Abstract
Results of field measurements of the swell-induced undulation of the wind speed taken from a Black Sea platform are presented. The wind speed and its fluctuations were measured at several heights between 1.3 and 21 m above the mean sea level under various wind and swell conditions. Parameters of the swell-induced undulations were derived from cross spectra of the wind-speed fluctuations and the sea-surface displacement. As found, the phase and the amplitude of the wind speed undulation in the layer from k p z = 0.1 to k p z = 3 (k p is the swell wavenumber) are in good agreement with the theory of inviscid shear flow over a wavy surface. The main feature of the vertical profile of the swell-induced undulation is the exponential attenuation of its amplitude with height typical for the potential flow over the fast running waves. At the lowest levels the potential undulations are significantly distorted by the wind-speed variations caused by the vertical displacements of the shear airflow relative to a fixed sensor. No direct impact of swell on the mean properties of the turbulent boundary layer at k p z > 0.1 is revealed. In particular, the mean wind-speed profile and spectra of the horizontal velocity in the inertial subrange obey Monin-Obukhov similarity theory.
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References
Ardhuin F, Chapron B, Collard F (2009) Observation of swell dissipation across oceans. Geophys Res Lett 36: L06607. doi:10.1029/2008GL037030
Babanin AV, Makin VK (2008) Effects of wind trend and gustiness on the sea drag: lake George study. J Geophys Res 113: C02015. doi:10.1029/2007JC004233
Babanin AV, Soloviev YuP (1987) Parameterization of the width of angular distribution of the wind wave energy at limited fetches. Izv Atmos Ocean Phys 23: 645–651
Belcher SE, Hunt JCR (1993) Turbulent shear flow over slowly moving waves. J Fluid Mech 251: 109–148
Britter ML, Hunt JCR, Mumford J (1979) The distortion of turbulence by a circular cylinder. J Fluid Mech 92: 269–301
Capon J (1969) High-resolution frequency-wavenumber spectrum analysis. Proc IEEE 57: 1408–1418
Davidson KL, Frank AK (1973) Wave-related fluctuations in the airflow above natural waves. Phys Oceanogr 3: 102–119
Donelan MA, Drennan WM, Katsaros KB (1997) The air-sea momentum flux in conditions of wind sea and swell. Phys Oceanogr 27: 2087–2098
Drennan WM, Kahma KK, Donelan MA (1999) On momentum flux and velocity spectra over waves. Boundary-Layer Meteorol 92: 489–515
Dupuis H, Guerin C, Hauzer D, Weill A, Nacass P, Drennan WM, Closhé S, Graber HC (2003) Impact of the flow distortion corrections on turbulent fluxes estimated by the inertial dissipation method during the FETCH experiment on R/V L’Atalante. J Geophys Res 108: 8064. doi:10.1029/2001JC001075
Dyer AJ (1974) A review of flux-profile relationships. Boundary-Layer Meteorol 7: 363–372
Edson JB, Fairall CW (1998) Similarity relationships in the marine atmospheric surface layer for terms in the TKE and scalar variance budgets. J Atmos Sci 55: 2311–2328
Edson JB, Fairall CW, Sullivan PP (2007) The coupled boundary layers and air-sea transfer experiment in low winds. Bull Am Meteorol Soc 88: 571–591
Garratt JR (1972) Studies of turbulence in the surface layer over water (Lough Neagh). Part II: Production and dissipation of velocity and temperature fluctuations. Q J Roy Meteorol Soc 98: 642–657
Geernaert GL, Hansen F, Courtney M, Herbers T (1993) Directional attributes of the ocean surface wind stress vector. J Geophys Res 98: 16571–16582
Grachev AA, Fairall CW (2001) Upward momentum transfer in the marine boundary layer. Phys Oceanogr 31: 1698–1711
Grachev AA, Fairall CW, Hare JE, Edson JB, Miller SD (2003) Wind stress vector over ocean waves. Phys Oceanogr 33: 2408–2429
Guo-Larsen XV, Makin VK, Smedman A-S (2003) Impact of waves on the sea drag: measurement in the Baltic Sea and a model interpretation. Glob Atmos Ocean Syst 9: 97–120
Hanley KE, Belcher SE (2008) Wave-driven wind jets in the marine atmospheric boundary layer. J Atmos Sci 65: 2646–2660
