• Anis, A., , and J. N. Moum, 1995: Surface wave-turbulence interactions: Scaling ε(z) near the sea surface. J. Phys. Oceanogr., 25, 20252044, doi:10.1175/1520-0485(1995)025<2025:SWISNT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bakhoday Paskyabi, M., , and I. Fer, 2014: The influence of surface gravity waves on the injection of turbulence in the upper ocean. Nonlinear Processes Geophys., 21, 713733, doi:10.5194/npg-21-713-2014.

    • Search Google Scholar
    • Export Citation
  • Benilov, A. Y., , and L. N. Ly, 2002: Modeling of surface waves breaking effects in the ocean upper layer. Math. Comput. Modell., 35, 191213, doi:10.1016/S0895-7177(01)00159-5.

    • Search Google Scholar
    • Export Citation
  • BioSonics, 2004: DT4 data file format specification. BioSonics Software and Engineering Library Rep. BS&E-2004-07-0009-1.3, 33 pp.

  • Craig, P. D., , and M. L. Banner, 1994: Modeling wave enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr., 24, 25462559, doi:10.1175/1520-0485(1994)024<2546:MWETIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dahl, P. H., , and A. T. Jessup, 1995: On bubble clouds produced by breaking waves: An event analysis of ocean acoustic measurements. J. Geophys. Res., 100, 50075020, doi:10.1029/94JC03019.

    • Search Google Scholar
    • Export Citation
  • D’Asaro, E. A., , J. Thomson, , A. Y. Shcherbina, , R. R. Harcourt, , M. F. Cronin, , M. A. Hemer, , and B. Fox‐Kemper, 2014: Quantifying upper ocean turbulence driven by surface waves. Geophys. Res. Lett., 41, 102107, doi:10.1002/2013GL058193.

    • Search Google Scholar
    • Export Citation
  • Dean, R. G., , and R. A. Dalrymple, 1991: Water Wave Mechanics for Engineers and Scientists. Advanced Series on Ocean Engineering, Vol. 2, World Scientific, 370 pp.

  • Depew, D. C., , A. W. Stevens, , R. E. H. Smith, , and R. E. Hecky, 2009: Detection and characterization of benthic filamentous algal stands on rocky substrata using a high frequency echosounder. Limnol. Oceanogr. Methods, 7, 693705, doi:10.4319/lom.2009.7.693.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., , E. F. Bradley, , D. P. Rogers, , J. B. Edson, , and G. S. Young, 1996: Bulk parameterization of air–sea fluxes in TOGA COARE. J. Geophys. Res., 101, 37473767, doi:10.1029/95JC03205.

    • Search Google Scholar
    • Export Citation
  • Farmer, D. M., , S. Vagle, , and M. Li, 1999: Wave breaking, turbulence and bubble distributions in the ocean surface layer. The Wind-Driven Air–Sea Interface, M. Banner, Ed., School of Mathematics, University of New South Wales, 187–192.

  • Feddersen, F., , J. H. Trowbridge, , and A. J. Williams III, 2007: Vertical structure of dissipation in the nearshore. J. Phys. Oceanogr., 37, 17641777, doi:10.1175/JPO3098.1.

    • Search Google Scholar
    • Export Citation
  • Gemmrich, J. R., 2010: Strong turbulence in the wave crest region. J. Phys. Oceanogr., 40, 583595, doi:10.1175/2009JPO4179.1.

  • Gemmrich, J. R., , and D. M. Farmer, 1999: Near-surface turbulence and thermal structure in a wind-driven sea. J. Phys. Oceanogr., 29, 480499, doi:10.1175/1520-0485(1999)029<0480:NSTATS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gemmrich, J. R., , and D. M. Farmer, 2004: Near-surface turbulence in the presence of breaking waves. J. Phys. Oceanogr., 34, 10671086, doi:10.1175/1520-0485(2004)034<1067:NTITPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gerbi, G. P., , J. H. Trowbridge, , E. A. Terray, , A. J. Plueddemann, , and T. Kukulka, 2009: Observations of turbulence in the ocean surface boundary layer: Energetics and transport. J. Phys. Oceanogr., 39, 10751096, doi:10.1175/2008JPO4044.1.

    • Search Google Scholar
    • Export Citation
  • Johnson, B. D., , and R. C. Cooke, 1979: Bubble population and spectra in coastal waters. J. Geophys. Res., 84, 37613766, doi:10.1029/JC084iC07p03761.

    • Search Google Scholar
    • Export Citation
  • Li, M., , C. Garrett, , and E. Skyllingstad, 2005: A regime diagram for classifying turbulent large eddies in the upper ocean. Deep-Sea Res. I, 52, 259278, doi:10.1016/j.dsr.2004.09.004.

    • Search Google Scholar
    • Export Citation
  • Loescher, K. A., , G. S. Young, , B. A. Colle, , and N. S. Winstead, 2006: Climatology of barrier jets along the Alaskan coast. Part I: Spatial and temporal distributions. Mon. Wea. Rev., 134, 437453, doi:10.1175/MWR3037.1.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., , P. P. Sullivan, , and C.-H. Moeng, 1997: Langmuir turbulence in the ocean. J. Fluid Mech., 334, 130, doi:10.1017/S0022112096004375.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys., 20, 851875, doi:10.1029/RG020i004p00851.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and A. Blumberg, 2004: Wave breaking and ocean surface thermal response. J. Phys. Oceanogr., 34, 693698, doi:10.1175/2517.1.

    • Search Google Scholar
    • Export Citation
  • Melville, W. K., 1996: The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech., 28, 279321, doi:10.1146/annurev.fl.28.010196.001431.

    • Search Google Scholar
    • Export Citation
  • Monahan, E. C., , and M. Lu, 1990: Acoustically relevant bubble assemblages and their dependence on meteorological parameters. IEEE J. Oceanic Eng., 15, 340349, doi:10.1109/48.103530.

    • Search Google Scholar
    • Export Citation
  • Neumann, G., 1952: On Wind Generated Waves with Special Reference to the Problem of Wave Forecasting. New York University, College of Engineering, Department of Meteorology, 136 pp.

  • Neumann, G., , and W. J. Pierson Jr., 1966: Principles of Physical Oceanography. Prentice-Hall, 545 pp.

  • Olson, J. B., , B. A. Colle, , N. A. Bond, , and N. Winstead, 2007: A comparison of two coastal barrier jet events along the southeast Alaskan coast during the SARJET field experiment. Mon. Wea. Rev., 135, 36423663, doi:10.1175/MWR3448.E1.

    • Search Google Scholar
    • Export Citation
  • Perkins, H., , F. De Strobel, , and L. Gauldesi, 2000: The Barny Sentinel trawl-resistant ADCP bottom mount: Design, testing, and application. IEEE J. Oceanic Eng., 25, 430436, doi:10.1109/48.895350.

    • Search Google Scholar
    • Export Citation
  • Plueddemann, A. J., , J. A. Smith, , D. A. Farmer, , R. A. Weller, , W. R. Crawford, , R. Pinkel, , S. Vagle, , and A. Gnanadesikan, 1996: Structure and variability of Langmuir circulation during the surface waves process program. J. Geophys. Res., 101, 35253543, doi:10.1029/95JC03282.

    • Search Google Scholar
    • Export Citation
  • Soloviev, A., , and R. Lukas, 2003: Observation of wave-enhanced turbulence in the near-surface layer of the ocean during TOGA COARE. Deep-Sea Res. I, 50, 371395, doi:10.1016/S0967-0637(03)00004-9.

    • Search Google Scholar
    • Export Citation
  • Soloviev, A., , and R. Lukas, 2014: Near-surface turbulence. The Near-Surface Layer of the Ocean, A. Soloviev and R. Lukas, Eds., Springer, 153–224.

  • Stabeno, P. J., , N. A. Bond, , A. J. Hermann, , N. B. Kachel, , C. W. Mordy, , and J. E. Overland, 2004: Meteorology and oceanography of the northern Gulf of Alaska. Cont. Shelf Res., 24, 859897, doi:10.1016/j.csr.2004.02.007.

    • Search Google Scholar
    • Export Citation
  • Steele, K. E., , and T. Mettlach, 1993: NDBC wave data-current and planned. Proc. Second Int. Symp. on Ocean Wave Measurement and Analysis, New Orleans, LA, ASCE, 198–207.

  • Stevens, A. W., , J. R. Lacy, , D. P. Finlayson, , and G. Gelfenbaum, 2008: Evaluation of a single-beam sonar system to map seagrass at two sites in northern Puget Sound, Washington. U.S. Geological Survey Scientific Investigations Rep. 2008-5009, 45 pp.

  • Stips, A., , H. Burchard, , K. Bolding, , H. Prandke, , A. Simon, , and A. Wüest, 2005: Measurement and simulation of viscous dissipation in the wave affected surface layer. Deep-Sea Res. II, 52, 11331155, doi:10.1016/j.dsr2.2005.01.012.

    • Search Google Scholar
    • Export Citation
  • Strong, B., , B. Brumley, , E. A. Terray, , and G. W. Stone, 2000: The performance of ADCP-derived directional wave spectra and comparison with other independent measurements. Proc. Oceans 2000 MTS/IEEE Conf. and Exhibition, Providence, RI, IEEE, 11951203, doi:10.1109/OCEANS.2000.881763.

  • Teague, W. J., , H. W. Wijesekera, , E. Jarosz, , D. B. Fribance, , A. Lugo-Fernández, , and Z. R. Hallock, 2013: Current and hydrographic conditions at the East Flower Bank in 2011. Cont. Shelf Res., 63, 4358, doi:10.1016/j.csr.2013.04.039.

    • Search Google Scholar
    • Export Citation
  • Teixeira, M. A. C., , and S. E. Belcher, 2010: On the structure of Langmuir turbulence. Ocean Modell., 31, 105119, doi:10.1016/j.ocemod.2009.10.007.

