dorsal/arxiv
View SchemaComplex Spaces In Hydrodynamics: Complex Navier-Stokes Equations
| Authors | Anatoly N. Panchenkov |
|---|---|
| Categories | |
| ArXiv ID | physics/0609159 |
| URL | https://arxiv.org/abs/physics/0609159 |
Abstract
The study is devoted to the development of new effective tools and methods of ana-lytical hydrodynamics, including problems of existence, smoothness and structure of laminar and turbulent flows. The main problem is complex Navier-Stokes equations and turbulence in complex spaces. The necessity of introducing complex spaces in hydrodynamics is deter-mined by the mechanism of transition of a laminar flow into a turbulent flow. The author pro-poses a non-traditional scenario of the transition: the cause of turbulence is in destruction (cessation of existence) of a laminar flow. The article contains the mathematical rationale for the necessity of development of the theory of turbulence in the complex configurational space: the complex configurational space is the natural area of existence of turbulence. Hydrody-namic flows are regarded as flows on entropy manifolds that [flows] are supported by the two symmetries: the symmetry of conservation of general entropy and the symmetry of duality of impulse representation. The new symmetry has been introduced and studied: the forminvari-ance of Helmholtz matrix of impulse density. The strict foundation has been provided for the known fact of chaotic mechanics: appearance of the new structure (a turbulent flow) is a result of interaction of two entities: dissipation and vorticity. On the deep level the phenomenology of turbulence in complex spaces is based on the transition from the mechanics of a material point to the mechanics of an oriented material point, that [transition] takes place in a current period of time.
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"abstract": "The study is devoted to the development of new effective tools and methods of\nana-lytical hydrodynamics, including problems of existence, smoothness and\nstructure of laminar and turbulent flows. The main problem is complex\nNavier-Stokes equations and turbulence in complex spaces. The necessity of\nintroducing complex spaces in hydrodynamics is deter-mined by the mechanism of\ntransition of a laminar flow into a turbulent flow. The author pro-poses a\nnon-traditional scenario of the transition: the cause of turbulence is in\ndestruction (cessation of existence) of a laminar flow. The article contains\nthe mathematical rationale for the necessity of development of the theory of\nturbulence in the complex configurational space: the complex configurational\nspace is the natural area of existence of turbulence. Hydrody-namic flows are\nregarded as flows on entropy manifolds that [flows] are supported by the two\nsymmetries: the symmetry of conservation of general entropy and the symmetry of\nduality of impulse representation. The new symmetry has been introduced and\nstudied: the forminvari-ance of Helmholtz matrix of impulse density. The strict\nfoundation has been provided for the known fact of chaotic mechanics:\nappearance of the new structure (a turbulent flow) is a result of interaction\nof two entities: dissipation and vorticity. On the deep level the phenomenology\nof turbulence in complex spaces is based on the transition from the mechanics\nof a material point to the mechanics of an oriented material point, that\n[transition] takes place in a current period of time.",
"arxiv_id": "physics/0609159",
"authors": [
"Anatoly N. Panchenkov"
],
"categories": [
"physics.flu-dyn"
],
"title": "Complex Spaces In Hydrodynamics: Complex Navier-Stokes Equations",
"url": "https://arxiv.org/abs/physics/0609159"
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