Large-scale circulation reversals explained by pendulum correspondence
We introduce a low-order dynamical system to describe thermal convection in an annular domain. The model derives systematically from a Fourier–Laurent truncation of the governing Navier–Stokes Boussinesq equations and accounts for spatial dependence of the flow and temperature fields. Comparison wit...
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| Veröffentlicht in: | Journal of fluid mechanics 2024-09, Vol.993, Article A3 |
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| creator | Moore, Nicholas J. Huang, Jinzi Mac |
| description | We introduce a low-order dynamical system to describe thermal convection in an annular domain. The model derives systematically from a Fourier–Laurent truncation of the governing Navier–Stokes Boussinesq equations and accounts for spatial dependence of the flow and temperature fields. Comparison with fully resolved direct numerical simulations (DNS) shows that the model captures parameter bifurcations and reversals of the large-scale circulation (LSC), including states of (i) steady circulating flow, (ii) chaotic LSC reversals and (iii) periodic LSC reversals. Casting the system in terms of the fluid's angular momentum and centre of mass (CoM) reveals equivalence to a damped pendulum with forcing that raises the CoM above the fulcrum. This formulation offers a transparent mechanism for LSC reversals, namely the inertial overshoot of a forced pendulum, and it yields an explicit formula for the frequency $f^*$ of regular LSC reversals in the high-Rayleigh-number (Ra) limit. This formula is shown to be in excellent agreement with DNS and produces the scaling law $f^* \sim {Ra}^{0.5}$. |
| doi_str_mv | 10.1017/jfm.2024.584 |
| format | Article |
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The model derives systematically from a Fourier–Laurent truncation of the governing Navier–Stokes Boussinesq equations and accounts for spatial dependence of the flow and temperature fields. Comparison with fully resolved direct numerical simulations (DNS) shows that the model captures parameter bifurcations and reversals of the large-scale circulation (LSC), including states of (i) steady circulating flow, (ii) chaotic LSC reversals and (iii) periodic LSC reversals. Casting the system in terms of the fluid's angular momentum and centre of mass (CoM) reveals equivalence to a damped pendulum with forcing that raises the CoM above the fulcrum. This formulation offers a transparent mechanism for LSC reversals, namely the inertial overshoot of a forced pendulum, and it yields an explicit formula for the frequency $f^*$ of regular LSC reversals in the high-Rayleigh-number (Ra) limit. This formula is shown to be in excellent agreement with DNS and produces the scaling law $f^* \sim {Ra}^{0.5}$.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2024.584</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Angular momentum ; Bifurcations ; Boussinesq approximation ; Boussinesq equations ; Cellular convection ; Chaos theory ; Convection ; Direct numerical simulation ; Domain names ; Dynamical systems ; Free convection ; JFM Papers ; Momentum ; Pendulums ; Rayleigh number ; Scaling ; Scaling laws ; Simulation ; Temperature dependence ; Temperature fields</subject><ispartof>Journal of fluid mechanics, 2024-09, Vol.993, Article A3</ispartof><rights>The Author(s), 2024. Published by Cambridge University Press.</rights><rights>The Author(s), 2024. Published by Cambridge University Press. 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This formulation offers a transparent mechanism for LSC reversals, namely the inertial overshoot of a forced pendulum, and it yields an explicit formula for the frequency $f^*$ of regular LSC reversals in the high-Rayleigh-number (Ra) limit. 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Fluid Mech</addtitle><date>2024-09-13</date><risdate>2024</risdate><volume>993</volume><artnum>A3</artnum><issn>0022-1120</issn><eissn>1469-7645</eissn><abstract>We introduce a low-order dynamical system to describe thermal convection in an annular domain. The model derives systematically from a Fourier–Laurent truncation of the governing Navier–Stokes Boussinesq equations and accounts for spatial dependence of the flow and temperature fields. Comparison with fully resolved direct numerical simulations (DNS) shows that the model captures parameter bifurcations and reversals of the large-scale circulation (LSC), including states of (i) steady circulating flow, (ii) chaotic LSC reversals and (iii) periodic LSC reversals. Casting the system in terms of the fluid's angular momentum and centre of mass (CoM) reveals equivalence to a damped pendulum with forcing that raises the CoM above the fulcrum. This formulation offers a transparent mechanism for LSC reversals, namely the inertial overshoot of a forced pendulum, and it yields an explicit formula for the frequency $f^*$ of regular LSC reversals in the high-Rayleigh-number (Ra) limit. This formula is shown to be in excellent agreement with DNS and produces the scaling law $f^* \sim {Ra}^{0.5}$.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2024.584</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0001-9578-7982</orcidid><orcidid>https://orcid.org/0000-0003-4277-5851</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Angular momentum Bifurcations Boussinesq approximation Boussinesq equations Cellular convection Chaos theory Convection Direct numerical simulation Domain names Dynamical systems Free convection JFM Papers Momentum Pendulums Rayleigh number Scaling Scaling laws Simulation Temperature dependence Temperature fields |
| title | Large-scale circulation reversals explained by pendulum correspondence |
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