Advertisement

Boundary-Layer Meteorology

, Volume 17, Issue 1, pp 57–91 | Cite as

The turbulent heat flux from arctic leads

  • E. L. Andreas
  • C. A. Paulson
  • R. M. William
  • R. W. Lindsay
  • J. A. Businger
Article

Abstract

The turbulent transfer of heat from Arctic leads in winter is one of the largest terms in the Arctic heat budget. Results from the AIDJEX Lead Experiment (ALEX) suggest that the sensible component of this turbulent heat flux can be predicted from bulk quantities. Both the exponential relation N = 0.14Rx0.72 and the linear relation N = 1.6 × 10−3Rx+ 1400 fit our data well. In these, N is the Nusselt number formed with the integrated surface heat flux, and Rx is the Reynolds number based on fetch across the lead. Because of the similarity between heat and moisture transfer, these equations also predict the latent heat flux. Over leads in winter, the sensible heat flux is two to four times larger than the latent heat flux.

The internal boundary layer (IBL) that develops when cold air encounters the relatively warm lead is most evident in the modified downwind temperature profiles. The height of this boundary layer, δ, depends on the fetch, x, on the surface roughness of the lead, z0 and on both downwind and upwind stability. A tentative, empirical model for boundary layer growth is % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaaiabes% 7aKbqaaiaadQhadaWgaaWcbaGaaGimaaqabaaaaOGaeyypa0JaeqOS% di2aaeWaaeaacqGHsisldaWcaaqaaiaadQhadaWgaaWcbaGaaGimaa% qabaaakeaacaWGmbaaaaGaayjkaiaawMcaamaaCaaaleqabaGaaGim% aiaac6cacaaI4aaaaOWaaeWaaeaadaWcaaqaaiaadIhaaeaacaWG6b% WaaSbaaSqaaiaaicdaaeqaaaaaaOGaayjkaiaawMcaamaaCaaaleqa% baGaaGimaiaac6cacaaI0aaaaaaa!472D!\[\frac{\delta }{{z_0 }} = \beta \left( { - \frac{{z_0 }}{L}} \right)^{0.8} \left( {\frac{x}{{z_0 }}} \right)^{0.4} \] where L is the Obukhov length based on the values of the momentum and sensible heat fluxes at the surface of the lead, and Β is a constant reflecting upwind stability.

Velocity profiles over leads are also affected by the surface nonhomogeneity. Besides being warmer than the upwind ice, the surface of the lead is usually somewhat rougher. The velocity profiles therefore tend to decelerate near the surface, accelerate in the mid-region of the IBL because of the intense mixing driven by the upward heat flux, and rejoin the upwind profiles above the boundary layer. The profiles thus have distinctly different shapes for stable and unstable upwind conditions.

