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<front>
<journal-meta>
<journal-id journal-id-type="publisher">NPG</journal-id>
<journal-title-group>
<journal-title>Nonlinear Processes in Geophysics</journal-title>
<abbrev-journal-title abbrev-type="publisher">NPG</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Nonlin. Processes Geophys.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1607-7946</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/npg-20-841-2013</article-id>
<title-group>
<article-title>Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface – Part 2: Wind–wave spectra</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Troitskaya</surname>
<given-names>Yu. I.</given-names>
<ext-link>https://orcid.org/0000-0002-3818-9211</ext-link>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Ezhova</surname>
<given-names>E. V.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Sergeev</surname>
<given-names>D. A.</given-names>
<ext-link>https://orcid.org/0000-0003-4910-3935</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Kandaurov</surname>
<given-names>A. A.</given-names>
<ext-link>https://orcid.org/0000-0002-0014-8887</ext-link>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Baidakov</surname>
<given-names>G. A.</given-names>
<ext-link>https://orcid.org/0000-0002-7231-3511</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Vdovin</surname>
<given-names>M. I.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Zilitinkevich</surname>
<given-names>S. S.</given-names>
<ext-link>https://orcid.org/0000-0002-3909-5436</ext-link>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Institute of Applied Physics RAS, Nizhniy Novgorod, Nizhniy Novgorod, Russia</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Finnish Meteorological Institute, Helsinki, Finland</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Department of Physics, University of Helsinki, Finland</addr-line>
</aff>
<aff id="aff4">
<label>4</label>
<addr-line>Department of Radiophysics, N.I. Lobachevski State University of Nizhniy Novgorod, Russia</addr-line>
</aff>
<aff id="aff5">
<label>5</label>
<addr-line>Institute of Geography RAS, Moscow, Russia</addr-line>
</aff>
<aff id="aff6">
<label>6</label>
<addr-line>Nansen Environmental and Remote Sensing Centre, Bergen, Norway</addr-line>
</aff>
<pub-date pub-type="epub">
<day>29</day>
<month>10</month>
<year>2013</year>
</pub-date>
<volume>20</volume>
<issue>5</issue>
<fpage>841</fpage>
<lpage>856</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2013 Yu. I. Troitskaya et al.</copyright-statement>
<copyright-year>2013</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://npg.copernicus.org/articles/20/841/2013/npg-20-841-2013.html">This article is available from https://npg.copernicus.org/articles/20/841/2013/npg-20-841-2013.html</self-uri>
<self-uri xlink:href="https://npg.copernicus.org/articles/20/841/2013/npg-20-841-2013.pdf">The full text article is available as a PDF file from https://npg.copernicus.org/articles/20/841/2013/npg-20-841-2013.pdf</self-uri>
<abstract>
<p>Drag and mass exchange coefficients are calculated within a self-consistent
problem for the wave-induced air perturbations and mean velocity and density
fields using a quasi-linear model based on the Reynolds equations with
down-gradient turbulence closure. This second part of the report is devoted
to specification of the model elements: turbulent transfer coefficients and
wave number-frequency spectra. It is shown that the theory agrees with
laboratory and field experimental data well when turbulent mass and momentum
transfer coefficients do not depend on the wave parameters. Among several
model spectra better agreement of the theoretically calculated drag
coefficients with TOGA (Tropical Ocean Global Atmosphere) COARE (Coupled
Ocean–Atmosphere Response Experiment) data is achieved for the Hwang
spectrum (Hwang, 2005) with the high frequency part completed by the Romeiser
spectrum (Romeiser et al., 1997).</p>
</abstract>