    • Search Google Scholar
    • Export Citation
  • Terray, E. A., , M. A. Donelan, , Y. C. Agrawal, , W. M. Drennan, , K. K. Kahma, , A. J. Williams III, , P. A. Hwang, , and S. A. Kitaigorodskii, 1996: Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr., 26, 792807, doi:10.1175/1520-0485(1996)026<0792:EOKEDU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1984: On the determination of Kv in the near-surface ocean from acoustic measurements of bubbles. J. Phys. Oceanogr., 14, 855863, doi:10.1175/1520-0485(1984)014<0855:OTDOIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1986: Measurements with an automatically recording inverted echo sounder; ARIES and the bubble clouds. J. Phys. Oceanogr., 16, 14621478, doi:10.1175/1520-0485(1986)016<1462:MWAARI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1992: Bubble clouds and the dynamics of the upper ocean. Quart. J. Roy. Meteor. Soc., 118, 122, doi:10.1002/qj.49711850302.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., , and A. J. Hall, 1983: The characteristics of breaking waves, bubble clouds, and near-surface currents observed using side-scan sonar. Cont. Shelf Res., 1, 353384, doi:10.1016/0278-4343(83)90003-1.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., , W. A. M. Nimmo Smith, , A. Graham, , and A. M. Thurnherr, 1999: Patterns in foam and shallow tidal flows. The Wind-Driven Air–Sea Interface, M. Banner, Ed., School of Mathematics, University of New South Wales, 257–264.

  • Thorpe, S. A., , T. R. Osborn, , D. M. Farmer, , and S. Vagle, 2003a: Bubble clouds and Langmuir circulation: Observations and models. J. Phys. Oceanogr., 33, 20132031, doi:10.1175/1520-0485(2003)033<2013:BCALCO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., , T. R. Osborn, , J. E. F. Jackson, , A. J. Hall, , and R. G. Lueck, 2003b: Measurements of turbulence in the upper-ocean mixing layer using Autosub. J. Phys. Oceanogr., 33, 122145, doi:10.1175/1520-0485(2003)033<0122:MOTITU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Toba, Y., 1978: Stochastic form of the growth of wind waves in a single-parameter representation with physical implications. J. Phys. Oceanogr., 8, 494507, doi:10.1175/1520-0485(1978)008<0494:SFOTGO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Trevorrow, M. V., 2003: Measurements of near surface bubble plumes in the open ocean with implication for high frequency sonar performance. J. Acoust. Soc. Amer., 114, 26722684, doi:10.1121/1.1621008.

    • Search Google Scholar
    • Export Citation
  • Vagle, S., , and D. M. Farmer, 1992: The measurement of bubble-size distributions by acoustical backscatter. J. Atmos. Oceanic Technol., 9, 630644, doi:10.1175/1520-0426(1992)009<0630:TMOBSD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Vagle, S., , C. McNeil, , and N. Steiner, 2010: Upper ocean bubble measurements from the NE Pacific and estimates of their role in air-sea gas transfer of the weakly soluble gases nitrogen and oxygen. J. Geophys. Res., 115, C12054, doi:10.1029/2009JC005990.

    • Search Google Scholar
    • Export Citation
  • Vagle, S., , J. Gemmrich, , and H. Czerski, 2012: Reduced upper ocean turbulence and changes to bubble size distributions during large downward heat flux events. J. Geophys. Res., 117, C00H16, doi:10.1029/2011JC007308.

    • Search Google Scholar
    • Export Citation
  • Wijesekera, H. W., , J. S. Allen, , and P. A. Newbergerl, 2003: Modeling study of turbulent mixing over the continental shelf: Comparison of turbulent closure schemes. J. Geophys. Res., 108, 3103, doi:10.1029/2001JC001234.

    • Search Google Scholar
    • Export Citation
  • Wijesekera, H. W., , D. W. Wang, , W. J. Teague, , E. Jarosz, , W. E. Rogers, , D. B. Fribance, , and J. N. Moum, 2013: Surface wave effects on high-frequency currents over a shelf edge bank. J. Phys. Oceanogr., 43, 16271647, doi:10.1175/JPO-D-12-0197.1.

    • Search Google Scholar
    • Export Citation
  • Wilson, J. G., , and J. E. Overland, 1986: Meteorology of the northern Gulf of Alaska. The Gulf of Alaska: Physical Environment and Biological Resources, D. W. Hood and S. T. Zimmerman, Eds., DOC/NOAA, 31–54.

  • Zedel, L., , and D. M. Farmer, 1991: Organized structures in subsurface bubble clouds: Langmuir circulation in the open ocean. J. Geophys. Res., 96, 88898900, doi:10.1029/91JC00189.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    The location map of the BWE field experiment; Barny (B1–B4) and string (S1–S4) moorings are marked by solid circles. The land-based weather station (NRL MET) and moored buoy (NDBC 46082) are indicated by an open triangle and circle, respectively. Depth contour lines (gray lines) are in 10-m intervals starting at 10 m. The darker contour lines are for depths of 50, 100, 150, 200, 250, and 300 m.

  • View in gallery

    Time–depth section of acoustic backscatter profiles in (a) a fixed coordinate zd distance measured upward from the echosounder and (b) wave-following coordinate zη distance measured downward from the wave surface η, shown as the solid line in (a). The color shading is the backscatter intensity 10 log10(Mυ) (dB). The wind speed and wave height are u5 = 21.1 m s−1 and Hs = 6.6 m, respectively (case 69; Table 2).

  • View in gallery

    Time history of (a) wind speed u5 at 5-m height, (b) wind direction θu at NDBC buoy 46082, (c) significant wave height Hs at the Lander (solid circles) and at the buoy (dashed line), (d) peak wave period Tp at the Lander (solid triangles) and at the buoy (dashed line), and (e) surface Stokes drift Us0 at the Lander.

  • View in gallery

    Time history of (a) surface wind stress τw, (b) surface air temperature (solid line) at 4-m height (Kayak Island station) and water temperature (dashed line) at 5-m depth from S1, (c) net surface heat flux Qnet, where negative Qnet represents upward heat flux, (d) Monin–Obukhov length Lmo, and (e) turbulent Langmuir number Lat at the Lander.

  • View in gallery

    Depth–time current velocity components (cm s−1) at the Lander: (a) zonal U, (b) meridional V, and (c) vertical W. (d) Potential temperature Tθ (°C), (e) salinity S (psu), and (f) potential density anomaly σt (kg m−3) at the S3 subsurface mooring. Depth is the distance measured downward from the mean water line.

  • View in gallery

    Variance-preserving frequency spectra of velocity components at the Lander: (a) U, (b) V, and (c) W at 15-m water depth. The semidiurnal tide (period: 12.42 h) and the diurnal tide (period: 24.48 h) are marked as circles and crosses, respectively.

  • View in gallery

    Time series of (a) friction velocity u*w (m s−1) and (b) depth profile of TKE. The color shading is log10(TKE) (cm2 s−2).

  • View in gallery

    Mean depth profile of TKE for the 81 cases (circles). The solid line represents the exponential function [(10)]. The crosses represent the mean aliasing variance profile of simulated wave orbital motions Δwave for the 81 cases. The dotted lines show 95% confidence intervals; z is the distance measured downward from the mean water line z = 0.

  • View in gallery

    The 10-min time history of acoustic backscatter depth profiles at winds u5 of (a) 8.9, (b) 13.7, (c) 16, and (d) 19.6 m s−1. Corresponding wave heights Hs are 4.1, 3.6, 6.0, and 8.7 m, respectively. They are for cases 26, 29, 16, and 70, respectively (Table 2). The color shading is 10 log10(Mυ) (dB), and zη is the distance measured downward from the free wave surface η.

  • View in gallery

    Profiles of 10-min-averaged backscatter 〈Mυ〉 at the four wind speeds (see Fig. 9) in (a) a wave-following coordinate zη and (b) zη/Hs, scaled by significant wave height. The e-folding length is calculated for the depth profile 〈Mυ〉 between zη/Hs = 1 and 2 as marked by the two horizontal lines in (b). The vertical line in (b) represents the empirical backscatter threshold (−50 dB) for identifying the bubble depth.

  • View in gallery

    Time series of (a) buoy wind speed u5 and (b) bubble depth Db (solid circles) and e-folding length λe (triangles).

  • View in gallery

    Wind speed u5 vs (a) bubble depth Db and (b) e-folding length λe. The thick dashed lines represent the empirical linear relationships by Vagle et al. (2010). The solid circles are u5 bin-averaged Db and λe. The length of the error bars represents two standard deviations.

  • View in gallery

    Profiles of 10-min-averaged backscatter 〈Mυ〉 for wind speed u5 ~ 14 m s−1. Case numbers are listed in Table 2, and the ratios of bubble depth to significant wave height Db/Hs are 2.9, 2.4, 2.7, 2.5, 4.3, and 2.1, respectively. The vertical dashed line represents the empirical backscatter threshold (−50 dB) used for identifying bubble depth.

  • View in gallery

    (a) Bubble depth scaled by wave height Db/Hs vs wave age Cp/u*a. The circles are data from the BWE experiment. The crosses are from Thorpe (1986), and u10 = 28u*a is used for replotting Thorpe’s data. (b) Bubble depth scaled by wavelength Db/Lp vs wave age Cp/u*a. Here, Lp is computed from the peak wave period Tp, using the linear dispersion relation. Bubble depth data with wind speeds less than 6 m s−1 are excluded. The solid circles are Cp/u*a bin-averaged Db/Hs and Db/Lp. The length of the error bars represents two standard deviations.

  • View in gallery

    Time series of (a) buoy wind speed u5 (b) eddy diffusion coefficients: Kυe [(2)] (triangles), KυD [(4)] (circles), and Kυu* (dashed line) based on wind speed and wave age [(7)].

  • View in gallery

    Eddy diffusion coefficients Kυe vs KυD. The thick dashed line represents the ratio 1:1.

  • View in gallery

    Wind speed u5 vs bin-averaged eddy diffusion coefficients KυD (solid circles) and Kυe (triangles). The length of the error bars represents two standard deviations of 〈KυD〉 (solid line) and 〈Kυe〉 (dashed line). Eddy diffusion data from Thorpe (1984) and Dahl and Jessup (1995) are represented, respectively, by crosses and asterisks. The gray line represents the empirical relationship of the eddy viscosity and wind speed (Neumann 1952).

