Acta Mechanica Sinica

, Volume 34, Issue 5, pp 793–811 | Cite as

Re-understanding the law-of-the-wall for wall-bounded turbulence based on in-depth investigation of DNS data

  • Bochao Cao
  • Hongyi XuEmail author
Research Paper


Based on direct numerical simulation (DNS) data of the straight ducts, namely square and rectangular annular ducts, detailed analyses were conducted for the mean streamwise velocity, relevant velocity scales, and turbulence statistics. It is concluded that turbulent boundary layers (TBL) should be broadly classified into three types (Type-A, -B, and -C) in terms of their distribution patterns of the time-averaged local wall-shear stress (\(\tau _\mathrm{w} )\) or the mean local frictional velocity (\(u_\tau )\). With reference to the Type-A TBL analysis by von Karman in developing the law-of-the-wall using the time-averaged local frictional velocity (\(u_\tau )\) as scale, the current study extended the approach to the Type-B TBL and obtained the analytical expressions for streamwise velocity in the inner-layer using ensemble-averaged frictional velocity (\(\bar{{u}}_\tau )\) as scale. These analytical formulae were formed by introducing the general damping and enhancing functions. Further, the research applied a near-wall DNS-guided integration to the governing equations of Type-B TBL and quantitatively proved the correctness and accuracy of the inner-layer analytical expressions for this type.


Direct numerical simulation (DNS) Wall-bounded turbulence Turbulent boundary layer 



The work was supported by the National Natural Science Foundation of China (91434112), the United Innovation Program of Shanghai Commercial Aircraft Engine (AR908) (the program was founded by Shanghai Municipal Commission of Economy and Information, Shanghai Municipal Education Commission and AECC Commercial Aircraft Engine Co., LTD), and the Shanghai Thousand Talents Program (EZH2126503). The National Supercomputer Center of China in Tianjin provided the critically important super-computing resources, TianHe system. The authors would like to thank Dr. Gavrilakis, Dr. Huser, and Dr. Biringen for sharing their DNS results. It is a pleasure to acknowledge the constructive discussions with Prof. Aiming Yang, Prof. Jun Huang, and Prof. Yingqing Zu at Fudan University.


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Aeronautics and Astronautics DepartmentFudan UniversityShanghaiChina

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