Skip to main content
SpringerLink
Log in

Characteristics of Turbulence Induced by Mechanical Waves in a Tank

  • STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

Three components of current velocity ui(i = x, y, z) induced by mechanical waves generated by a wave maker are measured in a wind-wave tank for three variants of dominant frequencies f0 and a set of significant wave heights Hs for each frequency. To study the degree of anisotropy of wave-induced turbulence and estimate its dissipation rate ε, standard deviations (SDs) σi and frequency spectra Si(f) are calculated for the components of the measured currents. By the proposed filtering procedure, the characteristics σiF and SiF(f) are calculated for the turbulent components of currents in which wave motions are filtered. It is shown that the SDs σi exhibit a strong anisotropy the degree of which varies with the variation of the wave parameters. For the turbulent components of the currents, the relation σxF ≈ σyF ≥ (1.5–3)σzF holds, which suggests a significant anisotropy of turbulence in the cases of horizontal and vertical motions. A semiphenomenological approach provides an analytical representation for σiF in terms of wave parameters. The spectra of the turbulent components for the horizontal velocity components SxF(f) and SyF(f) in the frequency range f > 2f0 are similar in shape and intensity and, as a rule, are characterized by a power-law decay in intensity with exponent –1.6 ± 0.1. In the same frequency range, the intensity of the spectra of the vertical velocity component SzF(f) is an order of magnitude lower and decreases according to the power law with exponent –2.0 ± 0.1. The power-law regions are interpreted as analogs of the Kolmogorov spectra due to the up-frequency energy transfer from orbital motions of mechanical waves. A phenomenological model of the spectrum with the decay law –2 is proposed, which makes it possible to determine the dissipation rate ε of the kinetic energy of turbulence from the intensity of the power-law region of Sz(f). Estimates of ε are obtained and its parameterization is constructed. Discussion and possible interpretation of the results are presented.

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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.

Similar content being viewed by others

REFERENCES

  1. G. G. Stokes, Trans. Cambridge Phil. Soc. 8, 441 (1847).

    Google Scholar 

  2. M. Longuet-Higgins, Phil. Trans. R. Soc. London, Ser. A 245, 535 (1953).

    Article  ADS  Google Scholar 

  3. J. L. Lumley and E. A. Terray, J. Phys. Oceanogr. 13, 2000 (1983).

    Article  ADS  Google Scholar 

  4. S. A. Kitaigorodskii, M. A. Donelan, L. Lumley, and E. A. Terray, J. Phys. Oceanogr. 13, 1988 (1983).

    Article  ADS  Google Scholar 

  5. E. A. Terray, M. A. Donelan, Y. C. Agrawal, et al., J. Phys. Oceanogr. 26, 792 (1996).

    Article  ADS  Google Scholar 

  6. T. S. van den Bremer and Ø. Breivik, Phil. Trans. R. Soc. London, Ser. A 376, 20170104 (2017).

    ADS  Google Scholar 

  7. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence (MIT Press, Cambridge, 1971), Vol. 2.

    Google Scholar 

  8. O. M. Phillips, The Dynamics of the Upper Ocean (Cambridge Univ. Press, Cambridge, UK, 1966).

    MATH  Google Scholar 

  9. P. Janssen, The Interaction of Ocean Waves and Wind (Cambridge Univ. Press, Cambridge, UK, 2004).

    Book  Google Scholar 

  10. O. Bühler, Waves and Mean Flows (Cambridge Univ. Press, Cambridge, UK, 2014).

    Book  Google Scholar 

  11. F. Qiao, Y. Yuan, J. Deng, et al., Phil. Trans. R. Soc. London, Ser. A 374, 20150201 (2016).

    ADS  Google Scholar 

  12. A. V. Babanin, Geophys. Res. Lett. 33, L20605 (2006).

    Article  ADS  Google Scholar 

  13. A. V. Babanin and B. K. Haus, J. Phys. Oceanogr. 39, 2675 (2009).

    Article  ADS  Google Scholar 

  14. A. Alberello, F. Frascoli, M. Onorato, and A. Toffoli, Wave Motion 84, 81 (2019).

    Article  MathSciNet  Google Scholar 

  15. J. H. Lee, J. P. Monty, J. Elsnab, et al., J. Phys. Oceanogr. 47, 1145 (2017).

    Article  ADS  Google Scholar 

  16. A. Y. Benilov, J. Geophys. Res. 117, C00J30 (2012).

    ADS  Google Scholar 

  17. A. V. Babanin and D. Chalikov, J. Geophys. Res. 117, C06010 (2012).

    ADS  Google Scholar 

  18. W. Tsai, S. Chen, and G. Lu, J. Phys. Oceanogr. 45, 174 (2015).

    Article  ADS  Google Scholar 

  19. I. B. Savelyev, E. Maxeiner, and D. Chalikov, J. Geophys. Res. 117, C00J13 (2012).

    ADS  Google Scholar 

  20. V. G. Polnikov, G. A. Baidakov, and Yu. I. Troitskaya, Bull. Russ. Acad. Sci.: Phys. 55, 492 (2019).

    Google Scholar 

  21. V. G. Polnikov and G. A. Baidakov, Bull. Russ. Acad. Sci.: Phys. 56, 200 (2020).

    Google Scholar 

  22. S. M. Kay, Modern Spectral Estimation, Theory and Application (Prentice Hall, Englewood Cliffs, NJ, 1988).

    MATH  Google Scholar 

  23. V. V. Efimov and G. N. Khristoforov, Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 7, 1290 (1971).

    Google Scholar 

  24. G. S. Golitsyn, Statistics and Dynamics of Natural Processes and Phenomena: Methods, Instrumentation, and Results (KRASAND, Moscow, 2012) [in Russian].

    Google Scholar 

Download references

ACKNOWLEDGMENTS

We are grateful to colleagues Hongyu Ma and Shumin Jiang and students Xue Wang and Chao Li from the First Institute of Oceanography for participating in the experiments. We are also grateful to anonymous reviewers for their numerous comments that helped significantly improve the text of the article.

Funding

This work was partially supported by the Russian Foundation for Basic Research (project no. 18-05-00161) and by the National Natural Science Foundation of China (project no. 41821004).

Author information

Authors and Affiliations

  1. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017, Moscow, Russia

    V. G. Polnikov

  2. First Institute of Oceanography, Ministry of Natural Resources, 266061, Qingdao, China

    F. Tsyao

Authors
  1. V. G. Polnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Tsyao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. G. Polnikov.

Additional information

Translated by I. Nikitin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Polnikov, V.G., Tsyao, F. Characteristics of Turbulence Induced by Mechanical Waves in a Tank. J. Exp. Theor. Phys. 132, 110–126 (2021). https://doi.org/10.1134/S1063776121010039

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776121010039

Search

Navigation