dorsal/arxiv
View SchemaRelativistic Mechanics of Continuous Media
| Authors | S. Sklarz, L. P. Horwitz |
|---|---|
| Categories | |
| ArXiv ID | physics/0104019 |
| URL | https://arxiv.org/abs/physics/0104019 |
| DOI | 10.1023/A:1017559901338 |
| Journal | Found.Phys. 31 (2001) 909-934 |
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 non-relatvistic limits. Finally, viscosity is introduced, bulk and shear viscosity constants are defined, and we formulate equations for the motion of a viscous fluid.
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"abstract": "In this work we study the relativistic mechanics of continuous media on a\nfundamental level using a manifestly covariant proper time procedure. We\nformulate equations of motion and continuity (and constitutive equations) that\nare the starting point for any calculations regarding continuous media. In the\nforce free limit, the standard relativistic equations are regained, so that\nthese equations can be regarded as a generalization of the standard procedure.\nIn the case of an inviscid fluid we derive an analogue of the Bernoulli\nequations. For irrotational flow we prove that the velocity field can be\nderived from a potential. If, in addition, the fluid is incompressible, the\npotential must obey the d\u0027Alembert equation, and thus the problem is reduced to\nsolving the d\u0027Alembert equation with specific boundary conditions (in both\nspace and time). The solutions indicate the existence of light velocity sound\nwaves in an incompressible fluid (a result known from previous literature\n[19]). Relaxing the constraints and allowing the fluid to become linearly\ncompressible, one can derive a wave equation from which the sound velosity can\nagain be computed. For a stationary background flow, it has been demonstrated\nthat the sound velocity attains its corrrect values for the incompressible and\nnon-relatvistic limits. Finally, viscosity is introduced, bulk and shear\nviscosity constants are defined, and we formulate equations for the motion of a\nviscous fluid.",
"arxiv_id": "physics/0104019",
"authors": [
"S. Sklarz",
"L. P. Horwitz"
],
"categories": [
"physics.flu-dyn",
"math-ph",
"math.MP",
"physics.acc-ph",
"physics.class-ph"
],
"doi": "10.1023/A:1017559901338",
"journal_ref": "Found.Phys. 31 (2001) 909-934",
"title": "Relativistic Mechanics of Continuous Media",
"url": "https://arxiv.org/abs/physics/0104019"
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