  • View in gallery

    Cubic of waterside friction velocity (u*w)3 vs bin-averaged eddy diffusion coefficients 〈KυD〉 (solid circles) and 〈Kυe〉 (triangles). The solid and dashed lines represent the eddy diffusivity coefficient predicted by (7) for young (δ = 15) and developed (δ = 70) sea states, respectively. The length of the error bars represents two standard deviations of 〈KυD〉 (solid line) and 〈Kυe〉 (dashed line).

  • View in gallery

    Time history of (a) u*w waterside friction velocity and (b) depth-averaged vertical energy diffusion [(11)], shear production [(12)], and energy dissipation rate [(13)] and [(14)] between 10- and 30-m depth.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 89 89 13
PDF Downloads 75 75 7

Turbulent Diffusivity under High Winds from Acoustic Measurements of Bubbles

View More View Less
  • 1 Naval Research Laboratory, Stennis Space Center, Mississippi
  • | 2 Oil Spill Recovery Institute, Cordova, Alaska
© Get Permissions
Full access

Abstract

Breaking surface waves generate layers of bubble clouds as air parcels entrain into the upper ocean through the action of turbulent motions. The turbulent diffusivity in the bubble cloud layer is investigated by combining measurements of surface winds, waves, bubble acoustic backscatter, currents, and hydrography. These measurements were made at water depths of 60–90 m on the shelf of the Gulf of Alaska near Kayak Island during late December 2012, a period when the ocean was experiencing winds and significant wave heights up to 22 m s−1 and 9 m, respectively. Vertical profiles of acoustic backscatter decayed exponentially from the wave surface with e-folding lengths of about 0.6 to 6 m, while the bubble penetration depths were about 3 to 30 m. Both e-folding lengths and bubble depths were highly correlated with surface wind and wave conditions. The turbulent diffusion coefficients, inferred from e-folding length and bubble depth, varied from about 0.01 to 0.4 m2 s−1. Analysis suggests that the turbulent diffusivity in the bubble layer can be parameterized as a function of the cube of the wind friction velocity with a proportionality coefficient that depends weakly on wave age. Furthermore, in the bubble layer, on average, the shear production of the turbulent kinetic energy estimated by the diffusion coefficients is a similar order of magnitude as the dissipation rate predicted by the wall boundary layer theory.

Corresponding author address: David W. Wang, Naval Research Laboratory, 1009 Balch Blvd., Stennis Space Center, MS 39529. E-mail: david.wang@nrlssc.navy.mil

Abstract

Breaking surface waves generate layers of bubble clouds as air parcels entrain into the upper ocean through the action of turbulent motions. The turbulent diffusivity in the bubble cloud layer is investigated by combining measurements of surface winds, waves, bubble acoustic backscatter, currents, and hydrography. These measurements were made at water depths of 60–90 m on the shelf of the Gulf of Alaska near Kayak Island during late December 2012, a period when the ocean was experiencing winds and significant wave heights up to 22 m s−1 and 9 m, respectively. Vertical profiles of acoustic backscatter decayed exponentially from the wave surface with e-folding lengths of about 0.6 to 6 m, while the bubble penetration depths were about 3 to 30 m. Both e-folding lengths and bubble depths were highly correlated with surface wind and wave conditions. The turbulent diffusion coefficients, inferred from e-folding length and bubble depth, varied from about 0.01 to 0.4 m2 s−1. Analysis suggests that the turbulent diffusivity in the bubble layer can be parameterized as a function of the cube of the wind friction velocity with a proportionality coefficient that depends weakly on wave age. Furthermore, in the bubble layer, on average, the shear production of the turbulent kinetic energy estimated by the diffusion coefficients is a similar order of magnitude as the dissipation rate predicted by the wall boundary layer theory.

Corresponding author address: David W. Wang, Naval Research Laboratory, 1009 Balch Blvd., Stennis Space Center, MS 39529. E-mail: david.wang@nrlssc.navy.mil

1. Introduction

The transfer of heat, gases, momentum, and energy between the atmosphere and the ocean are known to be connected with surface wave breaking, bubble generation, and mixing by wave- and shear-driven turbulence in the upper-ocean boundary layer (Anis and Moum 1995; Melville 1996). In general, surface wave breaking increases turbulent kinetic energy (TKE) and dissipation in the near-surface layer to a depth on the order of the wave height (Gerbi et al. 2009). The existence of a turbulent diffusion sublayer beneath the wave breaking layer has been suggested, where the vertical divergence of turbulent energy fluxes is in balance with the TKE dissipation and the shear production is small due to the weak background mean flow shear (Benilov and Ly 2002; Gerbi et al. 2009). Both observations (Thorpe et al. 2003a; Stips et al. 2005; Wijesekera et al. 2013; D’Asaro et al. 2014) and model simulations (McWilliams et al. 1997; Teixeira and Belcher 2010) show that the mixing associated with Langmuir circulation (Lc) is responsible for deepening of the mixed layer and increasing the eddy viscosity. It is likely that Lc can persist much longer and reach much deeper depths than those by the direct injection of breaking wave motions (Thorpe et al. 2003a). The turbulent motions in this sublayer play a key role by transporting energy downward (Feddersen et al. 2007). The quantification of the generation, transport, and dissipation of TKE is critically important for advancing our understanding and the development of mixing parameterizations in the oceanic boundary layer. However, because of the logistical difficulties of making near-surface measurements especially during high wind conditions, only a few measurements are available (Gemmrich and Farmer 1999, 2004; Soloviev and Lukas 2003; Thorpe et al. 2003b; Bakhoday Paskyabi and Fer 2014).

Field observations at strong winds show an increasing intensity and occurrence of breaking waves on the surface as whitecaps and bubble plumes in the water column. During the wave breaking process, bubbles are injected into the water column. Within about one wave period, larger fragmented bubbles quickly rise to the surface, contributing to the formation of foam (Farmer et al. 1999; Thorpe et al. 1999). The smaller bubbles (less than 100 μm radii) left beneath the surface persist much longer in the water column and are subject to turbulent motions (Thorpe et al. 2003b). Wave-induced turbulence is responsible for the breakup of bubbles and transport of fragmented bubbles into the water column (Vagle et al. 2012). The effects of dissolution and pressure in changing bubble radii are generally negligible during turbulent injection by breaking waves, which could last about 100 s and is comparable to the bubble life time (Thorpe and Hall 1983). Slow-rising small bubbles injected by breaking waves could be treated as passive tracers for depicting dynamic processes in the near-surface mixed layer (Thorpe 1992). Thorpe (1984, 1986) studied the vertical turbulent transport in the ocean boundary layer under weak to moderate winds by analyzing the eddy diffusion coefficient derived from bubble cloud acoustic backscatter profiles.

The objective of this study is to understand and characterize wave-affected turbulence dynamics in the mixed layer under high winds based on ocean and meteorological measurements collected off the coast of the northern Gulf of Alaska near Kayak Island in December 2012. Cyclonic storms dominate the atmospheric forcing in the Gulf of Alaska (Stabeno et al. 2004). These storms can interact with the steep coastal terrain to form strong Alaskan coastal wind jets, which are also referred to as “barrier jets” (Loescher et al. 2006; Olson et al. 2007). Barrier jets follow the coastal terrains and can persist for several days because the storms tend to linger as they spin down (Wilson and Overland 1986).

We focus on the analysis of vertical eddy diffusion coefficients estimated from time-averaged bubble acoustic backscatter profiles over a selected 12-day period when the maximum surface winds and significant wave heights reached 22 m s−1 and 9 m, respectively, and the background ocean and atmospheric conditions remained nearly uniform. Section 2 describes the experiment platforms and measurements. Section 3 describes the observed marine environmental conditions including surface winds, waves, background currents, and calculated net fluxes. Analyses of acoustic backscatter profile data on a surface-following coordinate are presented in section 4. Discussion is given in section 5, and a summary of major findings is provided in section 6.

2. Experiment platforms, sensors, and measurements

Hydrographic and velocity fields, profiles of acoustic backscatter, surface waves, and surface meteorology were collected in the coastal waters off Kayak Island, Alaska, over a 6-month period (October 2012 to March 2013) for the Naval Research Laboratory’s Breaking-Wave Effects under High Winds (BWE) program (Fig. 1). Instruments were deployed in a rectangular mooring network approximately parallel to the coast between the isobaths of 60 and 90 m (Fig. 1). The network’s alongshore and cross-shore distances are about 14 and 9 km, respectively. Instrument locations, data types, and water depths are given in Table 1. At the center of the network, a BioSonics DT-X echosounder (BioSonics 2004; Depew et al. 2009; Stevens et al. 2008) was deployed on an instrument platform (hereinafter referred to as the Lander) at about 1.5 m off the bottom. This echosounder has three vertically oriented upward-looking transducers that operate at 123, 208, and 430 kHz to provide measurements of echo intensity from breaking wave–induced bubbles within the water column directly above the Lander. The beamwidth is 6.5° for all three transducers. In this study, we chose to analyze the backscatter data collected at 208 kHz, similar to the operating frequencies used by Thorpe (1984; 1986), Dahl and Jessup (1995), Trevorrow (2003), and Vagle et al. (2010). The bubble radius that is resonant and particularly effective in scattering for the operating frequency of 208 kHz is about 16 μm at the water surface and approximately 27 μm at 20-m depth (Thorpe 1992; Vagle and Farmer 1992).

Fig. 1.
Fig. 1.

The location map of the BWE field experiment; Barny (B1–B4) and string (S1–S4) moorings are marked by solid circles. The land-based weather station (NRL MET) and moored buoy (NDBC 46082) are indicated by an open triangle and circle, respectively. Depth contour lines (gray lines) are in 10-m intervals starting at 10 m. The darker contour lines are for depths of 50, 100, 150, 200, 250, and 300 m.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Table 1.

Location of BWE mooring stations, water depth, sensors, and data types.

Table 1.

