An evaluation of the dissimilarity in heat and momentum transport through quadrant analysis for an unstable atmospheric surface layer flow

  • Subharthi ChowdhuriEmail author
  • Thara V. Prabha
Original Article


To elucidate the role of each fluid motion in the transport of momentum and heat fluxes in an unstable atmospheric surface layer (ASL) flow from single point measurements on a micrometeorological tower, we develop a novel method based on quadrant analysis where the contour maps of the turbulent statistics (fluxes, temperature variances and triple order moments between vertical velocity and temperature) are plotted on the quadrant planes between streamwise (u)–vertical (w) velocities, and vertical velocity (w)–temperature (T). We find that the dissimilarities in the heat and momentum transport with atmospheric stability are closely linked to the non-Gaussian nature of the joint probability density function (JPDF) between w and T. To highlight the changes in the fluid motions which cause this dissimilarity, we plot the contour maps of the third order moments between w and T on the u − w quadrant plane, and also of the streamwise momentum flux conditioned on every quadrant of u − w plane onto the T − w plane, referred to as octant analysis. The results indicate that in a highly-convective ASL, the cold downdrafts interspersed with strong ejections of hot fluid, carry a significant amount of both down-gradient and counter-gradient momentum flux, thus making the momentum transport inefficient. However, in a near-neutral ASL, the heat and momentum both are carried by the ejection and sweep quadrants of u − w quadrant plane, which indicates the temperature fluctuations are highly correlated with the high-speed and low-speed streaks commonly found in pure shear flows in the laboratory experiments.


Contour maps Gaussian distribution Joint probability density function Octant analysis Quadrant analysis Turbulent statistics 



The authors would like to acknowledge the kind support of the Ministry of Earth Sciences (MoES) to carry out this study. The help of the CAIPEEX-IGOC team, in collecting the data from these two field experiments is also gratefully acknowledged. The authors would also like to thank the two anonymous reviewers, whose comments were very helpful in improving the manuscript. The datasets used in this study can be made available to all the researchers by contacting TVP or SC at or at

Supplementary material

10652_2018_9636_MOESM1_ESM.docx (5.6 mb)
Supplementary material 1 (DOCX 5736 kb)