Keywords

Boundary Layer Heat Flux Nusselt Number Latent Heat Flux Surface Heat Flux 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andreas, E. L.: 1977, ‘Observations of Velocity and Temperature and Estimates of Momentum and Heat Fluxes in the Internal Boundary Layer over Arctic Leads’, Ph.D. Thesis, Oregon State University, School of Oceanography, 263 p.Google Scholar
  2. Andreas, E. L. and Paulson, C. A.: 1979, ‘Velocity Spectra and Cospectra and Integral Statistics over Arctic Leads’. (To be published in Quart. J. Royal Meteorol. Soc. 105 (466).)Google Scholar
  3. Badgley, F. I.: 1966, ‘Heat Budget at the Surface of the Arctic Ocean’, in Proceedings of the Symposium on the Arctic Heat Budget and Atmospheric Circulation, J. O. Fletcher (ed.), Rand Corporation (RM-5233-NSF), 267–277.Google Scholar
  4. Badgley, F. I., Paulson, C. A., and Miyake, M.: 1972, Profiles of Wind, Temperature, and Humidity over the Arabian Sea, University of Hawaii Press, 62p.Google Scholar
  5. Banke, E. G. and Smith, S. D.: 1971, ‘Wind Stress over Ice and over Water in the Beaufort Sea’, J. Geophys. Res. 76, 7368–7374.Google Scholar
  6. Blom, J. and Wartena, L.: 1969, ‘The Influence of Changes in Surface Roughness on the Development of the Turbulent Boundary Layer in the Lower Layers of the Atmosphere’, J. Atmos. Sci. 26, 255–265.Google Scholar
  7. Bradley, E. F.: 1968, ‘A Micrometeorological Study of Velocity Profiles and Surface Drag in the Region Modified by a Change in Surface Roughness’, Quart. J. Royal Meteorol. Soc. 94, 361–379.Google Scholar
  8. Bradley, E. F.: 1972, ‘The Influence of Thermal Stability on a Drag Coefficient Measured Close to the Ground’, Agric. Meteorol. 9, 183–190.Google Scholar
  9. Brutsaert, W.: 1975, ‘A Theory of Local Evaporation (or Heat Transfer) from Rough and Smooth Surfaces at Ground Level’, Water Resour. Res. 11, 543–550.Google Scholar
  10. Businger, J. A.: 1973, ‘Turbulent Transfer in the Atmospheric Surface Layer’, in Workshop on Micrometeorology, D. A. Haugen (ed.), American Meteorological Society, 67–100.Google Scholar
  11. Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, ‘Flux-Profile Relationships in the Atmospheric Surface Layer’, J. Atmos. Sci. 28, 181–189.Google Scholar
  12. Charnock, H.: 1955, ‘Wind Stress on Water: An Hypothesis’, Quart. J. Royal Meteorol. Soc. 81, 639.Google Scholar
  13. Charnock, H.: 1958, ‘A Note on Empirical Wind-Wave Formulae’, Quart. J. Royal Meteorol. Soc. 84, 443–447.Google Scholar
  14. Coachman, L. K.: 1966, ‘Production of Supercooled Water during Sea Ice Formation’, in Proceedings of the Symposium on the Arctic Heat Budget and Atmospheric Circulation, J. O. Fletcher (ed.), Rand Corporation (RM-5233-NSF), 497–529.Google Scholar
  15. Coantic, M. and Favre, A.: 1974, ‘Activities in, and Preliminary Results of, Air-Sea Interactions Research at I.M.S.T.’, Adv. Geophys. 18A, 391–405.Google Scholar
  16. Csanady, G. T.: 1974, ‘The “Roughness” of the Sea Surface in Light Winds’, J. Geophys. Res. 79, 2747–2751.Google Scholar
  17. Dyer, A. J.: 1974, ‘A Review of Flux-Profile Relationships’, Boundary-Layer Meteorol. 7, 363–372.Google Scholar
  18. Elliott, W. P.: 1958, ‘The Growth of the Atmospheric Internal Boundary Layer’, Trans., Am. Geophys. Union 39, 1048–1054.Google Scholar
  19. Garratt, J. R. and Hicks, B. B.: 1973, ‘Momentum, Heat and Water Vapour Transfer to and from Natural and Artificial Surfaces’, Quart. J. Royal Meteorol. Soc. 99, 680–687.Google Scholar
  20. Heiberg, A.: 1974, ‘AIDJEX Lead Experiment, Spring, 1974: Field Operations Report’, AIDJEX Bull. 26, 23–31.Google Scholar
  21. Hicks, B. B.: 1972, ‘Some Evaluations of Drag and Bulk Transfer Coefficients over Water Bodies of Different Sizes’, Boundary-Layer Meteorol. 3, 201–213.Google Scholar
  22. Holmgren, B. and Weller, G.: 1974, ‘Local Radiation Fluxes over Open and Freezing Leads in the Polar Pack Ice’, AIDJEX Bull. 27, 149–166.Google Scholar
  23. Kitaigorodskii, S. A.: 1968, ‘On the Calculation of the Aerodynamic Roughness of the Sea Surface’, Izv., Acad. Sci., USSR, Atmos. Oceanic Phys. 4, 498–502.Google Scholar
  24. Kitaigorodskii, S. A. and Volkov, Yu. 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., Acad. Sci., USSR, Atmos. Oceanic Phys. 1, 566–574.Google Scholar
  25. Kondo, J.: 1976, ‘Parameterization of Turbulent Transport in the Top Meter of the Ocean’, J. Phys. Oceanogr. 6, 712–720.Google Scholar
