Hostname: page-component-84b7d79bbc-g78kv Total loading time: 0 Render date: 2024-07-29T23:15:42.419Z Has data issue: false hasContentIssue false
  • English
  • Français

Observations of mean and wave orbital flows in the ocean’s upper centimetres

Published online by Cambridge University Press:  23 January 2020

Nathan J. M. Laxague Open the ORCID record for Nathan J. M. Laxague [Opens in a new window]  and
Christopher J. Zappa Open the ORCID record for Christopher J. Zappa [Opens in a new window]
Nathan J. M. Laxague*
Affiliation:
Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY 10964, USA
Christopher J. Zappa
Affiliation:
Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY 10964, USA
*
†Email address for correspondence: laxague@ldeo.columbia.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Sophisticated measurements of fluid velocity near to an undulating air–water boundary have traditionally been confined to the laboratory setting. Developments in camera technology and the opening of novel modes of analysis have allowed for sensitive measurements of the current profile in the ocean’s uppermost layer. Taking advantage of the Research Platform R/P FLIP as a ‘laboratory at sea’, here we present first-of-their-kind thermal and polarimetric camera-based observations of wave orbital velocities and mean shear flows in the upper centimetres of the ocean surface layer. Measurements reveal a well-defined logarithmic layer as seen in laboratory measurements and described by classical surface layer theory; however, substantial spread of observations is found at low levels of wind forcing, where the Stokes drift of swell may have a substantial impact on the near-surface current profile. A novel application of short time window Fourier transforms allows for the estimation of near-surface wave orbital velocity magnitudes. These are found to be in general agreement with the prescriptions of linear wave theory, although observations diverge from theory at high levels of wind forcing where the interface is subject to surface wave breaking. Finally, the surface gravity wave phase-coherent short wave growth is presented and discussed in the context of hydrodynamic wave and airflow modulation.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 887 , 25 March 2020 , A10
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alpers, W. & Rufenach, C. 1979 The effect of orbital motions on synthetic aperture radar imagery of ocean waves. IEEE Trans. Antennas Propag. 27 (5), 685–690.CrossRefGoogle Scholar
Anctil, F., Donelan, M. A., Drennan, W. M. & Graber, H. C. 1994 Eddy-correlation measurements of air–sea fluxes from a discus buoy. J. Atmos. Ocean. Technol. 11 (4), 1144–1150.2.0.CO;2>CrossRefGoogle Scholar
Ardhuin, F., Marié, L., Rascle, N., Forget, P. & Roland, A. 2009 Observation and estimation of Lagrangian, Stokes, and Eulerian currents induced by wind and waves at the sea surface. J. Phys. Oceanogr. 39 (11), 2820–2838.CrossRefGoogle Scholar
Banner, M. L. & Melville, W. K. 1976 On the separation of air flow over water waves. J. Fluid Mech. 77 (4), 825–842.CrossRefGoogle Scholar
Banner, M. L. & Peirson, W. L. 1998 Tangential stress beneath wind-driven air–water interfaces. J. Fluid Mech. 364, 115–145.CrossRefGoogle Scholar
Benilov, Y. A., Kouznetsov, O. A. & Panin, G. N. 1974 On the analysis of wind wave-induced disturbances in the atmospheric turbulent surface layer. Boundary-Layer Meteorol. 6, 269–285.CrossRefGoogle Scholar
