{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T22:05:57Z","timestamp":1768514757902,"version":"3.49.0"},"reference-count":105,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,31]],"date-time":"2018-12-31T00:00:00Z","timestamp":1546214400000},"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":["11672020,11490552"],"award-info":[{"award-number":["11672020,11490552"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Low-speed streaks in wall-bounded turbulence are the dominant structures in the near-wall turbulent self-sustaining cycle. Existing studies have well characterized their spanwise spacing in the buffer layer and below. Recent studies suggested the existence of these small-scale structures in the higher layer where large-scale structures usually receive more attention. The present study is thus devoted to extending the understanding of the streak spacing to the log layer. An analysis is taken on two-dimensional (2D) wall-parallel velocity fields in a smooth-wall turbulent boundary layer with     R  e \u03c4      = 440\u223c2400, obtained via either 2D Particle Image Velocimetry (PIV) measurement taken here or public Direct Numerical Simulation (DNS). Morphological-based streak identification analysis yields a     R e    -independent log-normal distribution of the streak spacing till the upper bound of the log layer, based on which an empirical model is proposed to account for its wall-normal growth. The small-scale part of the spanwise spectra of the streamwise fluctuating velocity below     y +     = 100 is reasonably restored by a synthetic simulation that distributes elementary streak units based on the proposed empirical streak spacing model, which highlights the physical significance of streaks in shaping the small-scale part of the velocity spectra beyond the buffer layer.<\/jats:p>","DOI":"10.3390\/e21010024","type":"journal-article","created":{"date-parts":[[2018,12,31]],"date-time":"2018-12-31T07:22:30Z","timestamp":1546240950000},"page":"24","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Wall-Normal Variation of Spanwise Streak Spacing in Turbulent Boundary Layer With Low-to-Moderate Reynolds Number"],"prefix":"10.3390","volume":"21","author":[{"given":"Wenkang","family":"Wang","sequence":"first","affiliation":[{"name":"Institute of Fluid Mechanics, Beihang University, Beijing 100191, China"}]},{"given":"Chong","family":"Pan","sequence":"additional","affiliation":[{"name":"Institute of Fluid Mechanics, Beihang University, Beijing 100191, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9523-7403","authenticated-orcid":false,"given":"Jinjun","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Fluid Mechanics, Beihang University, Beijing 100191, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,31]]},"reference":[{"key":"ref_1","first-page":"77","article-title":"Detailed flow-field observations in the transition process in a thick boundary layer","volume":"Volume 16","author":"Hama","year":"1954","journal-title":"Proceedings of the Heat Transfer and Fluid Mechanics Institute"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1021\/ie50541a020","article-title":"Dye displacement technique for velocity distribution measurements","volume":"47","author":"Ferrell","year":"1955","journal-title":"Ind. 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