Skip to main content
SpringerLink
Log in

On momentum flux and velocity spectra over waves

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

Data from a research tower in Lake Ontario are used to study the validity of Monin--Obukhov scaling in the marine atmospheric boundary layer under various wave conditions. It is found that over pure wind seas, the velocity spectra and cospectra follow established universal scaling laws. However, in the presence of swells outrunning weak winds, velocity spectra and cospectra no longer satisfy universal spectral shapes. Here, Monin–Obukhov similarity theory, and the classical logarithmic boundary layers, are no longer valid. It is further shown that, in the presence of such swells, the momentum flux can be significantly modified in comparison to pure wind sea values. The implications of these findings for bulk flux estimations and on the inertial dissipation method for calculating fluxes are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Busch, N. E.: 1973, 'On the Mechanics of Atmospheric Turbulence', in D. A. Haugen (ed.), Workshop on Micrometeorology, Amer. Meteorol. Soc., pp. 1–65.

  • Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, 'Flux-Profile Relationships in the Atmosphere Surface Layer', J. Atmos. Sci. 28, 181–189.

    Google Scholar 

  • Capon, J.: 1969, 'High-Resolution Frequency-Wavenumber Spectrum Analysis', Proc. IEEE 57, 1408–1418.

    Google Scholar 

  • Charnock, H.: 1955, 'Wind Stress on a Water Surface', Quart. J. Roy. Meteorol. Soc. 81, 639–640.

    Google Scholar 

  • Dobson, F. W., Smith, S. D., and Anderson, R. J.: 1994, 'Measuring the Relationship Between Wind Stress and Sea State in the Open Ocean in the Presence of Swell', Atmos-Ocean 32, 237–256.

    Google Scholar 

  • Donelan, M. A.: 1990, 'Air-Sea Interaction', in B. LeMéhauté and D. Hanes (eds.), The Sea: Ocean Engineering Science, Vol. 9, John Wiley and Sons, Inc., New York, pp. 239–292.

    Google Scholar 

  • Donelan, M. A., Birch, K. N., and Beesley, D. C.: 1974, 'Generalized Profiles of Wind Speed, Temperature and Humidity', in Proc. 17th conf. Great Lakes Res., pp. 369–388.

  • Donelan, M. A., Dobson, F.W., Smith, S. D., and Anderson, R. J.: 1993, 'On the Dependence of Sea Surface Roughness on Wave Development', J. Phys. Oceanog. 23, 2143–2149.

    Google Scholar 

  • Donelan, M. A., Drennan, W. M., and Katsaros, K. B.: 1997, 'The Air-Sea Momentum Flux in Conditions of Mixed Wind Sea and Swell', J. Phys. Oceanog. 27, 2087–2099.

    Google Scholar 

  • Donelan, M. A., Hamilton, J., and Hui, W. H.: 1985, 'Directional Spectra of Wind Generated Waves', Phil. Trans. Roy. Soc. London A315, 509–562.

    Google Scholar 

  • Donelan, M. A., Madsen, N., Kahma, K. K., Tsanis, I. K., and Drennan, W. M.: 1999, 'Apparatus for Atmospheric Boundary Layer Measurements over Waves', J. Atmos. Oceanic Tech. in press.

  • Donelan, M. A. and Motycka, J.: 1978, 'Miniature Drag Sphere Velocity Probe', Rev. Sci. Instrum. 49, 298–304.

    Google Scholar 

  • Drennan, W. M., Graber, H. C., and Donelan, M. A.: 1999, 'Evidence for the Effects of Swell and Unsteady Winds on Marine Wind Stress', J. Phys. Oceanog. 29, 1853–1864.

    Google Scholar 

  • Dyer, A. J. and Hicks, B. B.: 1970, 'Flux-Gradient Relationships in the Constant Flux Layer', Quart. J. Roy. Meteorol. Soc. 96, 715–721.

    Google Scholar 

  • Edson, J. B. and Fairall, C. W.: 1998, 'Similarity Relationships in the Marine Atmospheric Surface Layer for Terms in the TKE and Scalar Variance Budgets', J. Atmos. Sci. 55, 2311–2328.

    Google Scholar 

  • Edson, J. B., Fairall, C. W., Mestayer, P. G., and Larsen, S. E.: 1991, 'A Study of the Inertial-Dissipation Method for Computing Air-Sea Fluxes', J. Geophys. Res. 96, 10,689–10,711.

    Google Scholar 

  • Geernaert, G. L., Hansen, F., Courtney, M., and Herbers, T.: 1993, 'Directional Attributes of the Ocean Surface Wind Stress Vector', J. Geophys. Res. 98, 16,571–16,582.

    Google Scholar 

  • Geernaert, G. L., Katsaros, K. B., and Richter, K.: 1986, 'Variations of the Drag Coefficient and its Dependence on Sea State', J. Geophys. Res. 91, 7,667–7,679.

    Google Scholar 

  • Hicks, B. B.: 1972, 'Propeller Anemometers as Sensors of Atmospheric Turbulence', Boundary-Layer Meteorol. 3, 214–228.

    Google Scholar 

  • Högström, U.: 1996, 'Review of Some Basic Characteristics of the Atmospheric Surface Layer', Boundary-Layer Meteorol. 78, 215–246.

    Google Scholar 

  • Holland, J. Z., Chen, W., Almazan, J. A., and Elder, F. C.: 1981, 'Atmospheric Boundary Layer', in E. J. Aubert and T. L. Richards (eds.), IFYGL — The International Field Year for the Great Lakes, NOAA, Ann Arbor, pp. 109–167.

    Google Scholar 

  • Janssen, P. A. E. M.: 1989, 'Wave-Induced Stress and the Drag of Air Flow over Sea Waves', J. Phys. Oceanog. 19, 745–754.

