{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:01:50Z","timestamp":1760241710423,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,7]],"date-time":"2018-08-07T00:00:00Z","timestamp":1533600000000},"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":["1502237,51536008"],"award-info":[{"award-number":["1502237,51536008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Statistics of heat transfer in two-dimensional (2D) turbulent Rayleigh-B\u00e9nard (RB) convection for Pr=6,20,100 and 106 are investigated using the lattice Boltzmann method (LBM). Our results reveal that the large scale circulation is gradually broken up into small scale structures plumes with the increase of Pr, the large scale circulation disappears with increasing Pr, and a great deal of smaller thermal plumes vertically rise and fall from the bottom to top walls. It is further indicated that vertical motion of various plumes gradually plays main role with increasing Pr. In addition, our analysis also shows that the thermal dissipation is distributed mainly in the position of high temperature gradient, the thermal dissipation rate \u03b5\u03b8 already increasingly plays a dominant position in the thermal transport, \u03b5u can have no effect with increase of Pr. The kinematic viscosity dissipation rate and the thermal dissipation rate gradually decrease with increasing Pr. The energy spectrum significantly decreases with the increase of Pr. A scope of linear scaling arises in the second order velocity structure functions, the temperature structure function and mixed structure function(temperature-velocity). The value of linear scaling and the 2nd-order velocity decrease with increasing Pr, which is qualitatively consistent with the theoretical predictions.<\/jats:p>","DOI":"10.3390\/e20080582","type":"journal-article","created":{"date-parts":[[2018,8,7]],"date-time":"2018-08-07T11:20:23Z","timestamp":1533640823000},"page":"582","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Statistics of Heat Transfer in Two-Dimensional Turbulent Rayleigh-B\u00e9nard Convection at Various Prandtl Number"],"prefix":"10.3390","volume":"20","author":[{"given":"Hui","family":"Yang","sequence":"first","affiliation":[{"name":"Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China"},{"name":"State-Province Joint Engineering Lab of Fluid Transmission System Technology, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yikun","family":"Wei","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China"},{"name":"State-Province Joint Engineering Lab of Fluid Transmission System Technology, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zuchao","family":"Zhu","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China"},{"name":"State-Province Joint Engineering Lab of Fluid Transmission System Technology, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huashu","family":"Dou","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China"},{"name":"State-Province Joint Engineering Lab of Fluid Transmission System Technology, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuehong","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Mathematic Science, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4495","DOI":"10.1175\/1520-0442(2001)014<4495:TCATEB>2.0.CO;2","article-title":"Tropical convection and the energy balance at the top of the atmosphere","volume":"14","author":"Hartmann","year":"2011","journal-title":"J. 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