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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/npg-2018-48
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2018-48
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 10 Dec 2018

Research article | 10 Dec 2018

Review status
This discussion paper is a preprint. A revision of the manuscript is under review for the journal Nonlinear Processes in Geophysics (NPG).

Estimating vertically averaged energy dissipation rate

Nozomi Sugiura1, Shinya Kouketsu1, Shuhei Masuda1, Satoshi Osafune1, and Ichiro Yasuda2 Nozomi Sugiura et al.
  • 1Research and Development Center for Global Change, JAMSTEC, Yokosuka, Japan
  • 2Atmosphere and Ocean Research Institute, University of Tokyo, Chiba, Japan

Abstract. The energy dissipation rate is an important characteristic of turbulence; however, its magnitude in observational profiles can be misidentified owing to its erratic evolution. By analysing observed data from oceanic turbulence, we show that the vertical sequences of depth-averaged energy dissipation rates have a scaling property, and propose a method to suitably estimate the vertically averaged value by utilizing that property. For scaling in the observed profiles, we found that averaging neighbouring points increases the expected value of its logarithm proportionally to the logarithm of the averaging interval. Furthermore, the population mean can be estimated for the logarithm of the vertically averaged energy dissipation rate from a single observation profile, by scaling up and promoting the observed value at each depth to one that corresponds to the whole profile. The estimate allows to distinguish whether an observational profile exhibits a momentarily high value by intermittency or maintains high energy dissipation on average.

Nozomi Sugiura et al.
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Nozomi Sugiura et al.
Nozomi Sugiura et al.
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Short summary
The observed profiles of the turbulent energy dissipation rate look so erratic that we can hardly identify them as continuous curves. However, we found that each sequence has the striking feature of self-similarity. Using this, we can efficiently take ensemble statistics of the vertically averaged energy dissipation rate from a single observation profile, by scaling up and promoting the observed value at each depth to one that corresponds to the whole profile.
The observed profiles of the turbulent energy dissipation rate look so erratic that we can...
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