<counts><page-count count="16"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Apel, J. R.: An improved model of the ocean surface wave vector spectrum and its effects on radar backscatter, J. Geophys. Res., 99, 16269–16291, 1994.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Brut, A., Butet, A., Durand, P., Caniaux, G., and Planton, S.: Air-sea exchanges in the equatorial area from the EQUALANT99 dataset: Bulk parametrizations of turbulent fluxes corrected for airflow distortion, Q. J. R. Meteorol. Soc., 131, 2497–2538, 2005.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Cox, C. S. and Munk W. H.: Statistics of the sea surface derived from sun glitter, J. Marine Res., 13, 198–227, 1954.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Donelan, M. A. and Pierson, W. J.: Radar scattering and equilibrium ranges in wind-generated waves – with application to scatterometry, J. Geophys. Res. Oceans, 92, 4971–5029, 1987.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Drennan, W. M., Zhang, J., French, J. R., McCormick, C., and Black, P. G.: Turbulent fluxes in the hurricane boundary layer, Part II: Latent heat flux, J. Atmos. Sci., 64, 1103–1115, 2007.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Druzhinin, O. A., Troitskaya, Y. I., and Zilitinkevich, S. S.: Direct numerical simulation of a turbulent wind over a wavy water surface, J. Geophys. Res., 117, C00J05, &lt;a href=&quot;http://dx.doi.org/10.1029/2011JC007789&quot;&gt;https://doi.org/10.1029/2011JC007789&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Elfouhaily, T. B., Chapron, B., Katsaros, K. B., and Vandemark, D. J.: A unified directional spectrum for long and short wind-driven waves, J. Geophys. Res., 107, 15781–15796, 1997.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Fabricant, A. L.: Quasilinear theory of wind waves generation, Izvestiya, Atmos. Ocean. Phys., 12, 858–862, 1976.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Fairall, C. W., Bradley, E. F., Hare, J. E., Grachev, A. A., and Edson, J. B.: Bulk parameterization of air–sea fluxes: updates and verification for the COARE algorithm, J. Climate, 16, 571–591, 2003.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Haberman, R.: Wave-induced distortions of a slightly stratified shear flow: a nonlinear critical-layer effect, J. Fluid Mech., 58, 727–736, 1973.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Hwang, P. A.: A study of the wavenumber spectra of short water waves in the ocean, Part 2: spectral model and mean square slope, J. Atmos. Ocean. Technol., 14, 1174–1186, 1997.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Hwang, P. A.: Wave number spectrum and mean square slope of intermediate-scale ocean surface waves, J. Geophys. Res., 110, C10029, &lt;a href=&quot;http://dx.doi.org/10.1029/2005JC003002&quot;&gt;https://doi.org/10.1029/2005JC003002&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Hwang, P. A. and Wang, D. W.: An empirical investigation of source term balance of small scale surface waves, Geophys. Res. Lett., 31, L15301, &lt;a href=&quot;http://dx.doi.org/10.1029/2004GL020080&quot;&gt;https://doi.org/10.1029/2004GL020080&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Hwang, P. A., Atakturk, S., Sletten, M. A., and Trizna, D. B.: A study of the wavenumber spectra of short water waves in the ocean, J. Phys. Oceanogr., 26, 1266–1285, 1996.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Hwang, P. A., Wang, D. W., Walsh, E. J., Krabill, W. B., and Swift, R. N.: Airborne measurements of the wavenumber spectra of ocean surface waves, Part 1: spectral slope and dimensionless spectral coefficient, J. Phys. Oceanogr., 30, 2753–2767, 2001a.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Hwang, P. A., Wang, D. W., Walsh, E. J., Krabill, W. B., and Swift R. N.: Airborne measurements of the wavenumber spectra of ocean surface waves. Part 2: directional distribution, J. Phys. Oceanogr., 30, 2768–2787, 2001b.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Janssen, P. A. E. M.: Quasi-linear theory of wind wave generation applied to wave forecasting, J. Phys. Oceanogr., 21, 1631–1642, 1991.