{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:37:59Z","timestamp":1760146679386,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T00:00:00Z","timestamp":1732665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12072012","92252201","2022YFF0610805"],"award-info":[{"award-number":["12072012","92252201","2022YFF0610805"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["12072012","92252201","2022YFF0610805"],"award-info":[{"award-number":["12072012","92252201","2022YFF0610805"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities","award":["12072012","92252201","2022YFF0610805"],"award-info":[{"award-number":["12072012","92252201","2022YFF0610805"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>While thermal convection cells exhibit left\u2013right and top\u2013bottom symmetries at low Rayleigh numbers (Ra), the emergence of coherent flow structures, such as elliptical large-scale circulation in Rayleigh\u2013B\u00e9nard convection (RBC), breaks these symmetries as the Rayleigh number increases. Recently, spatial double-reflection symmetry was proposed and verified for two-dimensional RBC at a Prandtl number of 6.5 and Ra values up to 1010. In this study, we examined this new symmetry at a lower Prandtl number of 0.7 and across a wider range of Rayleigh numbers, from 107 to 1013. Our findings reveal that the double-reflection symmetry is preserved for the mean profiles and flow fields of velocity and temperature for Ra&lt;109, but it is broken at higher Rayleigh numbers. This asymmetry at high Ra values is inferred to be induced by a flow-pattern transition at Ra=109. Together with the previous study, our results demonstrate that the Prandtl number has an important influence on the symmetry preservation in RBC.<\/jats:p>","DOI":"10.3390\/sym16121583","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T07:18:42Z","timestamp":1732691922000},"page":"1583","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Asymmetry of Two-Dimensional Thermal Convection at High Rayleigh Numbers"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5456-4229","authenticated-orcid":false,"given":"Jian-Chao","family":"He","sequence":"first","affiliation":[{"name":"Institute of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun","family":"Bao","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4702-8735","authenticated-orcid":false,"given":"Xi","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"041001","DOI":"10.1103\/RevModPhys.92.041001","article-title":"Colloquium: Unusual dynamics of convection in the Sun","volume":"92","author":"Schumacher","year":"2020","journal-title":"Rev. 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