    Google Scholar 

  • Kaimal, J. C., Wyngaard, J. C., Izumi, Y., and Coté, O. R.: 1972, 'Spectral Characteristics of Surface-Layer Turbulence', Quart. J. Roy. Meteorol. Soc. 98, 563–589.

    Google Scholar 

  • Kitaigorodskii, S. A. and Volkov, Y. A.: 1965, 'On the Roughness Parameter of the Sea Surface and the Calculation of Momentum Flux in the Near-Water Layer of the Atmosphere', Izv., Atmos. Oceanic Phys. 1, 973–988.

    Google Scholar 

  • Large, W. G. and Pond, S.: 1981, 'Open Ocean Momentum Flux Measurements in Moderate to Strong Winds', J. Phys. Oceanog. 11, 324–336.

    Google Scholar 

  • MacCready, P. B. and Jex, H. R.: 1964, 'Response Characteristics and Meteorological Utilization of Propeller and Vane Wind Sensors', J. Appl. Meteorol. 3, 182–193.

    Google Scholar 

  • Makin, V. K. and Mastenbroek, C.: 1996, 'Impact of Waves on Air-Sea Exchange of Sensible Heat and Momentum', Boundary-Layer Meteorol. 79, 279–300.

    Google Scholar 

  • Miyake, M., Stewart, R. W., and Burling, R. W.: 1970, 'Spectra and Cospectra of Turbulence over Water', Quart. J. Roy. Meteorol. Soc. 96, 138–143.

    Google Scholar 

  • Monin, A. S., and Obukhov, A. M.: 1954, 'Basic Laws of Turbulent Mixing in the Ground Layer of the Atmosphere', Akad. Nauk. SSSR Geofiz. Inst. Tr. 151, 163–187.

    Google Scholar 

  • Obukhov, A. M.: 1946, 'Turbulence in an Atmosphere with a Non-Uniform Temperature', Boundary-Layer Meteorol. 2, 7–29.

    Google Scholar 

  • Rieder, K. F.: 1997, 'Analysis of Sea-Surface Drag Parameterizations in Open Ocean Conditions', Boundary-Layer Meteorol. 82, 355–377.

    Google Scholar 

  • Rieder, K. F. and Smith, J. A.: 1998, 'Removing Wave Effects from the Wind Stress Vector', J. Geophys. Res. 103, 1363–1374.

    Google Scholar 

  • Rieder, K. F., Smith, J. A., and Weller, R. A.: 1994, 'Observed Directional Characteristics of the Wind,Wind Stress and Surface Waves on the Open Ocean', J. Geophys. Res. 99, 22,589–22,596.

    Google Scholar 

  • Smedman, A. S., Högström, U., Bergström, H., Rutgersson, A., Kahma, K. K., and Pettersson, H.: 1999, 'A Case Study of Air-Sea Interaction during Swell Conditions', J. Geophys. Res., in press.

  • Smedman, A. S., Tjernström, M., and Högström, U.: 1994, 'The Near-Neutral Marine Atmospheric Boundary Layer with No Surface Shearing Stress: A Case Study', J. Atmos. Sci. 51, 3,399–3,411.

    Google Scholar 

  • Smith, S. D.: 1980, 'Wind Stress and Heat Flux over the Ocean in Gale Force Winds', J. Phys. Oceanog. 10, 709–726.

    Google Scholar 

  • Smith, S. D. and Anderson, R. J.: 1984, 'Spectra of Humidity, Temperature and Wind over the Sea at Sable Island, Nova Scotia', J. Geophys. Res. 89, 2,029–2,040.

    Google Scholar 

  • Smith, S. D., Anderson, R. J., Oost, W. A., Kraan, C., Maat, N., deCosmo, J., Katsaros, K. B., Davidson, K. L., Bumke, K., Hasse, L., and Chadwick, H. M.: 1992, 'Sea Surface Wind Stress and Drag Coefficients: The HEXOS Results', Boundary-Layer Meteorol. 60, 109–142.

    Google Scholar 

  • Smith, S. D., Fairall, C. W., Geernaert, G. L., and Hasse, L.: 1996, 'Air-Sea Fluxes: 25 Years of Progress', Boundary-Layer Meteorol. 78, 247–290.

    Google Scholar 

  • Stewart, R. W.: 1961, 'The Wave Drag of Wind over Water', J. Fluid Mech. 10, 189–194.

    Google Scholar 

  • Terray, E. A., Donelan, M. A., Agrawal, Y. C., Drennan, W. M., Kahma, K. K., Williams III, A. J., Hwang, P. A., and Kitaigorodskii, S. A.: 1996, 'Estimates of Kinetic Energy Dissipation under Breaking Waves', J. Phys. Oceanog. 26, 792–807.

    Google Scholar 

  • Yaglom, A. M.: 1977, 'Comments on Wind and Temperature Flux-Profile Relationships', Boundary-Layer Meteorol. 11, 89–102.

    Google Scholar 

  • Yelland, M. J. and Taylor, P. K.: 1996, 'Wind Stress Measurements from the Open Ocean', J. Phys. Oceanog. 26, 541–558.

    Google Scholar 

  • Zilitinkevich, S. S. and Chalikov, D. V.: 1968, 'Determining the Universal Wind Velocity and Temperature Profiles in the Atmospheric Boundary Layer', Izv., Atmos. Oceanic Phys. 4, 165–170.

    Google Scholar 

Download references

Authors
  1. William M. Drennan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kimmo K. Kahma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mark A. Donelan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Drennan, W.M., Kahma, K.K. & Donelan, M.A. On momentum flux and velocity spectra over waves. Boundary-Layer Meteorology 92, 489–515 (1999). https://doi.org/10.1023/A:1002054820455

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1002054820455

Search

Navigation