On the baroclinic instability of inviscid non-conducting Boussinesq equations with rotation in 3-D
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910062077804544 |
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| author | Mao, Jingjing Wang, Yan-Lin |
| author_facet | Mao, Jingjing Wang, Yan-Lin |
| contents | In this paper, we prove the nonlinear instability of a given vertical shear of velocity between two rigid plane for the 3-D inviscid, non-conducting Boussinesq equations with rotation. When the Rossby number is zero, this rotating inviscid Boussinesq system reduces to the nonlinear geostrophic limit model. For non-zero small Rossby numbers, we establish the nonlinear instability of the shear flow, which is consistent with that of the geostrophic limit model. The proof relies on constructing a precise approximate solution, which comprises a growing profile derived from the nonlinear geostrophic limit model and a higher-order asymptotic expansion with respect to the small Rossby number. Notice that the instabilities (growing modes) are driven by the physical boundaries. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_06835 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the baroclinic instability of inviscid non-conducting Boussinesq equations with rotation in 3-D Mao, Jingjing Wang, Yan-Lin Analysis of PDEs In this paper, we prove the nonlinear instability of a given vertical shear of velocity between two rigid plane for the 3-D inviscid, non-conducting Boussinesq equations with rotation. When the Rossby number is zero, this rotating inviscid Boussinesq system reduces to the nonlinear geostrophic limit model. For non-zero small Rossby numbers, we establish the nonlinear instability of the shear flow, which is consistent with that of the geostrophic limit model. The proof relies on constructing a precise approximate solution, which comprises a growing profile derived from the nonlinear geostrophic limit model and a higher-order asymptotic expansion with respect to the small Rossby number. Notice that the instabilities (growing modes) are driven by the physical boundaries. |
| title | On the baroclinic instability of inviscid non-conducting Boussinesq equations with rotation in 3-D |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.06835 |