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Numerical simulations of thermal convection on a hemisphere

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBRUNEAU, C.-H
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorFISCHER, Patrick
hal.structure.identifierHuazhong University of Science and Technology [Wuhan] [HUST]
dc.contributor.authorXIONG, Y.-L.
hal.structure.identifierLaboratoire Ondes et Matière d'Aquitaine [LOMA]
dc.contributor.authorKELLAY, H.
dc.date.created2017-12-21
dc.date.issued2018
dc.identifier.issn2469-990X
dc.description.abstractEnIn this paper we present numerical simulations of two-dimensional turbulent convection on a hemisphere. Recent experiments on a half soap bubble located on a heated plate have shown that such a configuration is ideal for studying thermal convection on a curved surface. Thermal convection and fluid flows on curved surfaces are relevant to a variety of situations, notably for simulating atmospheric and geophysical flows. As in experiments, our simulations show that the gradient of temperature between the base and the top of the hemisphere generates thermal plumes at the base that move up from near the equator to the pole. The movement of these plumes gives rise to a two-dimensional turbulent thermal convective flow. Our simulations turn out to be in qualitative and quantitative agreement with experiments and show strong similarities with Rayleigh-Bénard convection in classical cells where a fluid is heated from below and cooled from above. To compare to results obtained in classical Rayleigh-Bénard convection in standard three-dimensional cells (rectangular or cylindrical), a Nusselt number adapted to our geometry and a Reynolds number are calculated as a function of the Rayleigh number. We find that the Nusselt and Reynolds numbers verify scaling laws consistent with turbulent Rayleigh-Bénard convection: Nu ∝ Ra 0.31 and Re ∝ Ra 1/2. Further, a Bolgiano regime is found with the Bolgiano scale scaling as Ra −1/4. All these elements show that despite the significant differences in geometry between our simulations and classical 3D cells, the scaling laws of thermal convection are robust.
dc.description.sponsorshipcyclones dans des bulles de savon - ANR-10-BLAN-0410
dc.language.isoen
dc.publisherAmerican Physical Society
dc.title.enNumerical simulations of thermal convection on a hemisphere
dc.typeArticle de revue
dc.identifier.doi10.1103/PhysRevFluids.3.043502
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
dc.subject.halPhysique [physics]/Physique [physics]/Physique Numérique [physics.comp-ph]
dc.subject.halPhysique [physics]/Matière Condensée [cond-mat]/Matière Molle [cond-mat.soft]
bordeaux.journalPhysical Review Fluids
bordeaux.page043502
bordeaux.volume3
bordeaux.issue4
bordeaux.peerReviewedoui
hal.identifierhal-01803691
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01803691v1
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