The depth profile of backscatter intensity was sampled at 2 Hz with a 0.017-m vertical resolution. During the experiment, the backscatter intensity profiles were collected for 10 min starting at 0000, 0400, 0800, 1200, 1600, and 2000 UTC and for 60 min at 1100 UTC. The measured intensity was converted to volumetric backscatter strength, Mυ (m−1), by the use of the sonar equation (BioSonics 2004); Mυ is often expressed in decibels (10 log10Mυ). Figure 2a shows 10-min samples of acoustic backscatter data; here, the depth axis zd represents the vertical distance measured upward from the bottom-mounted echosounder. The instantaneous wave surface η is identified from the profile’s high backscatter intensity anomalies caused by the air–sea interface (Vagle and Farmer 1992; Gemmrich 2010). The measured backscatter data Mυ(zd) from the fixed bottom-mounted echosounder is remapped to a wave-following coordinate system Mυ(zη), where zη is the distance measured downward from the wave surface η (Fig. 2b). The remapping of bubble backscatter profiles reduces the aliasing effect on averaging due to the surface wave orbital motions. Measurements based on the wave-following coordinate are more suitable for studying near-surface turbulence (Soloviev and Lukas 2014).

Fig. 2.
Fig. 2.

Time–depth section of acoustic backscatter profiles in (a) a fixed coordinate zd distance measured upward from the echosounder and (b) wave-following coordinate zη distance measured downward from the wave surface η, shown as the solid line in (a). The color shading is the backscatter intensity 10 log10(Mυ) (dB). The wind speed and wave height are u5 = 21.1 m s−1 and Hs = 6.6 m, respectively (case 69; Table 2).

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Background turbulent motions are likely to modify spatial distributions of rising bubbles in the near surface. In general, larger bubbles rise rapidly to the surface, while microbubble populations are formed into diffused bubble plumes by advective–diffusive processes controlled by turbulent motions, background currents, buoyancy forcing, and gas exchange. The plumes can persist over time during the active wave breaking period (Monahan and Lu 1990; Vagle et al. 2012). In this study, the analysis focuses on the 10-min acoustic backscatter data acquired during a 12-day period. A total of 81 10-min records were analyzed, and environmental conditions for these records are given in Table 2.

Table 2.

Summary of ocean surface meteorological and wave conditions and variables derived from the 81 records: buoy wind speed at 5 m height u5, buoy wind direction θu, significant wave height Hs, peak wave period Tp, surface wind stress τu, surface air temperature from the NRL weather station Tair, SST from S1, net heat flux Qnet, bubble depth Db, e-folding length λe, eddy diffusion coefficient based on Db [(4)] KυD, eddy diffusion coefficient from λe [(2)] Kυe, eddy diffusion coefficient from friction velocity [(7)], Kυu*, and λe and Kυe are not available when Db < Hs (marked as *).

Table 2.

The surface wave conditions are described in terms of the significant wave height Hs and the peak wave period Tp, where , Sη(f) is the wave frequency spectrum, and f1 = 0.05 Hz and f2 = 0.5 Hz are the lower and upper cutoff–frequency limits for the integration, respectively. The wave frequency spectrum Sη is computed from 10-min time series of surface displacement η extracted from the backscatter profile data (Fig. 2a), and Tp (peak frequency fp) is the period of the spectral peak (Table 2). Ocean surface wave conditions were also measured at the Lander by a RDI acoustic Doppler current profiler (ADCP) equipped with a wave array system (Strong et al. 2000) and at a nearby NDBC buoy (ID 46082). The wave data from the Lander’s ADCP were collected every 2 h, and the buoy wave data were collected hourly. Measurements of wave heights and periods from the Lander mounted echosounder and ADCP (not shown here) and the NDBC buoy are similar (Figs. 3c,d).

Fig. 3.
Fig. 3.

Time history of (a) wind speed u5 at 5-m height, (b) wind direction θu at NDBC buoy 46082, (c) significant wave height Hs at the Lander (solid circles) and at the buoy (dashed line), (d) peak wave period Tp at the Lander (solid triangles) and at the buoy (dashed line), and (e) surface Stokes drift Us0 at the Lander.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

The surface Stokes drift is computed from Sη as , where ω = 2πf, k is the wavenumber, ω2 = gk tanh(kh), g is the gravitational acceleration, h is the water depth, and G(kh) = cosh(2kh)/sinh2(kh) is a dimensionless factor accounting for the wave shoaling effect at h. Here, ω1 and ω2 are the lower and upper cutoff–frequency limits for the integration, respectively. The estimated surface Stokes drifts (Fig. 3e) vary between 0.05 and 0.5 m s−1 and are closely related to the variation of surface winds. Surface meteorological conditions were measured at the NDBC buoy and at a land-based NRL weather station installed for the experiment on Kayak Island. The buoy winds were measured by a R. M. Young anemometer at 5 m above the sea surface. More details about the NDBC wave and meteorological sensors can be found in Steele and Mettlach (1993). The NRL land station measured wind speed and direction, air temperature, relative humidity, solar irradiance (downwelling shortwave radiation), and barometric pressure. The anemometer was approximately 8 m above the ground while the rest of the sensors were about 4 m above the ground with the exception of the barometer, which was installed in the control panel mounted 2 m above the ground. Measurements from the buoy and the NRL land station are used to estimate surface wind stress and net heat flux Qnet from the bulk flux algorithms (Fairall et al. 1996).

Ocean current data were collected by five upward-looking 300-kHz Teledyne RD Instruments (RDI) Workhorse ADCPs deployed at the Lander and at the four corners of the rectangular network (B1–B4; Fig. 1). The ADCPs were positioned off the bottom in trawl-resistant bottom mounts called Barnys (Perkins et al. 2000; Teague et al. 2013). The ADCPs consisted of four transducers each with a 20° beam angle to the vertical and sampled full water column profiles of zonal U, meridional V, and vertical W velocity components at 2-m vertical resolution. The deepest velocity bins were off the bottom by 4.7 m at B1, B2, B3, and B4 and by 5.7 m at the Lander. ADCP velocity data in the upper 10 m were discarded due to side-lobe interference in the ADCP beams. Ping intervals of the ADCPs were 10 s at B1, B2, and B4, 11.25 s at B3, and 2.5 s at the Lander. Current velocity component data are averaged every 15 min at B1, B2, B3, and B4 and every 2 min at the Lander. All of the ADCPs returned good quality data except for the ADCP at B4. Four subsurface string temperature–conductivity (TC) moorings (S1–S4) were deployed near B1–B4 (distances less than 170 m). The TC string moorings were equipped with either 11 or 15 instruments to measure pressure, temperature, and conductivity. The instruments consisted of Sea-Bird Electronics (SBE) 37 MicroCATs (MC; 8 or 12 on a line) and In-Situ Aqua TROLLs (AT; 3 on each line). The MC and AT instruments were evenly spaced on the lines at depth intervals of about 5 to 7 m and recorded data at 5- and 10-min intervals, respectively. A wave tide gauge (WTG; Sea-Bird Electronics 26 with an attached Sea-Bird Electronics 4 conductivity cell) was also installed on the Lander to record bottom pressure, temperature, and conductivity data every 30 min. Detailed discussions of instrumentation, data collection, sampling methods, and data processing for the long-term current and hydrographic observations are in Jarosz et al. (2016, manuscript submitted to J. Geophys. Res.). Here, we describe the subset of the data relevant to this study, that is, measurements made during late December storm events.

3. The December storm events

a. Surface meteorology

In late December 2012, a series of high wind events occurred over the BWE experiment site. Figure 3 shows the time series of winds from the nearby NDBC buoy and wave data from the buoy and the Lander during the high wind period between 23 December 2012 and 3 January 2013. The buoy wind speeds exceeded 15 m s−1 with maximum winds reaching 22 m s−1 (Fig. 3a). The strong easterly winds generated large surface waves with a maximum significant wave height of about 9 m (Fig. 3c). The averaged significant wave height and peak wave period were 4.5 m and 10.9 s, respectively (Figs. 3c,d; Table 2). The wave height and peak wave period during 28 and 29 December measured from the Lander at 73-m water depth were smaller than those from the deep-water NDBC buoy due to shoaling effects.

The surface wind stress τw, net surface heat flux Qnet (Wm−2), and Monin–Obukhov length Lmo (m) were estimated by following Fairall et al. (1996; Fig. 4). Here, we used wind speed from the NDBC buoy and sea surface temperature (SST) from S1 and air temperature, solar radiation, and relative humidity from the NRL weather station at Kayak Island. During the 12-day period, SST remained steady at about 6°C, and air temperature increased from −7° to 4°C as warmer air moved into the BWE area. Water temperatures closely followed the air temperatures after 24 December (Fig. 4b). The estimated heat flux remained mostly negative (upward) and less than 50 W m−2 on most occasions. The Monin–Obukhov length remained positive from near zero to about 3500 m, indicating surface buoyancy forcing was not a factor during high winds. The turbulent Langmuir number Lat = (u*w/Us0)0.5 was also estimated, where the friction velocity u*w is (τw/ρw)0.5 and ρw is the density of water. The estimated Lat varied between 0.16 and 0.45 with a mean value of 0.3. This is well within the Langmuir regime (Li et al. 2005; Wijesekera et al. 2013).

Fig. 4.
Fig. 4.

Time history of (a) surface wind stress τw, (b) surface air temperature (solid line) at 4-m height (Kayak Island station) and water temperature (dashed line) at 5-m depth from S1, (c) net surface heat flux Qnet, where negative Qnet represents upward heat flux, (d) Monin–Obukhov length Lmo, and (e) turbulent Langmuir number Lat at the Lander.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

b. Background currents and high-frequency energy

Figure 5 shows the depth–time sections of ADCP velocity components (U, V, and W) at the Lander and water temperatures, salinities, and densities within 40 m of the mean water line at the nearby S3. Westward flows were dominant and the vertical shears were weak (Fig. 5a). Data from the string mooring show a well-mixed water column (Figs. 5d,e).

Fig. 5.
Fig. 5.

