Self-organization in a stably stratified, valley-shaped enclosure heated from below
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| author | Stofanak, Patrick J. Xiao, Cheng-Nian Senocak, Inanc |
| author_facet | Stofanak, Patrick J. Xiao, Cheng-Nian Senocak, Inanc |
| contents | We observe the spontaneous onset of three-dimensional motion from a quiescent, purely conductive state of a stably stratified fluid in a V-shaped enclosure heated from below, which ultimately self-organizes into a two-dimensional steady state without any external forcing to the initial configuration. We identify a dominant three-dimensional instability through modal stability analysis. Direct numerical simulations confirm this instability but also reveal that, after an initial period of spontaneous three-dimensional growth, the flow gradually self-organizes into a steady two-dimensional state without external intervention. This self-organization manifests consistently for any arbitrary infinitesimal three-dimensional disturbance to the initial quiescent configuration. We demonstrate that the mechanism driving this self-organization is the increasing dominance of viscous dissipation over buoyant production of disturbance kinetic energy at later stages of flow evolution from the initial quiescent state. Our investigation reveals a flow scenario in which the most natural transition pathway to the final state involves passing through an intermediate state with a higher dimension than the final state itself. Specifically, our final flow state is less complex than the three-dimensional most unstable eigenvector predicted by linear stability analysis. We demonstrate that the entire flow evolution remains non-turbulent throughout and closely aligns with results from linear stability analysis, distinguishing the present flow dynamics from transient chaos, which also features complex transient states that eventually converge to a less complex final state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14887 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Self-organization in a stably stratified, valley-shaped enclosure heated from below Stofanak, Patrick J. Xiao, Cheng-Nian Senocak, Inanc Fluid Dynamics Adaptation and Self-Organizing Systems We observe the spontaneous onset of three-dimensional motion from a quiescent, purely conductive state of a stably stratified fluid in a V-shaped enclosure heated from below, which ultimately self-organizes into a two-dimensional steady state without any external forcing to the initial configuration. We identify a dominant three-dimensional instability through modal stability analysis. Direct numerical simulations confirm this instability but also reveal that, after an initial period of spontaneous three-dimensional growth, the flow gradually self-organizes into a steady two-dimensional state without external intervention. This self-organization manifests consistently for any arbitrary infinitesimal three-dimensional disturbance to the initial quiescent configuration. We demonstrate that the mechanism driving this self-organization is the increasing dominance of viscous dissipation over buoyant production of disturbance kinetic energy at later stages of flow evolution from the initial quiescent state. Our investigation reveals a flow scenario in which the most natural transition pathway to the final state involves passing through an intermediate state with a higher dimension than the final state itself. Specifically, our final flow state is less complex than the three-dimensional most unstable eigenvector predicted by linear stability analysis. We demonstrate that the entire flow evolution remains non-turbulent throughout and closely aligns with results from linear stability analysis, distinguishing the present flow dynamics from transient chaos, which also features complex transient states that eventually converge to a less complex final state. |
| title | Self-organization in a stably stratified, valley-shaped enclosure heated from below |
| topic | Fluid Dynamics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2312.14887 |