Dynamical stability and flow regimes in a stably stratified valley-shaped cavity heated from below
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866915266930147328 |
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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 investigate the three-dimensional stability of a stably stratified fluid in a valley-shaped cavity heated from below using linear stability analysis and direct numerical simulations. We first describe the pure-conduction flow state and derive a dimensionless criterion that provides a lower bound for the onset of instability, valid for any slope angle. We then examine the sequence of flow regimes for a slope angle of $α= 30^{\circ}$ and Prandtl number $Pr = 7$, including two-dimensional steady states, the emergence of a Hopf bifurcation, and the formation of steady and oscillatory three-dimensional structures preceding the transition to fully unsteady, chaotic flow. Although the nonlinear governing equations depend on two dimensionless parameters, we find that the flow dynamics across a wide parameter range collapse to depend on a single parameter--the composite stratification parameter $Π_c$. However, as the system becomes more unstable, sensitivity to the second parameter, $Π_h$, increases. We construct a regime map of all observed flow states as a function of $Π_c$ and $Π_h$, and confirm the onset of chaos using Lyapunov exponents. Across all regimes, asymmetric circulation remains the dominant flow structure, persisting even in time-averaged fields of chaotic states. Finally, we characterize heat transfer in the cavity using the Nusselt number, which scales as $Nu \sim Π_c^{0.43}$ or equivalently $Nu \sim Ra^{0.275}$. This result further establishes $Π_c$ as a key dimensionless parameter governing the flow dynamics preceding the chaotic regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical stability and flow regimes in a stably stratified valley-shaped cavity heated from below Stofanak, Patrick J. Xiao, Cheng-Nian Senocak, Inanc Fluid Dynamics We investigate the three-dimensional stability of a stably stratified fluid in a valley-shaped cavity heated from below using linear stability analysis and direct numerical simulations. We first describe the pure-conduction flow state and derive a dimensionless criterion that provides a lower bound for the onset of instability, valid for any slope angle. We then examine the sequence of flow regimes for a slope angle of $α= 30^{\circ}$ and Prandtl number $Pr = 7$, including two-dimensional steady states, the emergence of a Hopf bifurcation, and the formation of steady and oscillatory three-dimensional structures preceding the transition to fully unsteady, chaotic flow. Although the nonlinear governing equations depend on two dimensionless parameters, we find that the flow dynamics across a wide parameter range collapse to depend on a single parameter--the composite stratification parameter $Π_c$. However, as the system becomes more unstable, sensitivity to the second parameter, $Π_h$, increases. We construct a regime map of all observed flow states as a function of $Π_c$ and $Π_h$, and confirm the onset of chaos using Lyapunov exponents. Across all regimes, asymmetric circulation remains the dominant flow structure, persisting even in time-averaged fields of chaotic states. Finally, we characterize heat transfer in the cavity using the Nusselt number, which scales as $Nu \sim Π_c^{0.43}$ or equivalently $Nu \sim Ra^{0.275}$. This result further establishes $Π_c$ as a key dimensionless parameter governing the flow dynamics preceding the chaotic regime. |
| title | Dynamical stability and flow regimes in a stably stratified valley-shaped cavity heated from below |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2504.21173 |