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Jenkins, A. D.: Quasi-linear eddy-viscosity model for the flux of energy and momentum to wind waves using conservation-law equations in a curvilinear coordinate system, J. Phys. Oceanogr., 22, 843–858, 1992.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Liu, W. T., Katsaros, K. B., and Businger, J. A.: Bulk parameterization of air-sea exchanges of heat and water vapor including the molecular constraints at the interface, J. Atmos. Sci., 36, 1722–1735, 1979.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Makin, V. K. and Kudryavtsev, V. N.: Coupled sea surface-atmosphere model, Part 1. Wind over waves coupling, J. Geophys. Res., 104, 7613–7623, 1999.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Makin, V. K. and Mastenbroek, C.: Impact of waves on air–sea exchange of sensible heat and momentum, Bound.-Lay. Meteorol., 79, 279–300, 1996.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Makin, V. K., Kudryavtsev, V. N., and Mastenbroek, C.: Drag of the sea surface, Bound.-Lay. Meteorol., 73, 159–182, 1995.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Maslowe, S. A.: The generation of clear air turbulence by nonlinear waves, Stud. Appl. Math., 51, 1–16, 1972.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Monin, A. S. and Yaglom, A. M.: Statistical fluid dynamics, V.1. Gidrometeoizdat, St. Petersburg, 1992.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Ocampo-Torres, F. J., Donelan M. A., Merzi N., and Jia, F.: Laboratory measurements of mass transfer of carbon dioxide and water vapour for smooth and rough flow conditions, Tellus Ser. B, 46, 16–32, 1994.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Reutov, V. P.: Nonlinear growth rate of wind water waves and their excitation near the stability threshold, Radiophys. Quantum Electron., 38, 133–136, 1995.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Reutov, V. P. and Troitskaya, Yu. I.: Nonlinear effects due to water wave interactions with a turbulent wind, Izvestyia, Atmos. Ocean. Phys., 31, 792–801, 1996.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Romeiser, R., Alpers, W., and Wismann, V.: An improved composite surface model for the radar backscattering cross section of the ocean surface, J. Geophys. Res., 102, 25237–25250, 1997.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Smol&apos;yakov, A. V.: Quadrupole radiation spectrum of plane turbulent boundary layer, Sov. Phys. Acoust., 19, 271–276, 1973.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Troitskaya, Yu. I.: Viscous diffusion nonlinear critical layer in a stratified shear flow, J. Fluid Mech., 233, 25–48, 1991.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Troitskaya, Yu. I. and Rybushkina, G. V.: Quasi-linear model of interaction of surface waves with strong and hurricane winds, Izvestyia, Atmos. Ocean. Phys., 44, 621–645, 2008.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Troitskaya, Yu. I., Sergeev, D. A., Ermakova, O. S., and Balandina, G. N.: Statistical parameters of the air turbulent boundary layer over steep water waves measured by the DPIV technique, J. Phys. Oceanogr., 41, 1421–1454, 2011.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Troitskaya, Yu. I., Sergeev, D. A., Kandaurov, A. A., Baidakov, G. A, Vdovin, M. A., and Kazakov, V. I.: Laboratory and theoretical modeling of air-sea momentum transfer under severe wind conditions, J. Geophys. Res., 117, C00J21, &lt;a href=&quot;http://dx.doi.org/10.1029/2011JC007778&quot;&gt;https://doi.org/10.1029/2011JC007778&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Troitskaya, Yu. I., Ezhova, E. V., and Zilitinkevich, S. S.: Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface – Part 1: A harmonic wave, Nonlin. Processes Geophys., 20, 825–839, &lt;a href=&quot;http://dx.doi.org/10.5194/npg-20-825-2013&quot;&gt;https://doi.org/10.5194/npg-20-825-2013&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Zeng, X., Zhao, M., and Dickinson, R. E.: Comparison of bulk aerodynamic algorithms for the computation of sea surface fluxes using the TOGA COARE and TAO data, J. Climate, 11, 2628–2644, 1998.</mixed-citation>
</ref>
</ref-list>
</back>
</article>