  26. Kondo, J., Fujinawa, Y., and Naito, G.: 1973, ‘High-Frequency Components of Ocean Waves and Their Relation to the Aerodynamic Roughness’, J. Phys. Oceanogr. 3, 197–202.Google Scholar
  27. Kraus, E. B.: 1967, ‘Wind Stress Along the Sea Surface’, Adv. Geophys. 12, 213–255.Google Scholar
  28. Lindsay, R. W.: 1976, ‘Wind and Temperature Profiles Taken During the Arctic Leads Experiment’, Master's Thesis, University of Washington, Department of Atmospheric Sciences, 89p.Google Scholar
  29. Mangarella, P. A., Chambers, A. J., Street, R. L., and Hsu, E. Y.: 1971, ‘Energy and Mass Transfer through an Air-Water Interface’, Tech. Rept. No. 134, Stanford University, Department of Civil Engineering, 175p.Google Scholar
  30. Mangarella, P. A., Chambers, A. J., Street, R. L., and Hsu, E. Y.: 1973, ‘Laboratory Studies of Evaporation and Energy Transfer through a Wavy Air-Water Interface’, J. Phys. Oceanogr. 3, 93–101.Google Scholar
  31. Maykut, G. A.: 1978, ‘Energy Exchange over Young Sea Ice in the Central Arctic’, J. Geophys. Res. 83, 3646–3658.Google Scholar
  32. Miyake, M.: 1965, ‘Transformation of the Atmospheric Boundary Layer over Inhomogeneous Surfaces’, Scientific Rept., University of Washington, Department of Atmospheric Sciences, 63p.Google Scholar
  33. Miyake, M., Donelan, M., McBean, G., Paulson, C., Badgley, F., and Leavitt, E.: 1970, ‘Comparison of Turbulent Fluxes over Water Determined by Profile and Eddy Correlation Techniques’, Quart. J. Royal Meteorol. Soc. 96, 132–137.Google Scholar
  34. Panofsky, H. A. and Townsend, A. A.: 1964, ‘Change of Terrain Roughness and the Wind Profile’, Quart. J. Royal Meteorol. Soc. 90, 147–155.Google Scholar
  35. Paulson, C. A.: 1970, ‘The Mathematical Representation of Wind Speed and Temperature Profiles in the Unstable Atmospheric Surface Layer’, J. Appl. Meteorol. 9, 857–861.Google Scholar
  36. Paulson, C. A. and Smith, J. D.: 1974, ‘The AIDJEX Lead Experiment’, AIDJEX Bull. 23, 1–8.Google Scholar
  37. Phelps, G. T. and Pond, S.: 1971, ‘Spectra of the Temperature and Humidity Fluctuations and of the Fluxes of Moisture and Sensible Heat in the Marine Boundary Layer’, J. Atmos. Sci. 28, 918–928.Google Scholar
  38. Phillips, O. M.: 1969, The Dynamics of the Upper Ocean, Cambridge University Press, 261p.Google Scholar
  39. Plate, E. J. and Hidy, G. M.: 1967, ‘Laboratory Study of Air Flowing over a Smooth Surface onto Small Water Waves’, J. Geophys. Res. 72, 4627–4641.Google Scholar
  40. Rao, K. S., Wyngaard, J. C., and Coté, O. R.: 1974, ‘The Structure of the Two-Dimensional Internal Boundary Layer over a Sudden Change of Surface Roughness’, J. Atmos. Sci. 31, 738–746.Google Scholar
  41. Roll, H. U.: 1965, Physics of the Marine Atmosphere, Academic Press, 426p.Google Scholar
  42. Schlichting, H.: 1968, Boundary-Layer Theory, 6th ed., J. Kestin (Irans.), McGraw-Hill, 748p.Google Scholar
  43. Shreffler, J. H.: 1975, ‘A Numerical Model of Heat Transfer to the Atmosphere from an Arctic Lead’, Ph.D. Thesis, Oregon State University, School of Oceanography, 135p.Google Scholar
  44. Smith, S. D. and Banke, E. G.: 1975, ‘Variations of the Sea Surface Drag Coefficient with Wind Speed’, Quart. J. Royal Meteorol. Soc. 101, 665–673.Google Scholar
  45. Taylor, P. A.: 1969, ‘On Wind and Shear Stress Profiles above a Change in Surface Roughness’, Quart. J. Royal Meteorol. Soc. 95, 77–91.Google Scholar
  46. Taylor, P. A.: 1970, ‘A Model of Airflow above Changes in Surface Heat Flux, Temperature and Roughness for Neutral and Unstable Conditions’, Boundary-Layer Meteorol. 1, 18–39.Google Scholar
  47. Tennekes, H. and Lumley, J. L.: 1972, A First Course in Turbulence, MIT Press, 300p.Google Scholar
  48. Untersteiner, N.: 1964, ‘Calculation of Temperature Regime and Heat Budget of Sea Ice in the Central Arctic’, J. Geophys. Res. 69, 4755–4766.Google Scholar
  49. Vowinckel, E. and Taylor, B.: 1965, ‘Energy Balance of the Arctic: IV. Evaporation and Sensible Heat Flux over the Arctic Ocean’, Arch. Meteorol. Geophys. Bioklimatol., Ser. B 14, 36–52.Google Scholar
  50. Vugts, H. F. and Businger, J. A.: 1977, ‘Air Modification Due to a Step Change in Surface Temperature’, Boundary-Layer Meteorol. 11, 295–305.Google Scholar

Copyright information

© D. Reidel Publishing Co 1979

Authors and Affiliations

  • E. L. Andreas
    • 1
  • C. A. Paulson
    • 1
  • R. M. William
    • 1
  • R. W. Lindsay
    • 2
  • J. A. Businger
    • 2
  1. 1.School of Oceanography, Oregon State UniversityCorvallisUSA
  2. 2.Department of Atmospheric SciencesUniversity of WashingtonSeattleUSA

Personalised recommendations