Depth–time current velocity components (cm s−1) at the Lander: (a) zonal U, (b) meridional V, and (c) vertical W. (d) Potential temperature Tθ (°C), (e) salinity S (psu), and (f) potential density anomaly σt (kg m−3) at the S3 subsurface mooring. Depth is the distance measured downward from the mean water line.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Figure 6 shows the variance-preserving spectra of current velocity components at 15-m depth for the 12-day period. Horizontal velocity spectra (U and V) show most of the energy is at frequencies less than 0.5 cycles per hour (cph). The variance of the vertical velocity spectrum has most of the energy at higher frequencies between 0.5 cph and the Nyquist frequency of 15 cph (Fig. 6c). The high-frequency energy levels were largest near the Nyquist frequency, indicating that the 2-min sampling rate could only partially resolve higher-frequency vertical motions. By applying a 2-h high-pass filter to the velocity components, we separated high- and low-frequency components, expressed as U = UL + u′, V = VL + υ′, and W = WL + w′, where UL, VL, and WL are low-frequency components and u′, υ′, and w′ are high-frequency components (e.g., Wijesekera et al. 2013). Velocity fluctuations at frequencies higher than the Nyquist frequency were not included in the high-frequency components due to the averaging scheme used in ADCP sampling, and therefore we underestimate true strength of turbulent velocity components. The time averaging of squared high-pass velocities (u′, υ′, and w′) was used to approximate TKE, q2/2, where q2 = 〈u2〉 + 〈υ2〉 + 〈w2〉 and the angle brackets denote 10-min averaging. The TKE was dominated by horizontal components (Fig. 6). The time–depth variation of TKE is shown in Fig. 7b. The TKE was as large as 102 cm2 s−2 at a depth of 10 m, especially when winds were strong (Fig. 7a), and decayed rapidly with depth. The time variability of TKE is strongly correlated with that of wind stress (Fig. 7). Wave orbital velocities can alias the measurement of turbulent velocity fluctuations due to the sampling rate of the ADCP. However, in this study, aliasing from wave orbital velocities associated with the dominant wave motion is likely insignificant since the dominant wave periods are 3 to 5 times that of our 2.5-s sampling rate (Table 2). The effect of aliasing on variance is estimated to be less than 1 cm2 s−2 at a depth of 10 m, and the time-averaged vertical profile of TKE is about two orders of magnitude larger than a plausible contamination of velocity variance by wave orbital motions (Fig. 8). More detailed discussion of estimating wave orbital contamination is presented in the appendix.

Fig. 6.
Fig. 6.

Variance-preserving frequency spectra of velocity components at the Lander: (a) U, (b) V, and (c) W at 15-m water depth. The semidiurnal tide (period: 12.42 h) and the diurnal tide (period: 24.48 h) are marked as circles and crosses, respectively.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Fig. 7.
Fig. 7.

Time series of (a) friction velocity u*w (m s−1) and (b) depth profile of TKE. The color shading is log10(TKE) (cm2 s−2).

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Fig. 8.
Fig. 8.

Mean depth profile of TKE for the 81 cases (circles). The solid line represents the exponential function [(10)]. The crosses represent the mean aliasing variance profile of simulated wave orbital motions Δwave for the 81 cases. The dotted lines show 95% confidence intervals; z is the distance measured downward from the mean water line z = 0.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

4. The e-folding length and bubble depth

The occurrence, depth, and intensity of bubble clouds are closely related to the surface wind and wave conditions and turbulent motions including Langmuir circulation in the surface layer. The temporal and spatial evolutions of entrained bubbles arise from a combination of turbulence and advection associated with breaking waves and Langmuir circulation (Gemmrich and Farmer 1999; Thorpe et al. 2003a). To illustrate the bubble cloud temporal and spatial variations under moderate to high winds, time–depth acoustic backscatter intensity profiles for four selected cases with surface winds u5 of 8.9, 13.7, 16, and 19.6 m s−1 are shown in Fig. 9. The corresponding significant wave heights are 4.1, 3.6, 6.0, and 8.7 m, respectively. As winds increased, the bubble cloud coverage expanded and increased intensity and penetration depth (Fig. 9). The intensity of backscatter decays rapidly with depth as illustrated in the time-averaged profiles 〈Mυ〉 in Figs. 10a and 10b. The bubble statistics (such as e-folding length and bubble depth as discussed below) depend on the averaging time. We examined the impact of averaging time scales on the bubble statistics of 〈Mυ〉 by using the averaging time intervals from 5 to 900 s from the 60-min backscatter profile data. We noted large variabilities for the time scales less than 30 s. However, the statistics become independent of the averaging scale when the averaging scale is larger than 5 min. In the following analysis, the 10-min averaging scale was used, since it provides quasi-steady estimates of bubble statistics.

Fig. 9.
Fig. 9.

The 10-min time history of acoustic backscatter depth profiles at winds u5 of (a) 8.9, (b) 13.7, (c) 16, and (d) 19.6 m s−1. Corresponding wave heights Hs are 4.1, 3.6, 6.0, and 8.7 m, respectively. They are for cases 26, 29, 16, and 70, respectively (Table 2). The color shading is 10 log10(Mυ) (dB), and zη is the distance measured downward from the free wave surface η.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Fig. 10.
Fig. 10.

Profiles of 10-min-averaged backscatter 〈Mυ〉 at the four wind speeds (see Fig. 9) in (a) a wave-following coordinate zη and (b) zη/Hs, scaled by significant wave height. The e-folding length is calculated for the depth profile 〈Mυ〉 between zη/Hs = 1 and 2 as marked by the two horizontal lines in (b). The vertical line in (b) represents the empirical backscatter threshold (−50 dB) for identifying the bubble depth.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Vertical distributions of breaking wave bubbles decay exponentially with depth (e.g., Thorpe 1984, 1986), and the resulting vertical distribution of acoustic backscatter is approximated by an exponentially decaying function , where Mυ(0) is the backscatter at the surface and λe is the e-folding length that describes the decay rate; zη is the distance measured downward from the wave surface zη = 0. Here, we estimated the e-folding length by fitting an exponential profile to 〈Mυ〉 between zη = Hs and zη = 2Hs (indicated by the horizontal dotted lines in Fig. 10b). In addition to the e-folding length, we estimated the bubble penetration depth or the bubble depth Db, defined as the depth where 〈Mυ〉 decreases to an empirically determined threshold value of −50 dB. Similar techniques have been used to empirically determine bubble cloud depths with threshold levels of −50 (Dahl and Jessup 1995; Trevorrow 2003) and −60 dB (Thorpe 1986). We noted that the noise levels of some profiles were close to −60 dB (Fig. 10a), but the noise levels of many profiles were closer to −50 dB. As indicated in Fig. 10b, the bubble depth is about 2 to 4 times the wave height. Figure 11b shows the time variation of estimated bubble depths and e-folding lengths over the 12-day period. The close relationships between wind speed and bubble depth and e-folding length are shown in Fig. 12. For winds less than 10 m s−1, the relationships between wind and bubble depth and e-folding length are approximately linear and are similar to those by Vagle et al. (2010; Fig. 12). For winds higher than 10 m s−1, the relationships between wind speed and bubble depth and e-folding length became nonlinear and are much higher than those by Vagle et al. (2010). It is noted that bubble depth and e-folding length in Vagle et al. (2010) were derived from acoustic bubble backscatter data averaged over 2.25 h, while the current observations were based on 10-min-averaged backscatter profiles.

Fig. 11.
Fig. 11.

Time series of (a) buoy wind speed u5 and (b) bubble depth Db (solid circles) and e-folding length λe (triangles).

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Fig. 12.
Fig. 12.

Wind speed u5 vs (a) bubble depth Db and (b) e-folding length λe. The thick dashed lines represent the empirical linear relationships by Vagle et al. (2010). The solid circles are u5 bin-averaged Db and λe. The length of the error bars represents two standard deviations.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

As shown in Fig. 12, to first order, Db is a function of wind speed, but there is a noticeable variation in Db for a given wind speed band. Therefore, the variability in Db is further examined. Figure 13 shows six backscatter profiles for wind speeds u5 that only slightly varied between 13.9 and 14.1 m s−1, while Db/Hs varied from 2.1 to 4.3 (Table 2). Thorpe (1992) showed that during the early stages of sea state development surface wave breaking is dominated by plunging breakers with larger Db/Hs. As waves continue to develop, spilling breakers dominate the breaking processes with small Db/Hs. The wave development stage is represented by wave age δ = Cp/u*a, where Cp is the wave phase speed associated with peak wave period and u*a is the friction velocity in the atmospheric boundary layer. The relationship between bubble depth Db/Hs and wave age δ for wind speeds greater than 6 m s−1 is shown in Fig. 14a and is consistent with observations reported by Thorpe (1986, his Fig. 5). Both Thorpe (1986) and present observations show a similar trend of decreasing Db/Hs with increasing wave age (Fig. 14), and the relationship between Db/Hs and δ can be approximated as
e1
where β ≈ 70 was determined empirically from the wave age bin-averaged data between 15 ≤ δ ≤ 70. A similar trend was observed between wave age and bubble depth scaled by wavelength (Db/Lp; Fig. 14b), where Lp is the wavelength of the peak wave period Tp based on the dispersion relation for surface waves. This similarity is expected because wave heights and lengths of wind waves are closely related (Toba 1978).
Fig. 13.
Fig. 13.

Profiles of 10-min-averaged backscatter 〈Mυ〉 for wind speed u5 ~ 14 m s−1. Case numbers are listed in Table 2, and the ratios of bubble depth to significant wave height Db/Hs are 2.9, 2.4, 2.7, 2.5, 4.3, and 2.1, respectively. The vertical dashed line represents the empirical backscatter threshold (−50 dB) used for identifying bubble depth.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Fig. 14.
Fig. 14.

(a) Bubble depth scaled by wave height Db/Hs vs wave age Cp/u*a. The circles are data from the BWE experiment. The crosses are from Thorpe (1986), and u10 = 28u*a is used for replotting Thorpe’s data. (b) Bubble depth scaled by wavelength Db/Lp vs wave age Cp/u*a. Here, Lp is computed from the peak wave period Tp, using the linear dispersion relation. Bubble depth data with wind speeds less than 6 m s−1 are excluded. The solid circles are Cp/u*a bin-averaged Db/Hs and Db/Lp. The length of the error bars represents two standard deviations.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Downward movement of bubble clouds is driven by the convergence of Langmuir cells (e.g., Zedel and Farmer 1991; Plueddemann et al. 1996). These convergence zones have narrow spatial scales, which in turn require high spatial and temporal resolution velocity data to identify Langmuir cells. The 2-min-averaged ADCP velocities are not sufficient to determine Langmuir cell structure. Since bubble plumes are driven by Langmuir cells, their effects on backscattering distribution are explicitly included in the estimated e-folding and bubble depths from 10-min-averaged profiles of 〈Mυ〉.

