dorsal/arxiv
View SchemaDynamics and thermodynamics of axisymmetric flows: I. Theory
| Authors | Nicolas Leprovost, Bérengère Dubrulle, Pierre-Henri Chavanis |
|---|---|
| Categories | |
| ArXiv ID | physics/0505084 |
| URL | https://arxiv.org/abs/physics/0505084 |
| DOI | 10.1103/PhysRevE.73.046308 |
| Journal | Physical Review E 73 (2006) 046308 |
Abstract
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We derive relaxation equations which can be used as numerical algorithm to construct stable stationary solutions of axisymmetric flows. In a second part, we develop a thermodynamical approach to the equilibrium states at some fixed coarse-grained scale. We show that the resulting distribution can be divided in a universal part coming from the conservation of robust invariants and one non-universal determined by the initial conditions through the fragile invariants (for freely evolving systems) or by a prior distribution encoding non-ideal effects such as viscosity, small-scale forcing and dissipation (for forced systems). Finally, we derive a parameterization of inviscid mixing to describe the dynamics of the system at the coarse-grained scale.
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"abstract": "We develop new variational principles to study stability and equilibrium of\naxisymmetric flows. We show that there is an infinite number of steady state\nsolutions. We show that these steady states maximize a (non-universal)\n$H$-function. We derive relaxation equations which can be used as numerical\nalgorithm to construct stable stationary solutions of axisymmetric flows. In a\nsecond part, we develop a thermodynamical approach to the equilibrium states at\nsome fixed coarse-grained scale. We show that the resulting distribution can be\ndivided in a universal part coming from the conservation of robust invariants\nand one non-universal determined by the initial conditions through the fragile\ninvariants (for freely evolving systems) or by a prior distribution encoding\nnon-ideal effects such as viscosity, small-scale forcing and dissipation (for\nforced systems). Finally, we derive a parameterization of inviscid mixing to\ndescribe the dynamics of the system at the coarse-grained scale.",
"arxiv_id": "physics/0505084",
"authors": [
"Nicolas Leprovost",
"B\u00e9reng\u00e8re Dubrulle",
"Pierre-Henri Chavanis"
],
"categories": [
"physics.flu-dyn",
"cond-mat.stat-mech"
],
"doi": "10.1103/PhysRevE.73.046308",
"journal_ref": "Physical Review E 73 (2006) 046308",
"title": "Dynamics and thermodynamics of axisymmetric flows: I. Theory",
"url": "https://arxiv.org/abs/physics/0505084"
},
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