  1. 1.
    Adrian RJ, Ferreira RTDS, Boberg T (1986) Turbulent thermal convection in wide horizontal fluid layers. Exp Fluids 4:121–141. CrossRefGoogle Scholar
  2. 2.
    Antonia RA (1977) Similarity of atmospheric Reynolds shear stress and heat flux fluctuations over a rough surface. Bound Layer Meteorol 12:351–364. CrossRefGoogle Scholar
  3. 3.
    Cantwell B (1981) Organized motion in turbulent flow. Ann Rev Fluid Mech 13:457–515. CrossRefGoogle Scholar
  4. 4.
    Cava D, Schipa S, Giostra U (2005) Investigation of low-frequency perturbations induced by a steep obstacle. Bound Layer Meteorol 115:27–45. CrossRefGoogle Scholar
  5. 5.
    Chowdhuri S, Prabha TV, Karipot A, Dharamraj T, Patil MN (2015) Relationship between the momentum and scalar fluxes close to the ground during the Indian post-monsoon period. Bound Layer Meteorol 154:333–348. CrossRefGoogle Scholar
  6. 6.
    Chu CR, Parlange MB, Katul GG, Albertson JD (1996) Probability density functions of turbulent velocity and temperature in the atmospheric surface layer. Water Resour Res 32:1681–1688. CrossRefGoogle Scholar
  7. 7.
    Donateo A, Cava D, Contini D (2017) A case study of the performance of different detrending methods in turbulent-flux Estimation. Bound Layer Meteorol 164:19–37. CrossRefGoogle Scholar
  8. 8.
    Feŕiet JKD (1966) The Gram-Charlier approximation of the normal law and the statistical description of a homogenous turbulent flow near statistical equilibrium. David Taylor Model Basin Report No. 2013, Naval Ship Research and Development Centre, Washington, DCGoogle Scholar
  9. 9.
    Ghannam K, Duman T, Salesky ST, Chamecki M, Katul GG (2017) The non-local character of turbulence asymmetry in the convective atmospheric boundary layer. Q J R Meteorol Soc 143:494–507. CrossRefGoogle Scholar
  10. 10.
    Giostra U, Cava D, Schipa S (2002) Structure functions in a wall-turbulent shear flow. Bound Layer Meteorol 103:337–359. CrossRefGoogle Scholar
  11. 11.
    Greenhut GK, Khalsa SJS (1982) Updraft and downdraft Events in the atmospheric boundary layer over the equatorial Pacific ocean. J Atmos Sci 39:1803–1818.;2 CrossRefGoogle Scholar
  12. 12.
    Harikishan G, Padmakumari B, Maheshkumar RS, Pandithurai G, Min QL (2015) Macrophysical and microphysical properties of monsoon clouds over a rain shadow region in India from ground-based radiometric measurements. J Geophys Res Atmos 119:4736–4749. CrossRefGoogle Scholar
  13. 13.
    Hunt JCR, Kaimal JC, Gaynor JE (1988) Eddy structure in the convective boundary layer—new measurements and new concepts. Q J R Meteorol Soc 114:827–858. CrossRefGoogle Scholar
  14. 14.
    Kaimal JC (1969) Measurement of momentum and heat flux variations in the surface boundary layer. Radio Sci 4(12):1147–1153. CrossRefGoogle Scholar
  15. 15.
    Kader BA, Yaglom AM (1972) Heat and mass transfer laws for fully turbulent wall flows. Int J Heat Mass Transfer 15:2329–2351. CrossRefGoogle Scholar
  16. 16.
    Kulkarni JR, Maheskumar RS, Morwal SB, Padma Kumari B, Konwar M, Deshpande CG, Joshi RR, Bhalwankar RV, Pandithurai G, Safai PD, Narkhedkar SG, Dani KK, Nath A, Nair S, Sapre VV, Puranik PV, Kandalgaonkar S, Mujumdar VR, Khaladkar RM, Vijayakumar R, Prabha TV, Goswami BN (2012) The cloud aerosol interactions and precipitation enhancement experiment (CAIPEEX): overview and preliminary results. Curr Sci 102:413–425Google Scholar
  17. 17.
    Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows: their structure and measurement. Oxford University Press, New YorkGoogle Scholar
  18. 18.
    Khanna S, Brasseur JG (1998) Three-dimensional buoyancy- and shear-induced local structure of the atmospheric boundary layer. J Atmos Sci 55:710–743.;2 CrossRefGoogle Scholar
  19. 19.
    Katul GG, Kuhn G, Schieldge J, Hsieh CI (1997) The ejection-sweep character of scalar fluxes in the unstable surface layer. Bound-Layer Meteorol 83:1–26. CrossRefGoogle Scholar
  20. 20.
    Katul GG, Poggi D, Cava D, Finnigan J (2006) The relative importance of ejections and sweeps to momentum transfer in the atmospheric boundary layer. Bound Layer Meteorol 120:367–375. CrossRefGoogle Scholar
  21. 21.
    Li D, Bou-Zeid E (2011) Coherent structures and the dissimilarity of turbulent transport of momentum and scalars in the unstable atmospheric surface layer. Bound Layer Meteorol 140:243–262. CrossRefGoogle Scholar
  22. 22.
    Li Q, Gentine P, Mellado JP, McColl KA (2018) Implications of nonlocal transport and conditionally averaged statistics on Monin-Obukhov similarity theory and Townsend’s attached eddy hypothesis. J Atmos Sci 75:3403–3431. CrossRefGoogle Scholar
  23. 23.