Bourassa, M. A. 2000 Shear stress model for the aqueous boundary layer near the air–sea interface. J. Geophys. Res. Oceans 105 (C1), 1167–1176.CrossRefGoogle Scholar
Bowden, K. F. 1953 Note on wind drift in a channel in the presence of tidal currents. Proc. R. Soc. Lond. A 219 (1139), 426–446.Google Scholar
Bowden, K. F. & White, R. A. 1966 Measurements of the orbital velocities of sea waves and their use in determining the directional spectrum. Geophys. J. Intl 12 (1), 33–54.CrossRefGoogle Scholar
Breivik, Ø., Janssen, P. A. E. M. & Bidlot, J.-R. 2014 Approximate Stokes drift profiles in deep water. J. Phys. Oceanogr. 44 (9), 2433–2445.CrossRefGoogle Scholar
Brumer, S. E., Zappa, C. J., Anderson, S. P. & Dugan, J. P. 2016 Riverine skin temperature response to subsurface processes in low wind speeds. J. Geophys. Res. 121 (3), 1721–1735.CrossRefGoogle Scholar
Brunner, K., Kukulka, T., Proskurowski, G. & Law, K. L. 2015 Passive buoyant tracers in the ocean surface boundary layer: 2. Observations and simulations of microplastic marine debris. J. Geophys. Res. 120 (11), 7559–7573.CrossRefGoogle Scholar
Buckley, M. P. & Veron, F. 2016 Structure of the airflow above surface waves. J. Phys. Oceanogr. 46 (5), 1377–1397.CrossRefGoogle Scholar
Buckley, M. P. & Veron, F. 2017 Airflow measurements at a wavy air–water interface using PIV and LIF. Exp. Fluids 58 (11), 161.CrossRefGoogle Scholar
Buckley, M. P. & Veron, F. 2019 The turbulent airflow over wind generated surface waves. Eur. J. Mech. (B/Fluids) 73, 132–143.CrossRefGoogle Scholar
Bye, J. A. T. 1965 Wind-driven circulation in unstratified lakes. Limnol. Oceanogr. 10 (3), 451–458.CrossRefGoogle Scholar
Cheung, T. K. & Street, R. L. 1988 The turbulent layer in the water at an air–water interface. J. Fluid Mech. 194, 133–151.CrossRefGoogle Scholar
Churchill, J. H. & Csanady, G. T. 1983 Near-surface measurements of quasi-Lagrangian velocities in open water. J. Phys. Oceanogr. 13 (9), 1669–1680.2.0.CO;2>CrossRefGoogle Scholar
Churchill, J. H. & Pade, B. H.-G. 1980 Measurement of Near-surface Current in Cape Cod Bay Using Sighted Drogues. Woods Hole Oceanographic Institution.CrossRefGoogle Scholar
Craik, A. D. D. 2004 The origins of water wave theory. Annu. Rev. Fluid Mech. 36 (1), 1–28.CrossRefGoogle Scholar
Curcic, M., Chen, S. S. & Özgökmen, T. M. 2016 Hurricane-induced ocean waves and Stokes drift and their impacts on surface transport and dispersion in the Gulf of Mexico. Geophys. Res. Lett. 43 (6), 2773–2781.CrossRefGoogle Scholar
DiBenedetto, M. H., Ouellette, N. T. & Koseff, J. R. 2018 Transport of anisotropic particles under waves. J. Fluid Mech. 837, 320–340.CrossRefGoogle Scholar
Drennan, W. M., Kahma, K. K. & Donelan, M. A. 1999 On momentum flux and velocity spectra over waves. Boundary-Layer Meteorol. 92 (3), 489–515.CrossRefGoogle Scholar
Dugan, J. P. & Piotrowski, C. C. 2012 Measuring currents in a coastal inlet by advection of turbulent eddies in airborne optical imagery. J. Geophys. Res. 117, C03020.CrossRefGoogle Scholar
Durst, C. S. 1924 The relationship between current and wind. Q. J. R. Meteorol. Soc. 50 (210), 113–119.CrossRefGoogle Scholar
Edson, J. B., Hinton, A. A., Prada, K. E., Hare, J. E. & Fairall, C. W. 1998 Direct covariance flux estimates from mobile platforms at sea. J. Atmos. Ocean. Technol. 15 (1991), 547–562.2.0.CO;2>CrossRefGoogle Scholar
Falkovich, G. 2009 Could waves mix the ocean? J. Fluid Mech. 638, 1–4.CrossRefGoogle Scholar
Goldstein, H. 1950 Classical Mechanics. Addison-Wesley.Google Scholar
