Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Free convection frequency spectra of atmospheric turbulence over the sea

Abstract

Frequency spectra of atmospheric turbulenceS α (f) in the inertial subrange are considered in the free convection regime over the sea surface in a case of motionless instrument measurements (Eulerian frequency spectra). The frequency spectra formulaef * S α(f)/σ α 2 =c α(f */f)5/3 for wind velocity (α=1–3), temperature (α=t) and humidity (α=e) fluctuations are derived on the basis of similarity theory and the “−5/3 law”. These relations also can be derived from a consideration of convective large-scale advection of small eddies. The frequency scalef * = (N 1 β 2/∈)1/2 ≈ (βH/z 2)1/3 is the lower bound of the inertial subrange and it is of order 10−2 Hz.

The spectra formulae are compared with direct measurements of atmospheric turbulence from the fixed research tower in the coastal zone of the Black Sea in calm weather. It is shown that these formulae are realized at least over two to three decades of the frequency range (approximately from 10−2 to 10 Hz) and values of the numerical coefficients are found. The derived formulae can be used for calculations of sensible and latent heat fluxes by measuring the high-frequency range of spectra at a fixed point at low wind speeds when the conventional inertial dissipation method is not applicable.

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

References

  1. Adrian, R. J., Ferreira, R. T. D. S., and Boberg, T.: 1986, ‘Turbulent Thermal Convection in Wide Horizontal Fluid Layers (A Review)’,Experiments in Fluids.4, 121–141.

  2. Boubnov, B. M. and Golitsyn, G. S.: 1990, ‘Temperature and Velocity Field Regimes of Convective Motions in a Rotating Plane Fluid Layer’,J. Fluid Mech. 219, 215–239.

  3. Boubnov, B. M. and Ivanov, V. N.: 1988, ‘Time-Dependent Spectrum of Temperature Fluctuations for Free Turbulent Convection in a Fluid Layer’,Izvestiya, Acad. Sci., USSR, Atmos. Oceanic Phys. 24(5), 361–366 (English Edition).

  4. Bradley, E. F., Coppin, P. A., and Godfrey, J. C.: 1991, ‘Measurements of Sensible and Latent Heat Flux in Western Equatorial Pacific Ocean’,J. Geophys. Res. 96 (Supplement), 3375–3389.

  5. Deardorff, J. W.: 1970, ‘Convective Velocity and Temperature Scales for the Unstable Planetary Boundary Layer and for Rayleigh Convection’,J. Atmos. Sci. 27(8), 1211–1213.

  6. Deardorff, J. W. and Willis, G. E.: 1967, ‘Investigation of Turbulent Thermal Convection between Horizontal Plates’,J. Fluid Mech. 28(4), 675–705.

  7. Fairall, C. W. and Larsen, S. E.: 1986, ‘Inertial-Dissipation Methods and Turbulent Fluxes at the Air-Ocean Interface’,Boundary-Layer Meteorol. 34, 287–301.

  8. Fernando, H. J. S., Chen, R. R., and Boyer, D. L.: 1991, ‘Effects of Rotation on Convective Turbulence’,J. Fluid Mech. 228, 513–547.

  9. Foster, T. D.: 1971, ‘Intermittent Convection’,J. Geophys. Fluid Dyn. 2, 201–217.

  10. Foster, T. D. and Waller, S.: 1985, ‘Experiments on Convection at very High Rayleigh Numbers’,Phys. Fluids 28(2), 455–461.

  11. Geernaert, G. L., Davidson, K. L., Larsen, S. E., and Mikkelsen, T.: 1988, ‘Wind Stress Measurements during the Tower Ocean Wave and Radar Experiment’,J. Geophys. Res. 93(C11), 13913–13923.

  12. Godfrey, J. S. and Beljaars, A. C. M.: 1991, ‘On the Turbulent Fluxes of Buoyancy, Heat and Moisture at the Air-Sea Interface at Low Wind Speeds’,TOGA Notes 5, 1–4.

  13. Golitsyn, G. S.: 1979, ‘Simple Theoretical and Experimental Study of Convection with Some Geophysical Applications and Analogies’,J. Fluid Mech. 95(3), 567–608.

