Bounds on the Global Attractor of 2D Incompressible Turbulence in the Palinstrophy-Enstrophy-Energy Space
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910719934464000 |
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| author | Emami, Pedram Bowman, John C. |
| author_facet | Emami, Pedram Bowman, John C. |
| contents | Analytic bounds on the projection of the global attractor of 2D incompressible turbulence in the palinstrophy--enstrophy plane [Dascaliuc, Foias, and Jolly 2005, 2010] are observed to vastly overestimate the values obtained from numerical simulations. This is due to the lack of a good estimate for the inner product $(\cal{B}(u,u),A^2u)$ of the advection term and the biLaplacian. Sobolev inequalities like Ladyzhenskaya or Agmon's inequalities yield an upper bound that we show is not sharp. In fact, for statistically isotropic turbulence, the expected value of $(\cal{B}(u,u),A^2u)$ is zero. The implications for estimates on the behaviour of the global attractor are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19423 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounds on the Global Attractor of 2D Incompressible Turbulence in the Palinstrophy-Enstrophy-Energy Space Emami, Pedram Bowman, John C. Fluid Dynamics Analysis of PDEs Functional Analysis Analytic bounds on the projection of the global attractor of 2D incompressible turbulence in the palinstrophy--enstrophy plane [Dascaliuc, Foias, and Jolly 2005, 2010] are observed to vastly overestimate the values obtained from numerical simulations. This is due to the lack of a good estimate for the inner product $(\cal{B}(u,u),A^2u)$ of the advection term and the biLaplacian. Sobolev inequalities like Ladyzhenskaya or Agmon's inequalities yield an upper bound that we show is not sharp. In fact, for statistically isotropic turbulence, the expected value of $(\cal{B}(u,u),A^2u)$ is zero. The implications for estimates on the behaviour of the global attractor are discussed. |
| title | Bounds on the Global Attractor of 2D Incompressible Turbulence in the Palinstrophy-Enstrophy-Energy Space |
| topic | Fluid Dynamics Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2411.19423 |