Hao, X. & Shen, L. 2019 Wind–wave coupling study using LES of wind and phase-resolved simulation of nonlinear waves. J. Fluid Mech. 874, 391–425.CrossRefGoogle Scholar
Hara, T. & Plant, W. J. 1994 Hydrodynamic modulation of short wind–wave spectra by long waves and its measurement using microwave backscatter. J. Geophys. Res. 99 (C5), 9767–9784.CrossRefGoogle Scholar
Herbers, T. H. C., Lowe, R. L. & Guza, R. T. 1992 Field observations of orbital velocities and pressure in weakly nonlinear surface gravity waves. J. Fluid Mech. 245, 413–435.CrossRefGoogle Scholar
Isobe, A., Kubo, K., Tamura, Y., Kako, I., Nakashima, E. & Fujii, N. 2014 Selective transport of microplastics and mesoplastics by drifting in coastal waters. Mar. Pollut. Bull. 89, 324–330.CrossRefGoogle ScholarPubMed
von Kármán, T. 1939 The analogy between fluid friction and heat transfer. Trans. Am. Soc. Mech. Eng. 61, 705–710.Google Scholar
Larson, T. R. & Wright, J. W. 1975 Wind-generated gravity-capillary waves: laboratory measurement of temporal growth rates using microwave backscatter. J. Fluid Mech. 70, 417–436.CrossRefGoogle Scholar
Laxague, N. J. M., Haus, B. K., Ortiz-Suslow, D. G., Smith, C. J., Novelli, G., Dai, H., Özgökmen, T. M. & Graber, H. C. 2017 Passive optical sensing of the near-surface wind-driven current profile. J. Atmos. Ocean. Technol. 34 (5), 1097–1111.CrossRefGoogle Scholar
Laxague, N. J. M., Özgökmen, T. M., Haus, B. K., Novelli, G., Shcherbina, A. Y., Sutherland, P., Guigand, C. M., Lund, B., Mehta, S., Alday, M. et al. 2018a Observations of near-surface current shear help describe oceanic oil and plastic transport. Geophys. Res. Lett. 45 (1), 245–249.CrossRefGoogle Scholar
Laxague, N. J. M., Zappa, C. J., LeBel, D. A. & Banner, M. L. 2018b Spectral characteristics of gravity-capillary waves, with connections to wave growth and microbreaking. J. Geophys. Res. Oceans 123 (7), 4576–4592.CrossRefGoogle Scholar
Le Hénaff, M., Kourafalou, V. H., Paris, C. B., Helgers, J., Aman, Z. M., Hogan, P. J. & Srinivasan, A. 2012 Surface evolution of the deepwater horizon oil spill patch: combined effects of circulation and wind-induced drift. Environ. Sci. Technol. 46 (13), 7267–7273.CrossRefGoogle ScholarPubMed
Leckler, F., Ardhuin, F., Peureux, C., Benetazzo, A., Bergamasco, F. & Dulov, V. A. 2015 Analysis and interpretation of frequency-wavenumber spectra of young wind waves. J. Phys. Oceanogr. 45 (10), 2484–2496.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245 (903), 535–581.CrossRefGoogle Scholar
Lund, B., Graber, H. C., Tamura, H., Collins, C. O. & Varlamov, S. M. 2015 A new technique for the retrieval of near-surface vertical current shear from marine X-band radar images. J. Geophys. Res. 120 (12), 8466–8486.CrossRefGoogle Scholar
Lund, B., Haus, B. K., Horstmann, J., Graber, H. C., Carrasco, R., Laxague, N. J. M., Novelli, G., Guigand, C. M. & Özgökmen, T. M. 2018 Near-surface current mapping by shipboard marine X-band radar: a validation. J. Atmos. Ocean. Technol. 35 (5), 1077–1090.CrossRefGoogle Scholar
Mcleish, W. & Putland, G. E. 1975 Measurements of wind-driven flow profiles in the top millimeter of water. J. Phys. Oceanogr. 5 (3), 516–518.2.0.CO;2>CrossRefGoogle Scholar
Melville, W. K. 1996 The role of wave breaking in air–sea interaction. Annu. Rev. Fluid Mech. 28 (1), 279–321.CrossRefGoogle Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3 (2), 185–204.CrossRefGoogle Scholar
