Observations of Stably Stratified Shear-Driven Atmospheric Turbulence at Low and High Richardson Numbers

Thorsten Mauritsen Department of Meteorology, Stockholm University, Stockholm, Sweden

Search for other papers by Thorsten Mauritsen in
Current site
Google Scholar
PubMed
Close
and
Gunilla Svensson Department of Meteorology, Stockholm University, Stockholm, Sweden

Search for other papers by Gunilla Svensson in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Stably stratified shear-driven turbulence is analyzed using the gradient Richardson number, Ri, as the stability parameter. The method overcomes the statistical problems associated with the widely used Monin–Obukhov stability parameter. The results of the Ri-based scaling confirm the presence of three regimes: the weakly and the very stable regimes and the transition in between them. In the weakly stable regime, fluxes scale in proportion with variance, while in the very stable regime, stress and scalar fluxes behave differently. At large Ri, the velocity field becomes highly anisotropic and the turbulent potential energy becomes approximately equal to half of the turbulent kinetic energy. It appears that even in the strongly stable regime, beyond what is known as the critical gradient Richardson number, turbulent motions are present.

Corresponding author address: Thorsten Mauritsen, Department of Meteorology, Stockholm University, Svante Arrhenius Väg 12, Stockholm 106 91, Sweden. Email: thorsten@misu.su.se

Abstract

Stably stratified shear-driven turbulence is analyzed using the gradient Richardson number, Ri, as the stability parameter. The method overcomes the statistical problems associated with the widely used Monin–Obukhov stability parameter. The results of the Ri-based scaling confirm the presence of three regimes: the weakly and the very stable regimes and the transition in between them. In the weakly stable regime, fluxes scale in proportion with variance, while in the very stable regime, stress and scalar fluxes behave differently. At large Ri, the velocity field becomes highly anisotropic and the turbulent potential energy becomes approximately equal to half of the turbulent kinetic energy. It appears that even in the strongly stable regime, beyond what is known as the critical gradient Richardson number, turbulent motions are present.

Corresponding author address: Thorsten Mauritsen, Department of Meteorology, Stockholm University, Svante Arrhenius Väg 12, Stockholm 106 91, Sweden. Email: thorsten@misu.su.se

Save
  • Andreas, E. L., and B. B. Hicks, 2002: Comments on “Critical test of the validity of Monin–Obukhov similarity during convective conditions.”. J. Atmos. Sci., 59 , 26052607.

    • Search Google Scholar
    • Export Citation
  • Arya, S. P., 1991: Finite-difference errors in estimation of gradients in the atmospheric surface layer. J. Appl. Meteor., 30 , 251253.

    • Search Google Scholar
    • Export Citation
  • Baas, P., G. J. Steeneveld, B. J. H. van de Wiel, and A. A. M. Holtslag, 2006: Exploring self-correlation in flux–gradient relationships for stably stratified conditions. J. Atmos. Sci., 63 , 30453054.

    • Search Google Scholar
    • Export Citation
  • Businger, J. A., J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28 , 181189.

    • Search Google Scholar
    • Export Citation
  • Chandrasekhar, S., 1961: Hydrodynamic and Hydromagnetic Stability. Clarendon Press, 652 pp.

  • Cornish, C. R., C. S. Bretherton, and D. B. Percival, 2006: Maximal overlap wavelet statistical analysis with application to atmospheric turbulence. Bound.-Layer Meteor., 119 , 339374.

    • Search Google Scholar
    • Export Citation
  • Delage, Y., 1997: Parameterising sub-grid scale vertical transport in atmospheric models under statically stable conditions. Bound.-Layer Meteor., 82 , 2348.

    • Search Google Scholar
    • Export Citation
  • Duynkerke, P. G., 1998: Dynamics of cloudy boundary layers. Clear and Cloudy Boundary Layers, A. A. M. Holtslag and P. G. Duynkerke, Eds., Royal Netherlands Academy of Arts and Sciences, 199–218.

    • Search Google Scholar
    • Export Citation
  • Finnigan, J. J., and F. Einaudi, 1981: The interaction between an internal gravity wave and the planetary boundary layer. Part II: Effect of the wave on the turbulence structure. Quart. J. Roy. Meteor. Soc., 107 , 807832.

    • Search Google Scholar
    • Export Citation
  • Grachev, A. A., C. W. Fairall, P. O. G. Persson, E. L. Andreas, and P. Guest, 2005: Stable boundary-layer scaling regimes: The SHEBA data. Bound.-Layer Meteor., 116 , 201235.

    • Search Google Scholar
    • Export Citation
  • Hicks, B. B., 1978: Some limitations of dimensional analysis and power laws. Bound.-Layer Meteor., 14 , 567569.

  • Howard, L. N., 1961: Note on a paper of John W. Miles. J. Fluid Mech., 10 , 509512.

  • Howell, J. F., and L. Mahrt, 1997: Multiresolution flux decomposition. Bound.-Layer Meteor., 83 , 117137.

  • Klipp, C. L., and L. Mahrt, 2004: Flux gradient relationship, self-correlation and intermittency in the stable boundary layer. Quart. J. Roy. Meteor. Soc., 130 , 20872103.

    • Search Google Scholar
    • Export Citation
  • Kondo, J., O. Kanechika, and N. Yasuda, 1978: Heat and momentum transfers under strong stability in the atmospheric surface layer. J. Atmos. Sci., 35 , 10121102.