5. Estimating turbulent diffusivity coefficient

The vertical distribution of bubble concentration is primarily controlled by turbulent diffusion and by advection in Langmuir circulation (Thorpe et al. 2003a). Thorpe (1984) reports that some aspects of turbulence in the near-surface layer can be inferred from the microscale bubble distribution, since such bubbles can act as a tracer. Thorpe (1984) evaluated the eddy diffusion coefficient Kυ by solving the one-dimensional, steady-state, advection–diffusion equation representing the following processes: (i) turbulent transport of bubbles from the near-surface layer, (ii) buoyant bubbles rise at a constant speed, and (iii) bubble radius changes due to gas diffusion and compression from hydrostatic pressure. Thorpe (1984) proposed several formulations for estimating Kυ based on assumptions related to the vertical structure of the diffusivity coefficient, the rate of change of bubble radius, and the nature of the turbulent motions in the mixed layer. Here, for simplicity, the eddy diffusion coefficient is treated as a constant within the bubble layer, bubbles rise at a steady speed with a constant rate of change in radius, and the vertical distribution of bubbles is assumed to follow an exponentially decaying profile with depth. The resulting eddy diffusivity (which is also referred as turbulent diffusivity) is estimated from the e-folding length λe of the bubble vertical acoustic profile (Thorpe 1984):
e2
where λe is the e-folding length of the bubble distribution, wb is the rising speed of bubbles, and σ is the rate of change of bubble radius due to diffusion of gases and compression under hydrostatic pressure. The determination of wb and σ requires the bubble size distribution function and the lifetime of bubbles. However, such measurements were not made during BWE observations. By following Thorpe (1984), we used wb = 0.54 cm s−1, which corresponds to a bubble radius of 50 μm at the peak of bubble size distributions as observed by Johnson and Cooke (1979). We used σ = 0.018 s−1, which corresponds to the observed life time bubbles (~1 min) as observed in Thorpe and Hall (1983).
Alternatively, based on a scaling argument, the eddy diffusion coefficient in a wave-affected oceanic surface layer can be expressed from a representative velocity scale Vt and a length scale lt (e.g., Thorpe 1984):
e3
where the von Kármán constant κ is 0.41. Depth-dependent and depth-independent eddy diffusion coefficients can be derived from (3). The depth-dependent eddy diffusivity is for a constant shear stress layer; when Vt is set to the friction velocity u*w and lt = z, the vertical distance measured downward from the mean surface z = 0. By choosing the velocity scale as u*w and the vertical turbulent length scale as the bubble depth Db, the depth-independent eddy diffusivity can be expressed as
e4
The functional forms of the turbulent diffusivity given in the Mellor–Yamada closure (Mellor and Blumberg 2004) and by simple scaling arguments [(3)] are comparable. A similar constant turbulent diffusivity coefficient in the wave injection region was suggested by Thorpe et al. (2003a), where the length scale is represented by the wave height . Here, the turbulent or eddy diffusion coefficient in (4) was estimated with the bubble layer depth from the backscatter profiles for the length scale (Fig. 11; Table 2).

Both estimates of Kυe [(2)] and KυD [(4)] computed during the December storm events were comparable and closely followed the wind speed (Fig. 15). The Kυe and KυD varied between 0.01 and 0.5 m2 s−1 and are highly correlated (Fig. 16). Figure 17 shows the relationship between eddy diffusion coefficients and surface wind speeds. For comparison, eddy diffusion coefficients estimated by Thorpe (1984) from e-folding lengths and by Dahl and Jessup (1995) from bubble depths were also included in Fig. 17. Their observations were limited to wind speeds less than 10 m s−1. The general trend of increasing eddy diffusion coefficients with increasing winds can be found from all data sources for wind speeds up to 22 m s−1. As shown in Fig. 17, our eddy diffusivities are higher than those of Thorpe (1984) and lower than those of Dahl and Jessup (1995) for winds ranging from 6 to 10 m s−1. Our results are similar to the empirical relationship of eddy viscosity and wind speed (Neumann 1952; Neumann and Pierson 1966).

Fig. 15.
Fig. 15.

Time series of (a) buoy wind speed u5 (b) eddy diffusion coefficients: Kυe [(2)] (triangles), KυD [(4)] (circles), and Kυu* (dashed line) based on wind speed and wave age [(7)].

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Fig. 16.
Fig. 16.

Eddy diffusion coefficients Kυe vs KυD. The thick dashed line represents the ratio 1:1.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Fig. 17.
Fig. 17.

Wind speed u5 vs bin-averaged eddy diffusion coefficients KυD (solid circles) and Kυe (triangles). The length of the error bars represents two standard deviations of 〈KυD〉 (solid line) and 〈Kυe〉 (dashed line). Eddy diffusion data from Thorpe (1984) and Dahl and Jessup (1995) are represented, respectively, by crosses and asterisks. The gray line represents the empirical relationship of the eddy viscosity and wind speed (Neumann 1952).

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

6. Discussion

a. Parameterizing the eddy diffusion coefficient

Given the relationship between the bubble depth and the significant wave height shown in (1), the eddy diffusivity given in (4) can be rewritten as a function of friction velocity, wave height, and wave age:
e5
The equilibrium wind-wave similarity law (Toba 1978) shows that the normalized wave energy E is a function of air friction velocity u*a and wave age δ, and the resulting functional form is
e6
where E = Hs2/16, the gravitational acceleration g = 9.81 m s−2, and B = 0.051 (Toba 1978). The air friction velocity is computed from wind stress τw = ρa(u*a)2 = ρw(u*w)2, where ρw and ρa are water and air densities, respectively. By combining (5) and (6), we can express the vertical eddy diffusivity as a function of friction velocity and wave age by
e7
where α = 4kβB0.5(ρw/ρa). For β = 70 [(1)], B = 0.051 [(6)], and ρw/ρa ≈ 800, α has a value of about 2 × 104. Equation (7) shows that the eddy diffusivity is proportional to the cubic power of the friction wind velocity and square root of wave age. Given that δ varies between 15 and 70 (Fig. 14), the impact of wave age on the variation of eddy diffusivity for the range between 0.01 and 0.4 m2 s−1 is within about a factor of 2 (Fig. 18). Therefore, 〈Kυe〉 and 〈KυD〉 are well predicted by (7) at moderate to high winds, and, on average, eddy diffusivities are proportional to with a proportionality constant [(2 × 104)δ0.5] weakly dependent on the wave age.
Fig. 18.
Fig. 18.

Cubic of waterside friction velocity (u*w)3 vs bin-averaged eddy diffusion coefficients 〈KυD〉 (solid circles) and 〈Kυe〉 (triangles). The solid and dashed lines represent the eddy diffusivity coefficient predicted by (7) for young (δ = 15) and developed (δ = 70) sea states, respectively. The length of the error bars represents two standard deviations of 〈KυD〉 (solid line) and 〈Kυe〉 (dashed line).

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

b. Estimation of turbulence diffusion flux and shear production

The TKE balance in the ocean surface layer is controlled by a wide range of physical processes at different depths depending on the distance from the surface (e.g., Soloviev and Lukas 2014). The generation of TKE by surface wave breaking and subsequent dissipation of TKE play a vital role in setting air–sea fluxes. Below the wave breaking layer, the vertical transport of TKE by turbulent motions is an important component of the TKE balance (e.g., Benilov and Ly 2002; Gerbi et al. 2009). Below this diffusive sublayer, the shear production and dissipation balance hold (Craig and Banner 1994; Soloviev and Lukas 2014). To examine the relative importance of different terms in the TKE equation, we computed shear production, dissipation, and diffusion of TKE in the bubble layer. Here, the TKE equation is expressed as
e8
where ∂(q2/2)/∂t is the time derivative of TKE, Adv is the advection of TKE by mean currents, Pw is the pressure–velocity correlation term, Ft is the vertical transport of TKE by turbulent motions, Ps is the shear production term, and ε is the energy dissipation term. We did not have data to evaluate Adv and Pw. However, we suspect that Pw may not be small in the wave dominating boundary layer. The vertical transport of TKE by turbulent motions Ft is typically expressed in terms of the downgradient transport of diffusion energy flux (e.g., Mellor and Yamada 1982):
e9
where Kq is the vertical eddy diffusivity of TKE (q2/2). Here, the TKE is approximated from ADCP high-frequency velocity components (Figs. 7, 8), and Kq is estimated from bubble eddy diffusion coefficients (Fig. 15). As shown in Fig. 8, the mean profile of TKE below 10-m depth decays exponentially with depth and can be approximated as
e10
where αt (≈16) and Dt (≈30 m) are empirically determined to match the mean TKE profiles of the 81 records. By treating Kq as a constant in the bubble layer and by evaluating the second derivative of q2 from (10), we approximate the vertical diffusion of TKE:
e11
The shear production term Ps is
e12
where Km is the eddy viscosity coefficient and the vertical shear of UL and VL are computed from low-pass velocity components from the ADCP data. Here, KυD (5) is used for Km and Kq = 0.41Km (Wijesekera et al. 2003). In addition, the TKE dissipation rate predicted by the law of the wall scaling (Soloviev and Lukas 2014) is
e13
The enhanced TKE dissipation rate within the surface boundary layer proposed by Terray et al. (1996) is
e14
where the effective phase speed Ce = 0.5Cp, and Cp is wave phase speed of the dominant wave period Tp. The quantities Ft, Ps, εL, and εT were computed from (11) to (14) based on 10-min-averaged currents, winds, and eddy diffusivity estimates. Depth-averaged values , , , and were obtained by averaging between z = 10 m and z = 30 m and are plotted as a function of time in Fig. 19b. The shear production term Ps is the same order magnitude as the dissipation rate εL based on the wall boundary layer scaling. The turbulent diffusion of TKE Ft is about one order of magnitude smaller than the shear production, and the dissipation rate predicted from Terray et al. (1996) is one order of magnitude larger than the shear production term. The time-mean values of , , , and are 2.1 × 10−7, 2 × 10−6, 1.2 × 10−6, and 1.5 × 10−5 W kg−1, respectively, for the 81 records (Table 3). Our results suggest that in the bubble layer, that at least between one and two wave heights below the wave surface, the shear production is similar to the turbulent dissipation represented by the wall boundary layer theory [(13)]. Our estimates are consistent with observations reported by Thorpe et al. (2003b), who noted that waves and Lc have insignificant impact on the turbulence beyond a depth of 1.2Hs.
Fig. 19.
Fig. 19.

