{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T06:10:51Z","timestamp":1780553451930,"version":"3.54.1"},"reference-count":42,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,11]],"date-time":"2020-12-11T00:00:00Z","timestamp":1607644800000},"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":["91752203, 11772173, 11490553"],"award-info":[{"award-number":["91752203, 11772173, 11490553"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can be triggered at low Reynolds numbers (Re). High turbulence intensity represents strong ability of perturbation spread, and a maximum turbulence intensity is found for every test case as Re \u2265 950, where the turbulence fraction increases abruptly with Re. Skewness can reflect the velocity defects of localized turbulent patches and is revealed to become negative when Re is as low as about 660. It is shown that the third-order moments of the midplane streamwise velocities have minima, while the corresponding forth-order moments have maxima during the transition. These kinematic extremes and different variation scenarios of the friction coefficient during the transition are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit, a structure whose statistical properties are only weak functions of the Reynolds number.<\/jats:p>","DOI":"10.3390\/e22121399","type":"journal-article","created":{"date-parts":[[2020,12,13]],"date-time":"2020-12-13T20:56:57Z","timestamp":1607893017000},"page":"1399","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Intermittency, Moments, and Friction Coefficient during the Subcritical Transition of Channel Flow"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7035-0052","authenticated-orcid":false,"given":"Jinsheng","family":"Liu","sequence":"first","affiliation":[{"name":"Applied Mechanics Laboratory, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Xiao","sequence":"additional","affiliation":[{"name":"Center for Applied Physics and Technology, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mogeng","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianjun","family":"Tao","sequence":"additional","affiliation":[{"name":"Center for Applied Physics and Technology, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shengjin","family":"Xu","sequence":"additional","affiliation":[{"name":"Applied Mechanics Laboratory, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1017\/S0022112071002842","article-title":"Accurate solution of the Orr-Sommerfeld stability equation","volume":"50","author":"Orszag","year":"1971","journal-title":"J. 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