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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.02634 |
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| _version_ | 1866909083951431680 |
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| author | Jo, Min Jun Kim, Junha Lee, Jihoon |
| author_facet | Jo, Min Jun Kim, Junha Lee, Jihoon |
| contents | The quasi-geostrohpic (QG) equation has been used to capture the asymptotic dynamics of the rotating stratified Boussinesq flows in the regime of strong stratification and rapid rotation. In this paper, we establish the invalidity of such approximation when the rotation-stratification ratio is either fixed to be unity or tends to unity sufficiently slowly in the asymptotic regime: the difference between the rotating stratified Boussinesq flow and the corresponding QG flow remains strictly away from zero, independently of the intensities of rotation and stratification. In contrast, we also show that the convergence occurs when the rotation-stratification ratio is fixed to be a number other than unity or converges to unity sufficiently fast. As a corollary, we compute a lower bound of the convergence rate, which blows up as the rotation-stratification ratio goes to unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02634 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-convergence of the rotating stratified flows toward the quasi-geostrophic dynamics Jo, Min Jun Kim, Junha Lee, Jihoon Analysis of PDEs 35Q86, 35A01 The quasi-geostrohpic (QG) equation has been used to capture the asymptotic dynamics of the rotating stratified Boussinesq flows in the regime of strong stratification and rapid rotation. In this paper, we establish the invalidity of such approximation when the rotation-stratification ratio is either fixed to be unity or tends to unity sufficiently slowly in the asymptotic regime: the difference between the rotating stratified Boussinesq flow and the corresponding QG flow remains strictly away from zero, independently of the intensities of rotation and stratification. In contrast, we also show that the convergence occurs when the rotation-stratification ratio is fixed to be a number other than unity or converges to unity sufficiently fast. As a corollary, we compute a lower bound of the convergence rate, which blows up as the rotation-stratification ratio goes to unity. |
| title | Non-convergence of the rotating stratified flows toward the quasi-geostrophic dynamics |
| topic | Analysis of PDEs 35Q86, 35A01 |
| url | https://arxiv.org/abs/2209.02634 |