Dynamic Balances in a Wavy Boundary Layer

Tihomir Hristov Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland

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Jesus Ruiz-Plancarte Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

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Abstract

The authors analyze the influence of waves on the budgets of momentum flux and kinetic energy in the atmospheric flow over sea surface waves and use the findings to reinterpret the results from the earlier empirical studies on the subject. This analysis employs the framework of wave–mean flow interaction and experimental data collected recently over the open ocean. From a minimal set of plausible assumptions, limited to small-slope waves and uncorrelated turbulent and wave-induced motions in the wind, this study demonstrates that the budgets apply separately to the turbulent and the wave-induced flows. The explicit forms of the wave-supported fluxes of momentum and kinetic energy favor wave spectra ∝ ωβ, 4 ≤ β ≤ 5 for wind–wave equilibrium. These explicit forms also show that in common conditions at heights above one significant wave height from the unperturbed surface, the wave-supported fluxes are a small fraction of the total, of the order of 5%. The wave influence on the kinetic energy budget and on the shape of the wind profile is therefore also small at these heights and thus difficult to identify experimentally next to influences from nonstationarity or horizontal inhomogeneity. Consequently, the predictions of Monin–Obukhov phenomenology show little sensitivity to wave effects. This makes the phenomenology as valid over the ocean as it is over land, but a poor instrument for studying wind–wave interaction. Describing the wind–wave interaction through the dynamics and statistics of the wave-induced motion remains a viable and productive alternative.

Corresponding author address: Tihomir Hristov, Department of Mechanical Engineering, Johns Hopkins University, 3400 North Charles St., Baltimore, MD 21218. E-mail: tihomir.hristov@jhu.edu

Abstract

The authors analyze the influence of waves on the budgets of momentum flux and kinetic energy in the atmospheric flow over sea surface waves and use the findings to reinterpret the results from the earlier empirical studies on the subject. This analysis employs the framework of wave–mean flow interaction and experimental data collected recently over the open ocean. From a minimal set of plausible assumptions, limited to small-slope waves and uncorrelated turbulent and wave-induced motions in the wind, this study demonstrates that the budgets apply separately to the turbulent and the wave-induced flows. The explicit forms of the wave-supported fluxes of momentum and kinetic energy favor wave spectra ∝ ωβ, 4 ≤ β ≤ 5 for wind–wave equilibrium. These explicit forms also show that in common conditions at heights above one significant wave height from the unperturbed surface, the wave-supported fluxes are a small fraction of the total, of the order of 5%. The wave influence on the kinetic energy budget and on the shape of the wind profile is therefore also small at these heights and thus difficult to identify experimentally next to influences from nonstationarity or horizontal inhomogeneity. Consequently, the predictions of Monin–Obukhov phenomenology show little sensitivity to wave effects. This makes the phenomenology as valid over the ocean as it is over land, but a poor instrument for studying wind–wave interaction. Describing the wind–wave interaction through the dynamics and statistics of the wave-induced motion remains a viable and productive alternative.

Corresponding author address: Tihomir Hristov, Department of Mechanical Engineering, Johns Hopkins University, 3400 North Charles St., Baltimore, MD 21218. E-mail: tihomir.hristov@jhu.edu
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  • Berström, H., and A.-S. Smedman, 1995: Stably stratified flow in a marine atmospheric surface layer. Bound.-Layer Meteor., 72, 239265, doi:10.1007/BF00836335.

    • Search Google Scholar
    • Export Citation
  • Charnock, H., 1956: Statistics and aerodynamics of the sea surface. Nature, 177, 6263, doi:10.1038/177062a0.

  • Drazin, P. G., and W. H. Reid, 1981: Hydrodynamic Stability. Cambridge University Press, 525 pp.

  • Drennan, W. M., K. K. Kahma, and M. A. Donelan, 1999: On momentum flux and velocity spectra over waves. Bound.-Layer Meteor., 92, 489515, doi:10.1023/A:1002054820455.

    • Search Google Scholar
    • Export Citation
  • Edson, J. B., and C. W. Fairall, 1998: Similarity relationships in the marine atmospheric surface layer for terms in the TKE and scalar variance budgets. J. Atmos. Sci., 55, 23112328, doi:10.1175/1520-0469(1998)055<2311:SRITMA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Edson, J. B., C. W. Fairall, and P. Sullivan, 2006: Evaluation and continued improvements to the TOGA COARE 3.0 algorithm using CBLAST data. 27th Conf. on Hurricanes and Tropical Meteorology, Monterey, CA, Amer. Meteor. Soc., 7C.1. [Available online at https://ams.confex.com/ams/27Hurricanes/techprogram/paper_108533.htm.]

  • Foken, T., 2006: 50 years of the Monin–Obukhov similarity theory. Bound.-Layer Meteor., 119, 431447, doi:10.1007/s10546-006-9048-6.

    • Search Google Scholar
    • Export Citation
  • Grare, L., L. Lenain, and W. K. Melville, 2013: Wave-coherent airflow and critical layers over ocean waves. J. Phys. Oceanogr., 43, 21562172, doi:10.1175/JPO-D-13-056.1.

