Invariant properties of systems of equations of the mechanics of inhomogeneous fluids |
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| Authors: | VG Baidulov YuD Chashechkin |
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| Institution: | 1. Dr. Moses Strauss Department of Marine Geosciences, Charney School of Marine Sciences, University of Haifa, Mount Carmel, 31905 Haifa, Israel;2. INGEOSUR, CONICET, Departamento de Geología, Universidad Nacional del Sur, B8000ICN Bahía Blanca, Argentina;3. Section of Earth & Environmental Sciences, University of Geneva, 1205 Geneva, Switzerland;4. Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York 10964, NY, USA;5. Departamento de Biodiversidad y Biología Experimental, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, C1428EHA Buenos Aires, Argentina;6. Institute for Geophysics, John A. and Katherine G. Jackson School of Geosciences, University of Texas at Austin, TX 78758, USA;7. Institute of Geological Sciences and Oeschger Centre for Climate Change Research, University of Bern, 3012 Bern, Switzerland;8. Geology Department, University of Otago, 9054 Otago, New Zealand |
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| Abstract: | The invariant properties of the fundamental system of equations of the mechanics of inhomogeneous fluids and its widely used approximations are analysed by the methods of continuous group theory. Simplifying assumptions significantly alter the invariant properties of the systems of equations. Both extending and contracting the admissible symmetry group can occur and provide evidence of the violation of the conditions of equivalence between the original and derived systems. For example, the use of the incompressibility and Boussinesq approximations leads to extension of the concept of an inertial reference frame to all frames moving relative to one another with arbitrary linear acceleration. |
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