Time history of (a) u*w waterside friction velocity and (b) depth-averaged vertical energy diffusion [(11)], shear production [(12)], and energy dissipation rate [(13)] and [(14)] between 10- and 30-m depth.

Citation: Journal of Physical Oceanography 46, 5; 10.1175/JPO-D-15-0164.1

Table 3.

The mean values and 95% confidence interval (CI) of turbulent diffusion, shear production, and energy dissipation rates averaged over 10- to 30-m depth during the December storms (W kg−1).

Table 3.

7. Summary and conclusions

Acoustic backscatter intensity, hydrographic and velocity fields, surface wave statistics, and meteorological measurements were used to quantify the magnitude and temporal variability of near-surface turbulent diffusivities in the coastal waters off Kayak Island, Alaska, as part of the NRL’s Breaking-Wave Effects under High Winds (BWE) program. The analysis was focused on estimating vertical eddy diffusivity from time-averaged bubble acoustic backscatter profiles in a wave-following coordinate. We used a subset of acoustic data collected with an echosounder at 208 kHz for a period of 12 days in late December 2012. During the 12-day observational period, the strong and persistent easterly winds reached 22 m s−1 (Figs. 3a,b), with an average speed of about 12 m s−1, and generated large surface waves with a maximum significant wave height of about 9 m and an average height of 4.5 m (Fig. 3c). The sea surface temperature remained steady at about 6°C, and the air temperature increased from −7° to 4°C. The sea surface was experiencing cooling, and, on average, the net surface cooling was about 50 W m−2 (Fig. 4). The 81 10-min segments of acoustic backscatter profiles were analyzed. We used the observed vertical distribution of acoustic backscattering intensity from an upward-looking high-frequency echosounder to estimate near-surface turbulent diffusivity during high-wind conditions. The major observational findings and inferences of this study are as follows:

  • Bubble backscattering strength decayed exponentially with depth (Fig. 10). The e-folding length λe, estimated between one and two wave heights below the wave surface, varied from about 0.6 to 6 m and was highly correlated with wind speed (Fig. 8). Similar wind speed dependence was found in the bubble penetration depth or the bubble depth Db, where Db was defined as the depth at which the backscatter intensity drops to an empirical threshold of −50 dB (Dahl and Jessup 1995; Trevorrow 2003). The bubble depth varied from about 3 to 30 m. The bubble depth scaled by the wave height (Db/Hs) varied between 0.5 and 5 (Fig. 14a).
  • The turbulent diffusivity in a bubble cloud layer was estimated from acoustic backscatter data by following Thorpe (1984). Here, microscale bubble clouds were treated as a scalar field and the eddy diffusion coefficient Kυe was obtained by solving the one-dimensional, steady-state, advection–diffusion equation [(2)]. The turbulent diffusivity KυD estimated from the bubble depth based on scaling arguments [(4)] is consistent with the diffusivity Kυe and varied between 0.01 and 0.5 m2 s−1 (Fig. 15). Both Kυe and KυD are closely correlated with surface wind speeds between 5 and 22 m s−1 (Fig. 17).
  • In the bubble layer, the shear production of TKE at a depth below one significant wave height was a similar order of magnitude as the dissipation rate predicted by the wall boundary layer theory.
  • The turbulent diffusivity in the bubble layer (beyond about a depth of one significant wave height from the surface) can be parameterized as a function of the cube of the wind friction velocity with a proportionality coefficient that depends weakly on wave age (Fig. 18).

Acknowledgments

This work was sponsored by the Office of Naval Research in a Naval Research Laboratory (NRL) project referred to as Breaking-Wave Effects under High Winds (BWE). We thank the assistance provided by U. S. Coast Guard. We thank Mark Hulbert, Steve Sova, Andrew Quaid, and Justin Brodersen for their technical support. We also thank the captain, crew, and marine technicians of the R/V Oceanus and the crew of Sound Pacer for their assistance. We thank the two anonymous reviewers for their thorough and careful review of the manuscript and useful comments.

APPENDIX

Estimating Wave Orbital Velocity Aliasing

The aliasing of wave orbital velocity components on near-surface velocity measurements from an ADCP were evaluated by computing the surface wave contributions using a similar sampling method used in ADCP velocity estimates. ADCP velocities were sampled every 2.5 s with 2-min ensemble averaging over four beams. The aliasing due to wave orbital velocities associated with dominant wave motions was unlikely since our sampling rate (2.5 s) was 3–5 times faster than the dominant wave period. To quantify the velocity aliasing, horizontal and vertical components of wave orbital velocities, Uwave and Wwave, were simulated using wave height and wave period, Hs and Tp. They are expressed as (Dean and Dalrymple 1991)
ea1
where z is the depth measured downward from the mean water line z = 0, h is the water depth, θ is a random phase between −π and π, ωp = 2π/Tp, and the wavenumber kp is determined from Tp using the dispersion relationship (Dean and Dalrymple 1991). The mean particle velocity components and were computed from the Uwave and Wwave sampled at 2.5-s intervals for 2 min, the same as that used for ADCP current components. The aliasing variance of wave orbital velocity due to random phase averaging is then computed as . The depth profile of Δwave, averaged for the 81 cases, is shown in Fig. 8. The aliasing is insignificant, and the aliasing variance in general is at least one order of magnitude smaller than the TKE.

REFERENCES

  • Anis, A., , and J. N. Moum, 1995: Surface wave-turbulence interactions: Scaling ε(z) near the sea surface. J. Phys. Oceanogr., 25, 20252044, doi:10.1175/1520-0485(1995)025<2025:SWISNT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bakhoday Paskyabi, M., , and I. Fer, 2014: The influence of surface gravity waves on the injection of turbulence in the upper ocean. Nonlinear Processes Geophys., 21, 713733, doi:10.5194/npg-21-713-2014.

    • Search Google Scholar
    • Export Citation
  • Benilov, A. Y., , and L. N. Ly, 2002: Modeling of surface waves breaking effects in the ocean upper layer. Math. Comput. Modell., 35, 191213, doi:10.1016/S0895-7177(01)00159-5.

    • Search Google Scholar
    • Export Citation
  • BioSonics, 2004: DT4 data file format specification. BioSonics Software and Engineering Library Rep. BS&E-2004-07-0009-1.3, 33 pp.

  • Craig, P. D., , and M. L. Banner, 1994: Modeling wave enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr., 24, 25462559, doi:10.1175/1520-0485(1994)024<2546:MWETIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dahl, P. H., , and A. T. Jessup, 1995: On bubble clouds produced by breaking waves: An event analysis of ocean acoustic measurements. J. Geophys. Res., 100, 50075020, doi:10.1029/94JC03019.

    • Search Google Scholar
    • Export Citation
  • D’Asaro, E. A., , J. Thomson, , A. Y. Shcherbina, , R. R. Harcourt, , M. F. Cronin, , M. A. Hemer, , and B. Fox‐Kemper, 2014: Quantifying upper ocean turbulence driven by surface waves. Geophys. Res. Lett., 41, 102107, doi:10.1002/2013GL058193.

    • Search Google Scholar
    • Export Citation
  • Dean, R. G., , and R. A. Dalrymple, 1991: Water Wave Mechanics for Engineers and Scientists. Advanced Series on Ocean Engineering, Vol. 2, World Scientific, 370 pp.

  • Depew, D. C., , A. W. Stevens, , R. E. H. Smith, , and R. E. Hecky, 2009: Detection and characterization of benthic filamentous algal stands on rocky substrata using a high frequency echosounder. Limnol. Oceanogr. Methods, 7, 693705, doi:10.4319/lom.2009.7.693.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., , E. F. Bradley, , D. P. Rogers, , J. B. Edson, , and G. S. Young, 1996: Bulk parameterization of air–sea fluxes in TOGA COARE. J. Geophys. Res., 101, 37473767, doi:10.1029/95JC03205.

    • Search Google Scholar
    • Export Citation
  • Farmer, D. M., , S. Vagle, , and M. Li, 1999: Wave breaking, turbulence and bubble distributions in the ocean surface layer. The Wind-Driven Air–Sea Interface, M. Banner, Ed., School of Mathematics, University of New South Wales, 187–192.

  • Feddersen, F., , J. H. Trowbridge, , and A. J. Williams III, 2007: Vertical structure of dissipation in the nearshore. J. Phys. Oceanogr., 37, 17641777, doi:10.1175/JPO3098.1.

    • Search Google Scholar
    • Export Citation
  • Gemmrich, J. R., 2010: Strong turbulence in the wave crest region. J. Phys. Oceanogr., 40, 583595, doi:10.1175/2009JPO4179.1.

  • Gemmrich, J. R., , and D. M. Farmer, 1999: Near-surface turbulence and thermal structure in a wind-driven sea. J. Phys. Oceanogr., 29, 480499, doi:10.1175/1520-0485(1999)029<0480:NSTATS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gemmrich, J. R., , and D. M. Farmer, 2004: Near-surface turbulence in the presence of breaking waves. J. Phys. Oceanogr., 34, 10671086, doi:10.1175/1520-0485(2004)034<1067:NTITPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gerbi, G. P., , J. H. Trowbridge, , E. A. Terray, , A. J. Plueddemann, , and T. Kukulka, 2009: Observations of turbulence in the ocean surface boundary layer: Energetics and transport. J. Phys. Oceanogr., 39, 10751096, doi:10.1175/2008JPO4044.1.

    • Search Google Scholar
    • Export Citation
  • Johnson, B. D., , and R. C. Cooke, 1979: Bubble population and spectra in coastal waters. J. Geophys. Res., 84, 37613766, doi:10.1029/JC084iC07p03761.