Miles, J. W. 1959 On the generation of surface waves by shear flows. Part 2. J. Fluid Mech. 6 (4), 568–582.CrossRefGoogle Scholar
Morey, S. L., Wienders, N., Dukhovskoy, D. & Bourassa, M. A. 2018 Measurement characteristics of near-surface currents from ultra-thin drifters, drogued drifters, and HF radar. Remote Sensing 10 (10), 1633.CrossRefGoogle Scholar
Morlet, J., Arens, G., Fourgeau, E. & Giard, D. 1982 Wave propagation and sampling theory. Part I. Complex signal and scattering in multilayered media. Geophysics 47 (2), 203–221.CrossRefGoogle Scholar
Nystrom, E. A., Oberg, K. A. & Rehmann, C. R.2002 Measurement of turbulence with acoustic doppler current profilers – sources of error and laboratory results. In Annual Conference Proceedings. Hydraulic Measurements and Experimental Methods, pp. 1–10.Google Scholar
Okuda, K., Kawai, S. & Toba, Y. 1977 Measurement of skin friction distribution along the surface of wind waves. J. Oceanogr. Soc. Japan 33 (4), 190–198.CrossRefGoogle Scholar
Peirson, W. L. 1997 Measurement of surface velocities and shears at a wavy air–water interface using particle image velocimetry. Exp. Fluids 23 (5), 427–437.CrossRefGoogle Scholar
Peirson, W. L. & Banner, M. L. 2003 Aqueous surface layer flows induced by microscale breaking wind waves. J. Fluid Mech. 479, 1–38.CrossRefGoogle Scholar
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2 (5), 417–445.CrossRefGoogle Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.Google Scholar
Pizzo, N., Melville, W. K. & Deike, L. 2019 Lagrangian transport by nonbreaking and breaking deep-water waves at the ocean surface. J. Phys. Oceanogr. 49 (4), 983–992.CrossRefGoogle Scholar
Plant, W. J. 1982 A relationship between wind stress and wave slope. J. Geophys. Res. 87 (C3), 1961–1967.CrossRefGoogle Scholar
Plant, W. J. 1989 The modulation transfer function: concept and applications. In Radar Scattering from Modulated Wind Waves, pp. 155–172. Springer.CrossRefGoogle Scholar
Plant, W. J. 2009 The ocean wave height variance spectrum: wavenumber peak versus frequency peak. J. Phys. Oceanogr. 39 (9), 2382–2383.CrossRefGoogle Scholar
Plant, W. J., Keller, W. C., Hesany, V., Kara, T., Bock, E. J. & Donelan, M. A. 1999 Bound waves and Bragg scattering in a wind–wave tank. J. Geophys. Res. 104 (C2), 3243–3263.CrossRefGoogle Scholar
Plant, W. J. & Wright, J. W. 1977 Growth and equilibrium of short gravity waves in a wind–wave tank. J. Fluid Mech. 82 (4), 767–793.CrossRefGoogle Scholar
Plant, W. J. & Wright, J. W. 1980 Phase speeds of upwind and downwind traveling short gravity waves. J. Geophys. Res. 85 (C6), 3304–3310.CrossRefGoogle Scholar
Prandtl, L. 1910 Eine Beziehung zwischen Wiirmeaustausch und Stromungswiderstand der Fliissigkeit. Z. Phys. 11, 1072–1078.Google Scholar
Rodríguez, E., Wineteer, A., Perkovic-Martin, D., Gál, T., Stiles, B. W., Niamsuwan, N. & Rodriguez Monje, R. 2018 Estimating ocean vector winds and currents using a Ka-band pencil-beam doppler scatterometer. Remote Sensing 10 (4), 576.CrossRefGoogle Scholar
Romeiser, R., Suchandt, S., Runge, H., Steinbrecher, U. & Grunler, S. 2010 First analysis of TerraSAR-X Along-Track InSAR-Derived current fields. IEEE Trans. Geosci. Remote Sens. 48 (2), 820–829.CrossRefGoogle Scholar
Senet, C. M., Seemann, J. & Ziemer, F. 2001 The near-surface current velocity determined from image sequences of the sea surface. IEEE Trans. Geosci. Remote Sens. 39 (3), 492–505.CrossRefGoogle Scholar
