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Applied Mathematics and Mechanics >

2019 , Vol. 40 >Issue 3: 381 - 396

DOI: https://doi.org/10.1007/s10483-019-2448-8

Articles

Relationship between wall shear stresses and streamwise vortices in turbulent flows over wavy boundaries

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  • 1. Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;
    2. Department of Mechanical Engineering and Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55455, U. S. A

Received date: 2018-09-04

  Revised date: 2018-11-25

  Online published: 2019-03-01

Supported by

Project supported by the the National Natural Science Foundation of China (Nos. 91752205 and 11772172) and the “13th Five-Year Plan” Equipment Development Common Technology Pre-research (No. 41407020501)

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Abstract

The relationship between wall shear stresses and near-wall streamwise vortices is investigated via a direct numerical simulation (DNS) of turbulent flows over a wavy boundary with traveling-wave motion. The results indicate that the wall shear stresses are still closely related to the near-wall streamwise vortices in the presence of a wave. The wave age and wave phase significantly affect the distribution of a two-point correlation coefficient between the wall shear stresses and streamwise vorticity. For the slow wave case of c/Um=0.14, the correlation is attenuated above the leeward side while the distribution of correlation function is more elongated and also exhibits a larger vertical extent above the crest. With respect to the fast wave case of c/Um=1.4, the distribution of the correlation function is recovered in a manner similar to that in the flat-wall case. In this case, the maximum correlation coefficient exhibits only slight differences at different wave phases while the vertical distribution of the correlation function depends on the wave phase.

Key words： Taylor mapping; motion of bouncing ball; regular homoclinic point; bifurcation; periodic point; wall shear stress; near-wall streamwise vortex; two-point correlation; direct numerical simulation (DNS)

Cite this article

Lihao WANG, Weixi HUANG, Chunxiao XU, Lian SHEN, Zhaoshun ZHANG . Relationship between wall shear stresses and streamwise vortices in turbulent flows over wavy boundaries[J]. Applied Mathematics and Mechanics, 2019 , 40(3) : 381 -396 . DOI: 10.1007/s10483-019-2448-8

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