Harris DL (1966) The wave-driven wind. J Atmos Sci 23: 688–693
Hristov TS, Miller SD, Friehe CA (2003) Dynamical coupling of wind and ocean waves through wave-induced air flow. Nature 422: 55–58
Hsu CT, Hsu Y (1983) On the structure of turbulent flow over a progressive water wave: theory and experiment in a transformed, wave-following coordinate system. Part 2. J Fluid Mech 131: 123–153
Jenkins GM, Watts DG (1972) Spectral analysis and its applications. Part 2, Russian edn. Mir Publishers, USSR, 287 pp
Kaimal JC, Wyngaard JC, Izumi Y, Coté OR (1972) Spectral characteristics of surface-layer turbulence. Q J Roy Meteorol Soc 98: 563–589
Kitaigorodskii SA (1970) The physics of atmosphere and ocean interaction. Gidrometeoizdat, USSR, Leningrad, 284 pp
Kondo J, Fujinava Y, Naito G (1972) Wave-induced wind fluctuation over the sea. J Fluid Mech 51(part 4): 751–771
Kudryavtsev VN, Makin VK (2004) Impact of swell on the marine atmospheric boundary layer. Phys Oceanogr 34: 934–949
Kudryavtsev VN, Makin VK, Meirink JF (2001) Simplified model of the air flow above waves. Boundary-Layer Meteorol 100: 63–90
Large WG, Pond S (1981) Open ocean momentum flux measurements in moderate to strong winds. Phys Oceanogr 11: 324–336
Mastenbroek C, Makin VK, Garat MH, Giovanangeli JP (1996) Experimental evidence of the rapid distortion of turbulence in the air flow over water waves. J Fluid Mech 318: 273–302
Miles JW (1957) On the generation of surface waves by shear flow. J Fluid Mech 3: 185–204
Miller SD (1999) The structure of turbulent and wave-induced wind fields over open-ocean waves. PhD thesis, University of California, Irvine, 221 pp
Moat BI, Yelland MJ, Pascal RW (2006) Quantifying the airflow distortion over merchant ships. Part 1: Validation of a CFD model. J Atmos Oceanic Technol 23: 341–350
Pan J, Wang DW, Hwang PA (2005) A study of wave effects on wind stress over the ocean in a fetch-limited case. J Geophys Res 110: C02020. doi:10.1029/2003JC002258
Paulson CA (1970) Representation of wind speed and temperature profiles in the unstable atmospheric surface layer. J Appl Meteorol 9: 857–861
Rieder KF, Smith JA, Weller RA (1994) Observed directional characteristics of the wind, wind stress and surface waves on the open ocean. J Geophys Res 99: 22589–22596
Rutgersson A, Smedman AS, Högström U (2001) Use of conventional stability parameters during swell. J Geophys Res 106: 21117–21134
Smedman A-S, Högström U, Bergström H, Rutgersson A, Kahma KK, Pettersson H (1999) A case study of air-sea interaction during swell conditions. J Geophys Res 106: 25833–25851
Smith SD (1980) Wind stress and heat flux over the ocean in gale force winds. Phys Oceanogr 10: 709–726
Soloviev YuP, Ivanov VA (2007) Preliminary results of measurements of atmospheric turbulence over the sea. Phys Oceanogr 17: 154–172
Soloviev YuP, Korovushkin AI, Toloknov YuN (2004) Characteristics of a cup anemometer and a procedure of measuring the wind velocity. Phys Oceanogr 14: 173–186
Sullivan PP, Edson JB, Hristov T, McWilliams JC (2008) Large-eddy simulations and observations of atmospheric marine boundary layers above nonequilibrium surface waves. J Atmos Sci 65: 1225–1245
Volkov YuA (1969) The spectra of velocity and temperature fluctuations in air flow above the agitated sea-surface. Izv Atmos Ocean Phys 5: 723–730
Volkov YuA (1970) Turbulent flux of momentum and heat in the atmospheric surface layer over a disturbed sea-surface. Izv Atmos Ocean Phys 6: 770–774
Yefimov VV, Sizov AA (1969) Experimental research of the field of wind velocity over waves. Izv Atmos Ocean Phys 5: 930–942
Yelland MJ, Taylor PK (1996) Wind stress measurements from the open ocean. Phys Oceanogr 26: 541–558
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Soloviev, Y.P., Kudryavtsev, V.N. Wind-Speed Undulations Over Swell: Field Experiment and Interpretation. Boundary-Layer Meteorol 136, 341–363 (2010). https://doi.org/10.1007/s10546-010-9506-z
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DOI: https://doi.org/10.1007/s10546-010-9506-z