Siddiqui, M. H. K. & Loewen, M. R. 2007 Characteristics of the wind drift layer and microscale breaking waves. J. Fluid Mech. 573, 417–456.CrossRefGoogle Scholar
Siddiqui, M. H. K. & Loewen, M. R. 2010 Phase-averaged flow properties beneath microscale breaking waves. Boundary-Layer Meteorol. 134 (3), 499–523.CrossRefGoogle Scholar
Spalding, D. B. 1961 A single formula for the law of the wall. J. Appl. Mech. 28 (3), 455.CrossRefGoogle Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441–473.Google Scholar
Stommel, H. 1954 Serial observations of drift currents in the Central North Atlantic Ocean. Tellus 6 (3), 203–214.CrossRefGoogle Scholar
Streßer, M., Carrasco, R. & Horstmann, J. 2017 Video-based estimation of surface currents using a low-cost quadcopter. IEEE Geosci. Remote Sensing Lett. 14 (11), 2027–2031.CrossRefGoogle Scholar
Sullivan, P. P., Banner, M. L., Morison, R. P. & Peirson, W. L. 2017 Turbulent flow over steep steady and unsteady waves under strong wind forcing. J. Phys. Oceanogr. 48 (1), 3–27.CrossRefGoogle Scholar
Sullivan, P. P. & McWilliams, J. C. 2010 Dynamics of winds and currents coupled to surface waves. Annu. Rev. Fluid Mech. 42 (1), 19–42.CrossRefGoogle Scholar
Taylor, G. I. 1916 Conditions at the surface of a hot body exposed to the wind. British Aeronautical Research Communications 272, 423.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164 (919), 476–490.CrossRefGoogle Scholar
Teixeira, M. A. C. 2018 A model for the wind-driven current in the wavy oceanic surface layer: apparent friction velocity reduction and roughness length enhancement. J. Phys. Oceanogr. 48 (11), 2721–2736.CrossRefGoogle Scholar
Thornton, E. B. & Krapohl, R. F. 1974 Water particle velocities measured under ocean waves. J. Geophys. Res. 79 (6), 847–852.CrossRefGoogle Scholar
Veron, F., Saxena, G. & Misra, S. K. 2007 Measurements of the viscous tangential stress in the airflow above wind waves. Geophys. Res. Lett. 34 (19), L19603.CrossRefGoogle Scholar
Vollestad, P., Ayati, A. A. & Jensen, A. 2019 Microscale wave breaking in stratified air–water pipe flow. Phys. Fluids 31 (3), 032101.CrossRefGoogle Scholar
Webb, A. & Fox-Kemper, B. 2011 Wave spectral moments and Stokes drift estimation. Ocean Model. 40 (3–4), 273–288.CrossRefGoogle Scholar
Webb, A. & Fox-Kemper, B. 2015 Impacts of wave spreading and multidirectional waves on estimating Stokes drift. Ocean Model. 96, 49–64.CrossRefGoogle Scholar
Wu, J. 1975 Wind-induced drift currents. J. Fluid Mech. 68 (01), 49–70.CrossRefGoogle Scholar
Yang, D., Meneveau, C. & Shen, L. 2013 Dynamic modelling of sea-surface roughness for large-eddy simulation of wind over ocean wavefield. J. Fluid Mech. 726, 62–99.CrossRefGoogle Scholar
Zappa, C. J., Asher, W. E. & Jessup, A. T. 2001 Microscale wave breaking and air–water gas transfer. J. Geophys. Res. 106 (2000), 9385–9391.CrossRefGoogle Scholar
Zappa, C. J., Asher, W. E., Jessup, A. T., Klinke, J. & Long, S. R. 2004 Microbreaking and the enhancement of air–water transfer velocity. J. Geophys. Res. Oceans 109 (C8), doi:10.1029/2003JC001897.CrossRefGoogle Scholar
Zappa, C. J., Banner, M. L., Schultz, H., Corrada-Emmanuel, A., Wolff, L. B. & Yalcin, J. 2008 Retrieval of short ocean wave slope using polarimetric imaging. Meas. Sci. Technol. 19 (5), 055503.CrossRefGoogle Scholar
Zappa, C. J., Banner, M. L., Schultz, H., Gemmrich, J. R., Morison, R. P., Lebel, D. A. & Dickey, T. 2012 An overview of sea state conditions and air–sea fluxes during RaDyO. J. Geophys. Res. 117 (C7), doi:10.1029/2011JC007336.CrossRefGoogle Scholar