    • Search Google Scholar
    • Export Citation
  • Harris, D. L., 1966: The wave-driven wind. J. Atmos. Sci., 23, 688693, doi:10.1175/1520-0469(1966)023<0688:TWDW>2.0.CO;2.

  • Högström, U., A. Rutgersson, E. Sahlée, A.-S. Smedman, T. S. Hristov, W. M. Drennan, and K. K. Kahma, 2013: Air–sea interaction features in the Baltic Sea and at a Pacific trade-wind site: An inter-comparison study. Bound.-Layer Meteor., 147, 139163, doi:10.1007/s10546-012-9776-8.

    • Search Google Scholar
    • Export Citation
  • Hristov, T., S. Miller, and C. Friehe, 2003: Dynamical coupling of wind and ocean waves through wave-induced air flow. Nature, 422, 5558, doi:10.1038/nature01382.

    • Search Google Scholar
    • Export Citation
  • Janssen, P., 1999: On the effect of ocean waves on the kinetic energy balance and consequences for the inertial dissipation technique. J. Phys. Oceanogr., 29, 530534, doi:10.1175/1520-0485(1999)029<0530:OTEOOW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kaimal, J. C., and J. J. Finnigan, 1994: Atmospheric Boundary Layer Flows. Oxford University Press, 289 pp.

  • Lin, C., 1955: The Theory of Hydrodynamic Stability. Cambridge University Press, 155 pp.

  • Miles, J. W., 1957: On the generation of surface waves by shear flows. J. Fluid Mech., 3, 185204, doi:10.1017/S0022112057000567.

  • Miles, J. W., 1959: On the generation of surface waves by shear flows. Part 2. J. Fluid Mech., 6, 568582, doi:10.1017/S0022112059000830.

    • Search Google Scholar
    • Export Citation
  • Newell, A., and B. Rumpf, 2011: Wave turbulence. Annu. Rev. Fluid Mech., 43, 5978, doi:10.1146/annurev-fluid-122109-160807.

  • Panofsky, H. A., 1974: The atmospheric boundary layer below 150 meters. Annu. Rev. Fluid Mech., 6, 147177, doi:10.1146/annurev.fl.06.010174.001051.

    • Search Google Scholar
    • Export Citation
  • Rieder, K., and J. Smith, 1998: Removing wave effects from the wind stress vector. J. Geophys. Res., 103, 13631374, doi:10.1029/97JC02571.

    • Search Google Scholar
    • Export Citation
  • Ruggles, K. W., 1970: The vertical mean wind profile over the ocean for light to moderate winds. J. Appl. Meteor., 9, 389395, doi:10.1175/1520-0450(1970)009<0389:TVMWPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Schacher, G., K. Davidson, and T. Houlihan, 1981: Measurements of the rate of dissipation of turbulent kinetic energy, ε, over the ocean. Bound.-Layer Meteor., 20, 321330, doi:10.1007/BF00121376.

    • Search Google Scholar
    • Export Citation
  • Sjöblom, A., and A.-S. Smedman, 2002: The turbulent kinetic energy budget in the marine atmospheric surface layer. J. Geophys. Res., 107, 3142, doi:10.1029/2001JC001016.

  • Smedman, A.-S., U. Högström, E. Sahleè, W. Drennan, K. Kahma, H. Pettersson, and F. Zhang, 2009: Observational study of marine atmospheric boundary layer characteristics during swell. J. Atmos. Sci., 66, 27472763, doi:10.1175/2009JAS2952.1.

    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., J. C. McWilliams, and E. G. Patton, 2014: Large-eddy simulation of marine atmospheric boundary layers above a spectrum of moving waves. J. Atmos. Sci.,71, 4001–4027, doi:10.1175/JAS-D-14-0095.1.

  • Tennekes, H., and J. L. Lumley, 1972: A First Course in Turbulence. MIT Press, 300 pp.

  • Tollmien, W., 1931: The production of turbulence. National Advisory Committee for Aeronautics Tech. Memo. 609, 32 pp.

  • Van Atta, C. W., and W. Y. Chen, 1970: Structure functions of turbulence in the atmospheric boundary layer over the ocean. J. Fluid Mech., 44, 145159, doi:10.1017/S002211207000174X.

    • Search Google Scholar
    • Export Citation
  • Weiler, H. S., and R. W. Burling, 1967: Direct measurements of stress and spectra of turbulence in the boundary layer over the sea. J. Atmos. Sci., 24, 653664, doi:10.1175/1520-0469(1967)024<0653:DMOSAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wyngaard, J., 1992: Atmospheric turbulence. Annu. Rev. Fluid Mech., 24, 205233, doi:10.1146/annurev.fl.24.010192.001225.

  • Zakharov, V., and N. Filonenko, 1967: Energy spectrum for stochastic oscillations of the surface of a liquid. Sov. Phys. Dokl., 11, 881884.

    • Search Google Scholar
    • Export Citation
  • Zavadsky, A., and L. Shemer, 2012: Characterization of turbulent airflow over evolving water-waves in a wind-wave tank. J. Geophys. Res., 117, C00J19, doi:10.1029/2011JC007790.

    • Search Google Scholar
    • Export Citation
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