT........97H
 Keywords:

 Fluid Dynamics;
 Lie Groups;
 Symmetry;
 Invariance;
 Kinematics;
 Shock Waves;
 Thermodynamics;
 Fluid Mechanics and Heat Transfer