Energy spectrum of two-dimensional isotropic rapidly rotating turbulence
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909298206965760 |
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| author | Li, Peiyang Xie, Jin-Han |
| author_facet | Li, Peiyang Xie, Jin-Han |
| contents | We study a two-dimensional isotropic rotating system and obtain both theoretically and numerically a $K^{-2}$ energy spectrum under the rapidly rotating condition ($Ro\ll 1$), which was initially obtained by Zeman (1994) and Zhou (1995). In rotating turbulence, the $K^{-2}$ energy spectrum was proposed under the assumption of isotropy, however, the direction selectivity of rotation breaks isotropy, making this $K^{-2}$ spectrum not easily observable. To fill the gap between theoretical assumptions and realizability, we study the turbulence of inertial waves in an artificial two-dimensional isotropic rotating turbulence system. In the limit of a small Rossby number, we asymptotically derive a nonlinear amplitude equation for inertial waves, which gives the $K^{-2}$ spectrum using a strong turbulence argument. This scaling is justified by numerical simulations of both the amplitude equation and the original system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15106 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Energy spectrum of two-dimensional isotropic rapidly rotating turbulence Li, Peiyang Xie, Jin-Han Fluid Dynamics We study a two-dimensional isotropic rotating system and obtain both theoretically and numerically a $K^{-2}$ energy spectrum under the rapidly rotating condition ($Ro\ll 1$), which was initially obtained by Zeman (1994) and Zhou (1995). In rotating turbulence, the $K^{-2}$ energy spectrum was proposed under the assumption of isotropy, however, the direction selectivity of rotation breaks isotropy, making this $K^{-2}$ spectrum not easily observable. To fill the gap between theoretical assumptions and realizability, we study the turbulence of inertial waves in an artificial two-dimensional isotropic rotating turbulence system. In the limit of a small Rossby number, we asymptotically derive a nonlinear amplitude equation for inertial waves, which gives the $K^{-2}$ spectrum using a strong turbulence argument. This scaling is justified by numerical simulations of both the amplitude equation and the original system. |
| title | Energy spectrum of two-dimensional isotropic rapidly rotating turbulence |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2408.15106 |