  14. Golitsyn, G. S. and Grachev, A. A.: 1986, ‘Free Convection of Multicomponent Media and Parameterization of Air-Sea Interaction at Light Winds’,Ocean-Air Interactions. 1, 57–78.

  15. Grachev, A. A.: 1990, ‘Friction Law in the Free-Convection Limit’,Izvestiya, Acad. Sci., USSR, Atmos. Oceanic Phys. 26(11), 837–846 (English Edition).

  16. Gurvich, A. S. and Yurchenko, B. N.: 1980, ‘Frequency Spectra of Temperature Fluctuations in Turbulent Convection’,Izvestiya, Acad. Sci. USSR. Atmos. Oceanic Phys. 16(8), 612–615 (English Edition).

  17. Hunt, J. C. R.: 1984, ‘Turbulent Structure in Thermal Convection and Shear-Free Boundary-Layers’,J. Fluid Mech. 138, 161–184.

  18. Kader, B. A.: 1988, ‘Three-Level Structure of an Unstably Stratified Atmospheric Surface Layer’,Izvestiya, Acad. Sci., USSR, Atmos. Oceanic Phys. 24(12), 907–918 (English Edition).

  19. Kader, B. A. and Yaglom A. M.: 1990, ‘Mean Fields and Fluctuation Moments in Unstably Stratified Turbulent Boundary Layers’,J. Fluid. Mech. 212, 637–662.

  20. Kaimal, J. C., Wyngaard, J. C., Izumi, Y., and Cote, O. R.: 1972, ‘Spectral Characteristics of Surface-Layer Turbulence’,Quart. J. R. Meteorol. Soc. 98(417), 563–589.

  21. Kotsovinos, N. E.: 1991, ‘Turbulent Spectra in Free Convection Flow’,Phys. Fluids A. 3(1), 163–167.

  22. Large, W. G. and Poud, S.: 1981, ‘Open Ocean Momentum Flux Measurements in Moderate to Strong Winds’,J. Phys. Oceanogr. 11, 324–336.

  23. Liu, W. T., Katsaros, K. B., and Businger, J. A.: 1979, ‘Bulk Parameterization of Air-Sea Exchanges of Heat and Water Vapor Including the Molecular Constraints at the Interface’,J. Atmos. Sci. 36(9), 1722–1735.

  24. Monin, A. S. and Yaglom, A. M.: 1971,Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 1, MIT Press, Cambridge, Massachusetts.

  25. Monin, A. S. and Yaglom, A. M.: 1975,Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 2, MIT Press, Cambridge, Massachusetts.

  26. Obukhov, A. M.: 1959, ‘The Influence of Archimedes Forces on the Structure of the Temperature Field in a Turbulent Flow’,Doklady, Acad. Sci., USSR. 125(6), 1246–1248.

  27. She, Z. S.: 1989, ‘On the Scaling Laws of Thermal Convection’,Phys. Fluids A. 1(6), 911–913.

  28. Smith, S. D. and Anderson, R. J.: 1984, ‘Spectra of Humidity, Temperature, and Wind over the Sea at the Sable Island, Nova Scotia’,J. Geophys. Res. 89(C2), 2029–2040.

  29. Tennekes, H.: 1975, ‘Eulerian and Lagrangian Time Microscales in Isotropic Turbulence’,J. Fluid Mech. 67(3), 561–567.

  30. Tsukamoto, O., Ohtaki, E., Ishida, H., Horiguchi, M., and Mitsuta, Y.: 1990, ‘On-Board Direct Measurements of Turbulent Fluxes over the Open Sea’,J. Meteorol. Soc. Japan. 68(2), 203–211.

  31. Volkov, Yu. A., Grachev, A. A., and Matveev, D. T.: 1992, ‘Tranition from Aerodynamically Smooth to Rough Flow over the Sea Surface’,Izvestiya, Russian Acad. Sci. Atmos. Oceanic Phys. 28(7), 580–583 (English Edition).

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Grachev, A.A. Free convection frequency spectra of atmospheric turbulence over the sea. Boundary-Layer Meteorol 69, 27–42 (1994). https://doi.org/10.1007/BF00713293

Download citation

Keywords

  • Heat Flux
  • Advection
  • Frequency Spectrum
  • Latent Heat Flux
  • Free Convection