Stability of viscous three-dimensional stratified Couette flow via dispersion and mixing
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| Format: | Preprint |
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2024
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| _version_ | 1866913241410568192 |
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| author | Zelati, Michele Coti Del Zotto, Augusto Widmayer, Klaus |
| author_facet | Zelati, Michele Coti Del Zotto, Augusto Widmayer, Klaus |
| contents | This article explores the stability of stratified Couette flow in the viscous $3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal gravity waves. These mechanisms are of fundamentally different nature and relevant in complementary dynamical regimes. Our study combines them to establish a bound for the nonlinear transition threshold, which is quantitatively larger than the inverse Reynolds number $ν$, and increases with stronger stratification resp. gravity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_15312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of viscous three-dimensional stratified Couette flow via dispersion and mixing Zelati, Michele Coti Del Zotto, Augusto Widmayer, Klaus Analysis of PDEs Fluid Dynamics This article explores the stability of stratified Couette flow in the viscous $3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal gravity waves. These mechanisms are of fundamentally different nature and relevant in complementary dynamical regimes. Our study combines them to establish a bound for the nonlinear transition threshold, which is quantitatively larger than the inverse Reynolds number $ν$, and increases with stronger stratification resp. gravity. |
| title | Stability of viscous three-dimensional stratified Couette flow via dispersion and mixing |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2402.15312 |