Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region
The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensor S and rotation rate tensor Ω and calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations fo...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/147125 |
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| author | Igor Vigdorovich Holger Foysi |
| author_facet | Igor Vigdorovich Holger Foysi |
| author_sort | Igor Vigdorovich |
| collection | DOAJ |
| description | The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensor S and rotation rate tensor Ω and calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows. Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensors S and Ω are studied. The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensors S and Ω, in which the scalar coefficients depend on simultaneous invariants of these tensors. |
| format | Article |
| id | doaj-art-46d96e7be7934357b066d5a4e5d0d45a |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-46d96e7be7934357b066d5a4e5d0d45a2025-02-03T06:46:25ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/147125147125Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted RegionIgor Vigdorovich0Holger Foysi1Institute of Mechanics, Lomonosov Moscow State University, Michurinsky Avenue 1, Moscow 119192, RussiaChair of Fluid Mechanics, Universität Siegen, Paul-Bonatz-Straße 9–11, 57068 Siegen, GermanyThe purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensor S and rotation rate tensor Ω and calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows. Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensors S and Ω are studied. The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensors S and Ω, in which the scalar coefficients depend on simultaneous invariants of these tensors.http://dx.doi.org/10.1155/2015/147125 |
| spellingShingle | Igor Vigdorovich Holger Foysi Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region Advances in Mathematical Physics |
| title | Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region |
| title_full | Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region |
| title_fullStr | Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region |
| title_full_unstemmed | Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region |
| title_short | Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region |
| title_sort | simultaneous invariants of strain and rotation rate tensors and their admitted region |
| url | http://dx.doi.org/10.1155/2015/147125 |
| work_keys_str_mv | AT igorvigdorovich simultaneousinvariantsofstrainandrotationratetensorsandtheiradmittedregion AT holgerfoysi simultaneousinvariantsofstrainandrotationratetensorsandtheiradmittedregion |