    • Search Google Scholar
    • Export Citation
  • Louis, J. F., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Layer Meteor., 17 , 187202.

  • Mahrt, L., 1999: Stratified atmospheric boundary layers. Bound.-Layer Meteor., 90 , 375396.

  • Mahrt, L., and D. Vickers, 2005: Boundary layer adjustment over small-scale changes of surface heat flux. Bound.-Layer Meteor., 116 , 313330.

    • Search Google Scholar
    • Export Citation
  • Mahrt, L., and D. Vickers, 2006: Extremely weak mixing in stable conditions. Bound.-Layer Meteor., 119 , 1939.

  • Mahrt, L., J. Sun, W. Blumen, T. Delany, and S. Oncley, 1998: Nocturnal boundary-layer regimes. Bound.-Layer Meteor., 88 , 255278.

  • Miles, J., 1961: On the stability of heterogeneous shear flows. J. Fluid Mech., 10 , 496508.

  • Miles, J., 1986: Richardson’s criterion for the stability of stratified shear flow. Phys. Fluids, 29 , 34703471.

  • Monin, A. S., and A. M. Obukhov, 1954: Basic laws of turbulent mixing in the ground layer of the atmosphere. Akad. Nauk SSSR Geofiz. Inst. Tr., 151 , 163187.

    • Search Google Scholar
    • Export Citation
  • Nappo, C. J., 2002: An Introduction to Atmospheric Gravity Waves. Academic Press, 260 pp.

  • Nastrom, G., K. Gage, and W. H. Jasperson, 1984: Kinetic energy spectrum of large- and mesoscale atmospheric processes. Nature, 310 , 3638.

    • Search Google Scholar
    • Export Citation
  • Nieuwstadt, F. T. M., 1984: The turbulent structure of the stable, nocturnal boundary layer. J. Atmos. Sci., 41 , 22022216.

  • Obukhov, A. M., 1946: Turbulence in an atmosphere with inhomogeneous temperature. Tr. Inst. Teor. Geofiz. Akad. Nauk SSSR, 1 , 95115.

  • Pahlow, M., M. B. Parlange, and F. Porte-Agel, 2001: On Monin–Obukhov similarity in the stable atmospheric boundary layer. Bound.-Layer Meteor., 99 , 225248.

    • Search Google Scholar
    • Export Citation
  • Poulos, G. S., and S. P. Burns, 2003: An evaluation of bulk Ri-based surface layer flux formulas for stable and very stable conditions with intermittent turbulence. J. Atmos. Sci., 60 , 25232537.

    • Search Google Scholar
    • Export Citation
  • Poulos, G. S., and Coauthors, 2002: CASES-99: A comprehensive investigation of the stable nocturnal boundary layer. Bull. Amer. Meteor. Soc., 83 , 555581.

    • Search Google Scholar
    • Export Citation
  • Richardson, L. F., 1920: The supply of energy from and to atmospheric eddies. Proc. Roy. Soc. London, A97 , 354373.

  • Schumann, U., and T. Gerz, 1995: Turbulent mixing in stably stratified shear flows. J. Appl. Meteor., 34 , 3348.

  • Smedman, A-S., X. G. Larsen, U. Högstro, K. K. Kahma, and H. Pettersson, 2003: Effect of sea state on the momentum exchange over the sea during neutral conditions. J. Geophys. Res., 108 .3367, doi:10.1029/2002JC001526.

    • Search Google Scholar
    • Export Citation
  • Sorbjan, Z., 2006: Local structure of turbulence in stably-stratified boundary layers. J. Atmos. Sci., 63 , 15261537.

  • Tjernström, M., 1993: Turbulence length scales in stably stratified free shear flow analyzed from slant aircraft profiles. J. Appl. Meteor., 32 , 948963.

    • Search Google Scholar
    • Export Citation
  • Tjernström, M., 2005: The summer arctic boundary layer during the Arctic Ocean Experiment 2001 (AOE-2001). Bound.-Layer Meteor., 117 , 536.

    • Search Google Scholar
    • Export Citation
  • Uttal, T., and Coauthors, 2002: Surface heat budget of the Arctic Ocean. Bull. Amer. Meteor. Soc., 83 , 255275.

  • Van de Wiel, B. J. H., A. F. Moene, O. K. Hartogensis, H. A. R. De Bruin, and A. A. M. Holtslag, 2003: Intermittent turbulence in the stable boundary layer over land. Part III: A classification for observations during CASES-99. J. Atmos. Sci., 60 , 25092522.

    • Search Google Scholar
    • Export Citation
  • Vickers, D., and L. Mahrt, 2003: The cospectral gap and turbulent flux calculations. J. Atmos. Oceanic Technol., 20 , 660672.

  • Vickers, D., and L. Mahrt, 2006: A solution for flux contamination by mesoscale motions with very weak turbulence. Bound.-Layer Meteor., 118 , 431447.

    • Search Google Scholar
    • Export Citation
  • Vogelezang, D. H. P., and A. A. M. Holtslag, 1996: Evaluation and model impacts of alternative boundary-layer height formulations. Bound.-Layer Meteor., 81 , 245269.

    • Search Google Scholar
    • Export Citation
  • Wilczak, J. M., S. P. Oncley, and S. A. Stage, 2001: Sonic anemometer tilt correction algorithms. Bound.-Layer Meteor., 99 , 127150.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 698 319 26
PDF Downloads 556 200 22