• Bannon, P. R., and T. L. Salem, 1995: Aspects of the baroclinic boundary layer. J. Atmos. Sci., 52, 574596, https://doi.org/10.1175/1520-0469(1995)052<0574:AOTBBL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Beare, R. J., and M. J. P. Cullen, 2010: A semi-geostrophic model incorporating well-mixed boundary layers. Quart. J. Roy. Meteor. Soc., 136, 906917, https://doi.org/10.1002/qj.612.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berger, B. M., and B. Grisogono, 1998: The baroclinic variable eddy viscosity Ekman layer, an approximate analytical solution. Bound.-Layer Meteor., 87, 363380, https://doi.org/10.1023/A:1001076030166.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brown, A. R., 1996: Large-eddy simulation and parametrization of the baroclinic boundary-layer. Quart. J. Roy. Meteor. Soc., 122, 17791798, https://doi.org/10.1002/qj.49712253603.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Constantin, A., and R. S. Johnson, 2019: Atmospheric Ekman flows with variable eddy viscosity. Bound.-Layer Meteor., 170, 395414, https://doi.org/10.1007/s10546-018-0404-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ekman, V. M., 1905: On the influence of the Earth’s rotation on ocean-currents. Ark. Mat. Astron. Fys., 2, 1–52.

  • Gauthier, P., M. Buehner, and L. Fillion, 1998: Background-error statistics modelling in a 3D variational data assimilation scheme: Estimation and impact on the analyses. Proc. ECMWF Workshop, Reading, England, ECMWF, 131–145.

  • Ghannam, K., and E. Bou-Zeid, 2020: Baroclinicity and directional shear explain departures from the logarithmic wind profile. Quart. J. Roy. Meteor. Soc., 147, 443464, https://doi.org/10.1002/qj.3927.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grisogono, B., 1995: A generalized Ekman layer profile with gradually varying eddy diffusivities. Quart. J. Roy. Meteor. Soc., 121, 445453, https://doi.org/10.1002/qj.49712152211.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gutman, L. N., 1972: Introduction to the Nonlinear Theory of Mesoscale Meteorological Processes. Israel Program for Scientific Translations, 224 pp.

  • Hess, M. M., M. Hieber, A. Mahalov, and J. Saal, 2010: Nonlinear stability of Ekman boundary layers. Bull. London Math. Soc., 42, 691706, https://doi.org/10.1112/blms/bdq029.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holton, J. R., 1992: An Introduction to Dynamic Meteorology. Academic Press, 507 pp.

  • Jiang, Q., 2012a: A linear theory of three-dimensional land–sea breezes. J. Atmos. Sci., 69, 18901909, https://doi.org/10.1175/JAS-D-11-0137.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jiang, Q., 2012b: On offshore propagating diurnal waves. J. Atmos. Sci., 69, 15621581, https://doi.org/10.1175/JAS-D-11-0220.1.

  • Kobe, H., 2014: Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluid. American Mathematical Society, 127 pp.

  • Li, Y., and J. Chao, 2016: An analytical solution for three-dimensional sea–land breeze. J. Atmos. Sci., 73, 4154, https://doi.org/10.1175/JAS-D-14-0329.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, J. C., and C. Gerbig, 2005: Accounting for the effect of transport errors on tracer inversions. Geophys. Res. Lett., 32, L01802, https://doi.org/10.1029/2004GL021127.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mahrt, L. J., and W. Schwerdtfeger, 1970: Ekman spirals for exponential thermal wind. Bound.-Layer Meteor., 1, 137145, https://doi.org/10.1007/BF00185735.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Makar, P. A., R. Nissen, A. Teakes, J. Zhang, M. D. Moran, H. Yau, and C. diCenzo, 2014: Turbulent transport, emissions and the role of compensating errors in chemical transport models. Geosci. Model Dev., 7, 10011024, https://doi.org/10.5194/gmd-7-1001-2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Momen, M., E. Bou-Zeid, M. B. Parlange, and M. Giometto, 2018: Modulation of mean wind and turbulence in the atmospheric boundary layer by baroclinicity. J. Atmos. Sci., 75, 37973821, https://doi.org/10.1175/JAS-D-18-0159.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer-Verlag, 710 pp.