    Lu SS, Willmarth WW (1973) Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J Fluid Mech 60:481–511. CrossRefGoogle Scholar
  24. 24.
    Mahrt L (1991) Eddy asymmetry in the sheared heated boundary layer. J Atmos Sci 48:472–492.;2 CrossRefGoogle Scholar
  25. 25.
    Maitani T, Shaw RH (1990) Joint probability analysis of momentum and heat fluxes at a deciduous forest. Bound Layer Meteorol 52:283–300. CrossRefGoogle Scholar
  26. 26.
    McBean GA (1974) The turbulent transfer mechanisms: a time domain analysis. Q J R Meteorol Soc 100:53–66. CrossRefGoogle Scholar
  27. 27.
    Nakagawa H, Nezu I (1977) Prediction of the contributions to the Reynolds stress from bursting events in open-channel flows. J Fluid Mech 80(1):99–128. CrossRefGoogle Scholar
  28. 28.
    Nagano Y, Tagawa M (1988) Statistical characteristics of wall turbulence with a passive scalar. J Fluid Mech 196:157–185. CrossRefGoogle Scholar
  29. 29.
    Nagano Y, Tagawa M (1990) A structural turbulence model for triple products of velocity and scalar. J Fluid Mech 215:639–657. CrossRefGoogle Scholar
  30. 30.
    Narasimha R, Kumar RS, Prabhu A, Kailas SV (2007) Turbulent flux events in a nearly neutral atmospheric boundary layer. Philos Trans R Soc A 365:841–858. CrossRefGoogle Scholar
  31. 31.
    Patil MN, Dharmaraj T, Waghmare RT, Prabha TV, Kulkarni JK (2014) Measurements of carbon dioxide and heat fluxes during monsoon-2011 season over rural site of India by eddy covariance technique. J Earth Syst Sci 123:177–185. CrossRefGoogle Scholar
  32. 32.
    Prabha TV, Khain A, Maheshkumar RS, Pandithurai G, Kulkarni JR, Konwar M, Goswami BN (2011) Microphysics of pre-monsoon and monsoon clouds as seen from in situ measurements during CAIPEEX. J Atmos Sci 68:1882–1901. CrossRefGoogle Scholar
  33. 33.
    Prabha TV, Leclerc MY, Karipot A, Hollinger DY (2007) Low-frequency effects on eddy covariance fluxes under the influence of a low-level jet. J Appl Meteor Climatol 46:338–352. CrossRefGoogle Scholar
  34. 34.
    Raupach MR (1981) Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J Fluid Mech 108:363–382. CrossRefGoogle Scholar
  35. 35.
    Robinson SK (1991) Coherent motions in the turbulent boundary layer. Ann Rev Fluid Mech 23:601–639. CrossRefGoogle Scholar
  36. 36.
    Salesky ST, Chamecki M, Bou-Zeid E (2017) On the nature of the transition between roll and cellular organization in the convective boundary layer. Bound Layer Meteorol 163:41–68. CrossRefGoogle Scholar
  37. 37.
    Sathyanadh A, Prabha TV, Balaji B, Resmi EA, Karipot A (2017) Evaluation of WRF PBL parameterization schemes against direct observations during a dry event over the Ganges valley. J Atmos Res 193:125–141. CrossRefGoogle Scholar
  38. 38.
    Suzuki H, Suzuki K, Sato T (1988) Dissimilarity between heat and momentum transfer in a turbulent boundary layer disturbed by a cylinder. Int J Heat Mass Transfer 31:259–265. CrossRefGoogle Scholar
  39. 39.
    Shaw RH, Tavangar J, Ward DP (1983) Structure of the Reynolds stress in a canopy layer. J Clim Appl Meteorol 22:1922–1931.;2 CrossRefGoogle Scholar
  40. 40.
    Tennekes H, Lumley JL (1972) A first course in turbulence. MIT press, CambridgeGoogle Scholar
  41. 41.
    Vickers D, Mahrt L (1997) Quality control and flux sampling problems for tower and aircraft data. J Atmos Oceanic Technol 14:512–526.;2 CrossRefGoogle Scholar
  42. 42.
    Wilczak JM (1984) Large-scale eddies in the unstably stratified atmospheric surface layer. Part I: velocity and temperature structure. J Atmos Sci 41:3537–3550.;2 CrossRefGoogle Scholar
  43. 43.
    Wang L, Li D, Gao Z, Sun T, Guo X, Bou-Zeid E (2014) Turbulent transport of momentum and scalars above an urban canopy. Bound Layer Meteorol 150:485–511. CrossRefGoogle Scholar
  44. 44.
    Wallace JM (2016) Quadrant analysis in turbulence research: history and evolution. Ann Rev Fluid Mech 48:131–158. CrossRefGoogle Scholar
  45. 45.
    Wallace JM, Brodkey RS, Eckelmann H (1972) The wall region in turbulent shear flow. J Fluid Mech 54:39–48. CrossRefGoogle Scholar
  46. 46.
    Warhaft Z (2000) Passive scalars in turbulent flows. Ann Rev Fluid Mech 32:203–240. CrossRefGoogle Scholar
  47. 47.
    Wyngaard J, Moeng CH (1992) Parameterizing the turbulent diffusion through the joint probability density. Bound Layer Meteorol 60:1–13. CrossRefGoogle Scholar
  48. 48.
    Zhuang Y (1995) Dynamics and energetics of convective plumes in the atmospheric surface layer. J Atmos Sci 52:1712–1722.;2 CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Indian Institute of Tropical MeteorologyPashan, PuneIndia

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