Relativistic Mechanics of Continuous Media
Abstract
In this work we study the relativistic mechanics of continuous media on a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the starting point for any calculations regarding continuous media. In the force free limit, the standard relativistic equations are regained, so that these equations can be regarded as a generalization of the standard procedure. In the case of an inviscid fluid we derive an analogue of the Bernoulli equations. For irrotational flow we prove that the velocity field can be derived from a potential. If, in addition, the fluid is incompressible, the potential must obey the d'Alembert equation, and thus the problem is reduced to solving the d'Alembert equation with specific boundary conditions (in both space and time). The solutions indicate the existence of light velocity sound waves in an incompressible fluid (a result known from previous literature [19]). Relaxing the constraints and allowing the fluid to become linearly compressible, one can derive a wave equation from which the sound velosity can again be computed. For a stationary background flow, it has been demonstrated that the sound velocity attains its corrrect values for the incompressible and nonrelatvistic limits. Finally, viscosity is introduced, bulk and shear viscosity constants are defined, and we formulate equations for the motion of a viscous fluid.
 Publication:

arXiv eprints
 Pub Date:
 April 2001
 arXiv:
 arXiv:physics/0104019
 Bibcode:
 2001physics...4019S
 Keywords:

 Physics  Fluid Dynamics;
 Physics  Accelerator Physics;
 Physics  Classical Physics;
 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 Latex, 44 pages, 5 figures