    • Crossref
    • Export Citation
  • Pedlosky, J., 2008: On the weakly nonlinear Ekman layer: Thickness and flux. J. Atmos. Sci., 38, 13341339, https://doi.org/10.1175/2007JPO3830.1.

    • Search Google Scholar
    • Export Citation
  • Plate, J. E., 1987: Aerodynamic characteristics of atmospheric boundary layers. U.S. Dept. of Energy Rep., 190 pp.

  • Schaefer, J. T., 1973: On the solution of the generalized Ekman equation. Mon. Wea. Rev., 101, 535537, https://doi.org/10.1175/1520-0493(1973)101<0535:OTSOTG>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shapiro, A., and E. Fedorovich, 2008: Coriolis effects in homogeneous and inhomogeneous katabatic flows. Quart. J. Roy. Meteor. Soc., 134, 353370, https://doi.org/10.1002/qj.217.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp.

    • Crossref
    • Export Citation
  • Sun, J., and Coauthors, 2015: Review of wave-turbulence interactions in the stable atmospheric boundary layer. Rev. Geophys., 53, 956993, https://doi.org/10.1002/2015RG000487.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yamada, T., 1976: On the similarity functions A, B and C of the planetary boundary layer. J. Atmos. Sci., 33, 781793, https://doi.org/10.1175/1520-0469(1976)033<0781:OTSFAO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, X., 1991: A study of nonhydrostatic effects in idealized sea breeze systems. Bound.-Layer Meteor., 54, 183208, https://doi.org/10.1007/BF00119419.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 195 195 7
Full Text Views 56 51 1
PDF Downloads 72 69 2

Coupling of Wind and Potential Temperature in an Ekman Model in the Stratified Atmospheric Boundary Layer

View More View Less
  • 1 aEnvironment and Climate Change Canada, Toronto, Ontario, Canada
  • | 2 bKey Laboratory of Regional Climate-Environment for Temperate East Asia, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
Restricted access

Abstract

A linear Ekman model in the stratified atmospheric boundary layer (ABL) is proposed based on the steady-state version of the linearized three-dimensional primitive equations with the inclusion of the vertical diffusivity. Due to the inclusion of the potential temperature equation and hydrostatic equation, pressure and potential temperature couple with wind in the proposed model, and thus are not arbitrarily specified variables as in previous studies on the baroclinicity in the Ekman model. The extended thermal wind balance equation and the Ekman potential vorticity equation are derived to describe the coupling. The two equations, along with the equation describing the constraint on potential temperature, are employed to derive the analytical solutions of the proposed Ekman model. Because potential temperature is not a specified variable but part of the solution, the derived analytical solutions have very different forms from those derived in previous studies. The differences illustrate the impact of the inclusion of the potential temperature equation and hydrostatic equation on wind, pressure, and potential temperature in the proposed Ekman model. It is found that the computed wind profiles based on the proposed model can capture some important features of the observed wind profiles.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Shuzhan Ren, Shuzhan.Ren@canada.ca

Abstract

A linear Ekman model in the stratified atmospheric boundary layer (ABL) is proposed based on the steady-state version of the linearized three-dimensional primitive equations with the inclusion of the vertical diffusivity. Due to the inclusion of the potential temperature equation and hydrostatic equation, pressure and potential temperature couple with wind in the proposed model, and thus are not arbitrarily specified variables as in previous studies on the baroclinicity in the Ekman model. The extended thermal wind balance equation and the Ekman potential vorticity equation are derived to describe the coupling. The two equations, along with the equation describing the constraint on potential temperature, are employed to derive the analytical solutions of the proposed Ekman model. Because potential temperature is not a specified variable but part of the solution, the derived analytical solutions have very different forms from those derived in previous studies. The differences illustrate the impact of the inclusion of the potential temperature equation and hydrostatic equation on wind, pressure, and potential temperature in the proposed Ekman model. It is found that the computed wind profiles based on the proposed model can capture some important features of the observed wind profiles.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Shuzhan Ren, Shuzhan.Ren@canada.ca
Save