    • Search Google Scholar
    • Export Citation
  • Li, M., , C. Garrett, , and E. Skyllingstad, 2005: A regime diagram for classifying turbulent large eddies in the upper ocean. Deep-Sea Res. I, 52, 259278, doi:10.1016/j.dsr.2004.09.004.

    • Search Google Scholar
    • Export Citation
  • Loescher, K. A., , G. S. Young, , B. A. Colle, , and N. S. Winstead, 2006: Climatology of barrier jets along the Alaskan coast. Part I: Spatial and temporal distributions. Mon. Wea. Rev., 134, 437453, doi:10.1175/MWR3037.1.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., , P. P. Sullivan, , and C.-H. Moeng, 1997: Langmuir turbulence in the ocean. J. Fluid Mech., 334, 130, doi:10.1017/S0022112096004375.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys., 20, 851875, doi:10.1029/RG020i004p00851.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., , and A. Blumberg, 2004: Wave breaking and ocean surface thermal response. J. Phys. Oceanogr., 34, 693698, doi:10.1175/2517.1.

    • Search Google Scholar
    • Export Citation
  • Melville, W. K., 1996: The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech., 28, 279321, doi:10.1146/annurev.fl.28.010196.001431.

    • Search Google Scholar
    • Export Citation
  • Monahan, E. C., , and M. Lu, 1990: Acoustically relevant bubble assemblages and their dependence on meteorological parameters. IEEE J. Oceanic Eng., 15, 340349, doi:10.1109/48.103530.

    • Search Google Scholar
    • Export Citation
  • Neumann, G., 1952: On Wind Generated Waves with Special Reference to the Problem of Wave Forecasting. New York University, College of Engineering, Department of Meteorology, 136 pp.

  • Neumann, G., , and W. J. Pierson Jr., 1966: Principles of Physical Oceanography. Prentice-Hall, 545 pp.

  • Olson, J. B., , B. A. Colle, , N. A. Bond, , and N. Winstead, 2007: A comparison of two coastal barrier jet events along the southeast Alaskan coast during the SARJET field experiment. Mon. Wea. Rev., 135, 36423663, doi:10.1175/MWR3448.E1.

    • Search Google Scholar
    • Export Citation
  • Perkins, H., , F. De Strobel, , and L. Gauldesi, 2000: The Barny Sentinel trawl-resistant ADCP bottom mount: Design, testing, and application. IEEE J. Oceanic Eng., 25, 430436, doi:10.1109/48.895350.

    • Search Google Scholar
    • Export Citation
  • Plueddemann, A. J., , J. A. Smith, , D. A. Farmer, , R. A. Weller, , W. R. Crawford, , R. Pinkel, , S. Vagle, , and A. Gnanadesikan, 1996: Structure and variability of Langmuir circulation during the surface waves process program. J. Geophys. Res., 101, 35253543, doi:10.1029/95JC03282.

    • Search Google Scholar
    • Export Citation
  • Soloviev, A., , and R. Lukas, 2003: Observation of wave-enhanced turbulence in the near-surface layer of the ocean during TOGA COARE. Deep-Sea Res. I, 50, 371395, doi:10.1016/S0967-0637(03)00004-9.

    • Search Google Scholar
    • Export Citation
  • Soloviev, A., , and R. Lukas, 2014: Near-surface turbulence. The Near-Surface Layer of the Ocean, A. Soloviev and R. Lukas, Eds., Springer, 153–224.

  • Stabeno, P. J., , N. A. Bond, , A. J. Hermann, , N. B. Kachel, , C. W. Mordy, , and J. E. Overland, 2004: Meteorology and oceanography of the northern Gulf of Alaska. Cont. Shelf Res., 24, 859897, doi:10.1016/j.csr.2004.02.007.

    • Search Google Scholar
    • Export Citation
  • Steele, K. E., , and T. Mettlach, 1993: NDBC wave data-current and planned. Proc. Second Int. Symp. on Ocean Wave Measurement and Analysis, New Orleans, LA, ASCE, 198–207.

  • Stevens, A. W., , J. R. Lacy, , D. P. Finlayson, , and G. Gelfenbaum, 2008: Evaluation of a single-beam sonar system to map seagrass at two sites in northern Puget Sound, Washington. U.S. Geological Survey Scientific Investigations Rep. 2008-5009, 45 pp.

  • Stips, A., , H. Burchard, , K. Bolding, , H. Prandke, , A. Simon, , and A. Wüest, 2005: Measurement and simulation of viscous dissipation in the wave affected surface layer. Deep-Sea Res. II, 52, 11331155, doi:10.1016/j.dsr2.2005.01.012.

    • Search Google Scholar
    • Export Citation
  • Strong, B., , B. Brumley, , E. A. Terray, , and G. W. Stone, 2000: The performance of ADCP-derived directional wave spectra and comparison with other independent measurements. Proc. Oceans 2000 MTS/IEEE Conf. and Exhibition, Providence, RI, IEEE, 11951203, doi:10.1109/OCEANS.2000.881763.

  • Teague, W. J., , H. W. Wijesekera, , E. Jarosz, , D. B. Fribance, , A. Lugo-Fernández, , and Z. R. Hallock, 2013: Current and hydrographic conditions at the East Flower Bank in 2011. Cont. Shelf Res., 63, 4358, doi:10.1016/j.csr.2013.04.039.

    • Search Google Scholar
    • Export Citation
  • Teixeira, M. A. C., , and S. E. Belcher, 2010: On the structure of Langmuir turbulence. Ocean Modell., 31, 105119, doi:10.1016/j.ocemod.2009.10.007.

    • Search Google Scholar
    • Export Citation
  • Terray, E. A., , M. A. Donelan, , Y. C. Agrawal, , W. M. Drennan, , K. K. Kahma, , A. J. Williams III, , P. A. Hwang, , and S. A. Kitaigorodskii, 1996: Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr., 26, 792807, doi:10.1175/1520-0485(1996)026<0792:EOKEDU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1984: On the determination of Kv in the near-surface ocean from acoustic measurements of bubbles. J. Phys. Oceanogr., 14, 855863, doi:10.1175/1520-0485(1984)014<0855:OTDOIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1986: Measurements with an automatically recording inverted echo sounder; ARIES and the bubble clouds. J. Phys. Oceanogr., 16, 14621478, doi:10.1175/1520-0485(1986)016<1462:MWAARI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1992: Bubble clouds and the dynamics of the upper ocean. Quart. J. Roy. Meteor. Soc., 118, 122, doi:10.1002/qj.49711850302.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., , and A. J. Hall, 1983: The characteristics of breaking waves, bubble clouds, and near-surface currents observed using side-scan sonar. Cont. Shelf Res., 1, 353384, doi:10.1016/0278-4343(83)90003-1.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., , W. A. M. Nimmo Smith, , A. Graham, , and A. M. Thurnherr, 1999: Patterns in foam and shallow tidal flows. The Wind-Driven Air–Sea Interface, M. Banner, Ed., School of Mathematics, University of New South Wales, 257–264.

  • Thorpe, S. A., , T. R. Osborn, , D. M. Farmer, , and S. Vagle, 2003a: Bubble clouds and Langmuir circulation: Observations and models. J. Phys. Oceanogr., 33, 20132031, doi:10.1175/1520-0485(2003)033<2013:BCALCO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., , T. R. Osborn, , J. E. F. Jackson, , A. J. Hall, , and R. G. Lueck, 2003b: Measurements of turbulence in the upper-ocean mixing layer using Autosub. J. Phys. Oceanogr., 33, 122145, doi:10.1175/1520-0485(2003)033<0122:MOTITU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Toba, Y., 1978: Stochastic form of the growth of wind waves in a single-parameter representation with physical implications. J. Phys. Oceanogr., 8, 494507, doi:10.1175/1520-0485(1978)008<0494:SFOTGO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Trevorrow, M. V., 2003: Measurements of near surface bubble plumes in the open ocean with implication for high frequency sonar performance. J. Acoust. Soc. Amer., 114, 26722684, doi:10.1121/1.1621008.

    • Search Google Scholar
    • Export Citation
  • Vagle, S., , and D. M. Farmer, 1992: The measurement of bubble-size distributions by acoustical backscatter. J. Atmos. Oceanic Technol., 9, 630644, doi:10.1175/1520-0426(1992)009<0630:TMOBSD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Vagle, S., , C. McNeil, , and N. Steiner, 2010: Upper ocean bubble measurements from the NE Pacific and estimates of their role in air-sea gas transfer of the weakly soluble gases nitrogen and oxygen. J. Geophys. Res., 115, C12054, doi:10.1029/2009JC005990.

    • Search Google Scholar
    • Export Citation
  • Vagle, S., , J. Gemmrich, , and H. Czerski, 2012: Reduced upper ocean turbulence and changes to bubble size distributions during large downward heat flux events. J. Geophys. Res., 117, C00H16, doi:10.1029/2011JC007308.

    • Search Google Scholar
    • Export Citation
  • Wijesekera, H. W., , J. S. Allen, , and P. A. Newbergerl, 2003: Modeling study of turbulent mixing over the continental shelf: Comparison of turbulent closure schemes. J. Geophys. Res., 108, 3103, doi:10.1029/2001JC001234.

    • Search Google Scholar
    • Export Citation
  • Wijesekera, H. W., , D. W. Wang, , W. J. Teague, , E. Jarosz, , W. E. Rogers, , D. B. Fribance, , and J. N. Moum, 2013: Surface wave effects on high-frequency currents over a shelf edge bank. J. Phys. Oceanogr., 43, 16271647, doi:10.1175/JPO-D-12-0197.1.

    • Search Google Scholar
    • Export Citation
  • Wilson, J. G., , and J. E. Overland, 1986: Meteorology of the northern Gulf of Alaska. The Gulf of Alaska: Physical Environment and Biological Resources, D. W. Hood and S. T. Zimmerman, Eds., DOC/NOAA, 31–54.

  • Zedel, L., , and D. M. Farmer, 1991: Organized structures in subsurface bubble clouds: Langmuir circulation in the open ocean. J. Geophys. Res., 96, 88898900, doi:10.1029/91JC00189.

    • Search Google Scholar
    • Export Citation
Save