Critical dimension for hydrodynamic turbulence
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914912917258240 |
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| author | Verma, Mahendra K. |
| author_facet | Verma, Mahendra K. |
| contents | Hydrodynamic turbulence exhibits nonequilibrium behaviour with $k^{-5/3}$ energy spectrum, and equilibrium behaviour with $k^{d-1}$ energy spectrum and zero viscosity, where $d$ is the space dimension. Using recursive renormalization group {in Craya-Herring basis}, we show that the nonequilibrium solution is valid only for $d < 6$, whereas equilibrium solution with zero viscosity is the only solution for $d>6$. Thus, $d=6$ is the critical dimension for hydrodynamic turbulence. In addition, we show that the energy flux changes sign from positive to negative near $d=2.15$. We also compute the energy flux and Kolmogorov's constants for various $d$'s, and observe that our results are in good agreement with past numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07573 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical dimension for hydrodynamic turbulence Verma, Mahendra K. Statistical Mechanics High Energy Physics - Theory Hydrodynamic turbulence exhibits nonequilibrium behaviour with $k^{-5/3}$ energy spectrum, and equilibrium behaviour with $k^{d-1}$ energy spectrum and zero viscosity, where $d$ is the space dimension. Using recursive renormalization group {in Craya-Herring basis}, we show that the nonequilibrium solution is valid only for $d < 6$, whereas equilibrium solution with zero viscosity is the only solution for $d>6$. Thus, $d=6$ is the critical dimension for hydrodynamic turbulence. In addition, we show that the energy flux changes sign from positive to negative near $d=2.15$. We also compute the energy flux and Kolmogorov's constants for various $d$'s, and observe that our results are in good agreement with past numerical results. |
| title | Critical dimension for hydrodynamic turbulence |
| topic | Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2408.07573 |