Skip to main content
SpringerLink
Log in

An extended similarity in channel turbulence

  • Published:
Journal of Hydrodynamics Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In this paper, Liutex similarity is extended and revised in channel turbulence. Liutex similarity is free from viscous dissipation, relaxing the very high Reynolds number assumption of K41. Liutex similarity hypothesis in 2-D channel turbulence is first proposed and estimated, which denotes that the statistical properties of Liutex field are uniquely and universally determined by the scale l, Liutex vortex number density n(A) with each area A and mean dissipation rate of square of Liutex magnitude ηL. The Liutex spectrum is EL (k) ∼ C[n(A)1/2ηL]1/3k−5/3 in the inertial range where energy spectrum exhibits double cascades. The scaling behaviors of Liutex spectrum in 2-D are independent of Reynolds number. Liutex structure functions are defined as Liutexp (l) ≡ 〈[δR∥(l)]p〉 which are in dependent of scales. It is found that Liutexp (l) ∼ C′(ηL)p/3l0 by dimensional analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Liu C., Gao Y., Tian S. et al. Rortex-A new vortex vector definition and vorticity tensor and vector decompositions [J]. Physics of Fluids, 2018, 30(3): 034103.

    Article  Google Scholar 

  2. Gao Y., Liu C. Rortex and comparison with eigenvalue-based vortex identification criteria [J]. Physics of Fluids, 2018, 30(8): 085107.

    Article  Google Scholar 

  3. Wang Y. Q., Gao Y. S., Liu J. M. et al. Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition [J]. Journal of Hydrodynamics, 2019, 31(3): 464–474.

    Article  Google Scholar 

  4. Dong X., Gao Y., Liu C. New normalized Rortex/vortex identification method [J]. Physics of Fluids, 2019, 31(1): 011701.

    Article  Google Scholar 

  5. Liu J., Liu C. Modified normalized Rortex/vortex identification method [J]. Physics of Fluids, 2019, 31(6): 061704.

    Article  Google Scholar 

  6. Shrestha P., Nottage C., Yu Y. et al. Stretching and shearing contamination analysis for Liutex and other vortex identification methods [J]. Advances in Aerodynamics, 2021, 3(1): 1–20.

    Article  Google Scholar 

  7. Yu Y., Shrestha P., Alvarez O. et al. Investigation of correlation between vorticity, Q, λci, λ2, Δ and Liutex [J]. Computers and Fluids, 2021, 225: 104977.

    Article  MathSciNet  Google Scholar 

  8. Liu J., Gao Y., Liu C. An objective version of the Rortex vector for vortex identification [J]. Physics of Fluids, 2019, 31(6): 065112.

    Article  Google Scholar 

  9. Xu W., Gao Y., Deng Y. et al. An explicit expression for the calculation of the Rortex vector [J]. Physics of Fluids, 2019, 31(9): 095102.

    Article  Google Scholar 

  10. Xu W. Q., Wang Y. Q., Gao Y. S. et al. Liutex similarity in turbulent boundary layer [J]. Journal of Hydrodynamics, 2019, 31(6): 1259–1262.

    Article  Google Scholar 

  11. Kraichnan R. H. Inertial ranges in two-dimensional turbulence [J]. Physics of Fluids, 1967, 10(7): 1417–1423.

    Article  Google Scholar 

  12. Benzi R., Patarnello S., Santangelo P. Self-similar coherent structures in two-dimensional decaying turbulence [J]. Journal of Physics A: Mathematical and General, 1999, 21(5): 1221.

    Article  Google Scholar 

  13. Benzi R., Colella M., Briscolini M. et al. A simple point vortex model for two-dimensional decaying turbulence [J]. Physics of Fluids A Fluid Dynamics, 1992, 4(5): 1036–1039.

    Article  Google Scholar 

  14. Carnevale G. F., Mcwilliams J. C., Pomeau Y. et al. Evolution of vortex statistics in two-dimensional turbulence [J]. Physical Review Letters, 1991, 66(21): 2735–2737.

    Article  Google Scholar 

  15. Weiss J. B., Mcwilliam J. Temporal scaling behavior of decaying two-dimensional turbulence [J]. Physics of Fluids A Fluid Dynamics, 1993, 5(3): 608–621.

    Article  Google Scholar 

  16. Li J., Xia Y., Qiu X. et al. Vortex statistics of a cylinder wake flow close to the wall based on IB-LBM [J]. Modern Physics Letters B, 2019, 33(29): 1950364.

    Article  MathSciNet  Google Scholar 

  17. Li J., Xia Y., Qiu X. et al. Vortex statistics in two-dimensional turbulence based on IB-LBM [J]. Modern Physics Letters B, 2019, 33(36): 1950453.

    Article  MathSciNet  Google Scholar 

  18. Xia Y., Qiu X., Qian Y. Numerical simulation of two-dimensional turbulence based on immersed boundary lattice Boltzmann method [J]. Computers and Fluids, 2019, 195: 104321.

    Article  MathSciNet  Google Scholar 

  19. Bruneau C. H., Kellay H. Experiments and direct numerical simulations of two-dimensional turbulence [J]. Physical Review E, 2005, 71(4): 046305.

    Article  Google Scholar 

  20. Feng Z. G., Michaelides E. E. The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems [J]. Journal of Computational Physics, 2004, 195(2): 602–628.

    Article  Google Scholar 

  21. Feng Z. G., Michaelides E. E. Proteus: A direct forcing method in the simulations of particulate flows [J]. Journal of Computational Physics, 2005, 202(1): 20–51.

    Article  Google Scholar 

Download references

Acknowledgements

We thank Prof. Chaoqun Liu, Dr. Yi-qian Wang for useful discussions and comments. The research is sponsored by Shuguang Program supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission in China (Grant No. 18SG53), the Double Innovation Program of Jiangsu Province, China, 2018.

Author information

Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Jiang-hua Li & Xiang Qiu

  2. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai, 201418, China

    Jiang-hua Li & Yu-xian Xia

  3. School of Science, Shanghai Institute of Technology, Shanghai, 201418, China

    Xiang Qiu & Yuan Fu

  4. School of Mathematical Sciences, Soochow University, Suzhou, 215006, China

    Yue-hong Qian

  5. College of Urban Construction and Safety Engineering, Shanghai Institute of Technology, Shanghai, 201418, China

    Jia-hua Li

Authors
  1. Jiang-hua Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu-xian Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiang Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yue-hong Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jia-hua Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yuan Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiang Qiu.

Additional information

Projects supported by the National Natural Science Foundation of China (Grant No. 91952102, 12032016), the National Key Research and Development Program of China (Grant No. 2018YFB0204404).

Biography: Jiang-hua Li (1994-), Male, Ph. D. Candidate

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Jh., Xia, Yx., Qiu, X. et al. An extended similarity in channel turbulence. J Hydrodyn 33, 782–786 (2021). https://doi.org/10.1007/s42241-021-0062-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42241-021-0062-4

Key words

Search

Navigation