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Dissipation Rate of Turbulence in a Water Layer under Wind Waves Based on Data of a Laboratory Experiment

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Abstract

The aim of this work is to obtain estimates and parameterization of the dissipation rate of the turbulence kinetic energy (TKE dissipation), ε, induced in the upper water layer by the presence of wind waves at the surface. For this purpose, data from the laboratory measurements of the wind waves and three components of currents at six horizons in the upper water layer and four different winds are used. The measurements are performed in the wind-wave channel of the Institute of Applied Physics, Russian Academy of Sciences (IAP RAS) [1, 2]. It is established that, for most horizons, Kolmogorov-type ranges with the property \({{S}_{{Uz}}}(f) \propto {{f}^{{ - 5/3}}}\) are clearly seen in the frequency spectra \({{S}_{{Uz}}}(f)\) for the vertical velocity component Uz of the flow induced by wind and waves. Using the algorithms described in [3, 4], this fact allows us to obtain estimates of the TKE dissipation at the corresponding horizons and then establish the dependence of ε on the friction velocity \({{u}_{*}}\), the height of waves at the surface a0, the peak frequency of the spectrum ωp, and the depth of the horizon z. An analysis of the results (according to the available data) makes it possible to propose a parameterization of the form ε ≈ 0.00025\(u_{*}^{3}{{a}_{0}}/{{z}^{2}}\) for which a physical interpretation is proposed.

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Notes

  1. The same formula was used by authors of [12–14] when passing from empirical spectra \({{S}_{U}}(\omega )\) to model spectra \({{S}_{U}}(k)\).

  2. Here, we note that the dependence \(\varepsilon \propto a_{0}^{3}\) was obtained in the case of mechanical wave on the surface in the experiment [15]. This experiment requires a special consideration due to the absence of wind.

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ACKNOWLEDGMENTS

We are grateful to colleagues from the Institute of Applied Physics taking part in the experiments.

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 18-05-00161.

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Authors and Affiliations

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

    V. G. Polnikov

  2. Institute of Applied Physics, Russian Academy of Sciences, 603950, Nizhny Novgorod, Russia

    G. A. Baidakov & Yu. I. Troitskaya

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  1. V. G. Polnikov
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  2. G. A. Baidakov
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  3. Yu. I. Troitskaya
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Correspondence to V. G. Polnikov.

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Translated by A. Nikol’skii

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Polnikov, V.G., Baidakov, G.A. & Troitskaya, Y.I. Dissipation Rate of Turbulence in a Water Layer under Wind Waves Based on Data of a Laboratory Experiment. Izv. Atmos. Ocean. Phys. 55, 492–501 (2019). https://doi.org/10.1134/S0001433819050104

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