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Correlation equation for the marine drag coefficient and wave steepness

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Abstract

This work questions, starting from dimensional considerations, the generality of the belief that the marine drag coefficient levels off with increasing wind speed. Dimensional analysis shows that the drag coefficient scales with the wave steepness as opposed to a wave-age scaling. A correlation equation is employed here that uses wave steepness scaling at low aspect ratios (inverse wave steepnesses) and a constant drag coefficient at high aspect ratios. Invoked in support of the correlation are measurements sourced from the literature and at the FINO1 platform in the North Sea. The correlation equation is then applied to measurements recorded from buoys during the passage of hurricanes Rita, Katrina (2005) and Ike (2008). Results show that the correlation equation anticipates the expected levelling off in deeper water, but a drag coefficient more consistent with a Charnock type relation is also possible in more shallower water. Some suggestions are made for proceeding with a higher-order analysis than that conducted here.

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Notes

  1. C D10n and the wave age both contain the friction velocity, u  ∗ .

  2. San Clemente Ocean Probing Experiment

  3. Humidity Exchange Over Sea

  4. ftp://ftp.etl.noaa.gov/users/cfairall/fluxdata/scope/SCOPE2.TXT

  5. http://www.ndbc.noaa.gov

  6. http://www.ndbc.noaa.gov/station_page.php?station=42001

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Acknowledgements

This work was done within the VERITAS project (work package 5 of OWEA) which is funded by the German Ministry of the Environment (BMU) via the PTJ (FKZ 0325060). FINO1 measurements have been provided by the German wind energy association (DEWI) and the German maritime and hydrographic agency (BSH) (many thanks to Olaf Outzen) and processed by Matthias Türk. The measurements made available online by C. Fairall, A. Grachev and the NOAA National Buoy Center are gratefully acknowledged. Many thanks to the reviewers who helped refine the focus of the original manuscript.

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  1. Institute of Meteorology and Climate Research (IMK-IFU), Karlsruhe Institute of Technology (KIT), Garmisch-Partenkirchen, Germany

    Richard J. Foreman & Stefan Emeis

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  1. Richard J. Foreman
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  2. Stefan Emeis
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Correspondence to Richard J. Foreman.

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Foreman, R.J., Emeis, S. Correlation equation for the marine drag coefficient and wave steepness. Ocean Dynamics 62, 1323–1333 (2012). https://doi.org/10.1007/s10236-012-0565-1

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  • DOI: https://doi.org/10.1007/s10236-012-0565-1

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