Katabatic flow with Coriolis effect and gradually varying eddy diffusivity

Original Paper

Abstract

Katabatic flows over high-latitude long glaciers experience the Coriolis force. A sloped atmospheric boundary-layer (ABL) flow is addressed which partly diffuses upwards, and hence, becomes progressively less local. We present the analytical and numerical solutions for (U ,V, θ) depending on (z, t) in the katabatic flow, where U and V are the downslope and cross-slope wind components and θ is the potential temperature perturbation. A Prandtl model that accounts for the Coriolis effect, via f, does not approach a steady state, because V diffuses upwards in time; the rest, i.e., (U, θ), are similar to that in the classic Prandtl model. The V component behaves in a similar manner as the solution to the 1st Stokes (but inhomogeneous) problem. A WKB approach to the problem of the sloped ABL winds is outlined in the light of a modified Ekman-Prandtl model with gradually varying eddy diffusivity K(z). Ideas for parameterizing these high-latitude persistent flows in climate models are revealed.

Keywords

Low-level jet Prandtl model Strongly stable boundary layer 
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References

  1. Bender CM, Orszag SA (1978) Advanced mathematical methods for scientists and engineers. Mc Graw-Hill, Inc., New York, 593 ppGoogle Scholar
  2. Defant F (1949) Zur theorie der Hangwinde, nebst Bemerkungen zur Theorie der Bergund Talwinde. Arch Meteor Geophys Biokl Ser A1:421–450CrossRefGoogle Scholar
  3. Denby B (1999) Second-order modelling of turbulence in katabatic flows. Boundary-Layer Meteorol 92:67–100CrossRefGoogle Scholar
  4. Egger J (1990) Thermally forced flows: theory. In: Blumen W (ed) Atmospheric processes over complex terrain. American Meteorological Society, Boston, MA, pp 43–57Google Scholar
  5. Gordon AL, Comiso JC (1988) Polynyas in the Southern Ocean. Sci Am 258(6):90–97CrossRefGoogle Scholar
  6. Grisogono B (1995) A generalized Ekman layer profile within gradually varying eddy diffusivities. Quart J Roy Meteorol Soc 121:445–453CrossRefGoogle Scholar
  7. Grisogono B, Oerlemans J (2001a) Katabatic flow: analytic solution for gradually varying eddy diffusivities. J Atmos Sci 58:3349–3354CrossRefGoogle Scholar
  8. Grisogono B, Oerlemans J (2001b) A theory for the estimation of surface fluxes in simple katabatic flows. Quart J Roy Meteorol Soc 127:2725–2739CrossRefGoogle Scholar
  9. Grisogono B, Oerlemans J (2002) Justifying the WKB approximation in the pure katabatic flows. Tellus 54A:453–463Google Scholar
  10. Grisogono B (2003) Post-onset behaviour of the pure katabatic flow. Boundary-Layer Meteorol 107:157–175CrossRefGoogle Scholar
  11. King JC, Conneley WM, Derbyshire SH (2001) Sensitivity of modelled Antarctic climate to surface and boundary-layer flux parameterizations. Quart J Roy Meteorol Soc 127:779–794CrossRefGoogle Scholar
  12. Kundu PK, Cohen IM (2002) Fluid mechanics, 2nd ed. Academic Press, San Diego, Calif., London, 730 ppGoogle Scholar
  13. Mahrt L (1982) Momentum balance of gravity flows. J Atmos Sci 39:2701–2711CrossRefGoogle Scholar
  14. Munro DS (1989) Surface roughness and bulk heat transfer on a glacier: comparison with eddy correlation. J Glaciol 35:343–348Google Scholar
  15. Munro DS (2004) Revisiting bulk heat transfer on the Peyto glacier in light of the OG parameterization. J Glaciol 50:590–600Google Scholar
  16. Munro DS, Davies JA (1978) On fitting the log-linear model to wind speed and temperature profiles over a melting glacier. Boundary-Layer Meteorol 15:423–437CrossRefGoogle Scholar
  17. Oerlemans J (1998) The atmospheric boundary layer over melting glaciers. In: Holtslag AAM, Duynkerke PG (eds) Clear and cloudy boundary layers. Royal Netherlands Academy of Arts and Sciences, Place, VNE 48, ISBN 90-6984-235-1: 129–153Google Scholar
  18. Parish TR, Bromwich DH (1991) Continental-scale simulation of the Antarctic katabatic wind regime. J Climate 4:135–146CrossRefGoogle Scholar
  19. Parmhed O, Oerlemans J, Grisogono B (2004) Describing the surface fluxes in the katabatic flow on Breidamerkurjokull, Iceland. Quart J Roy Meteorol Soc 130:1137–1151CrossRefGoogle Scholar
  20. Parmhed O, Kos I, Grisogono B (2005) An improved Ekman layer approximation for smooth eddy diffusivity profiles. Boundary-Layer Meteorol 115:399–407CrossRefGoogle Scholar
  21. Renfrew IA, Anderson PS (2002) The surface climatology of an ordinary katabatic wind regime in Coats Land, Antarctica. Tellus 54A:463–484Google Scholar
  22. Renfrew IA (2004) The dynamics of idealized katabatic flow over a moderate slope and ice shelf. Quart J Roy Meteorol Soc 130:1023–1045CrossRefGoogle Scholar
  23. Renfrew IA, Anderson PS (2006) Profiles of katabatic flow in summer and winter over coats land, Antarctica. Quart J Roy Meteorol Soc 132:779–882CrossRefGoogle Scholar
  24. Söderberg S, Parmhed O (2006) Numerical modelling of katabatic flow over a melting outflow glacier. Boundary-Layer Meteorol 120:509–534CrossRefGoogle Scholar
  25. Stiperski I, Kavčič I, Grisogono B, Durran DR (2007) Including Coriolis effects in the Prandtl model for katabatic flow. Quart J Roy Meteorol Soc 133:101–106CrossRefGoogle Scholar
  26. Van den Broeke MR, van Lipzig NPM, van Meijgaard E (2002) Momentum budget of the East-Antarctic atmospheric boundary layer: results of a regional climate model. J Atmos Sci 59:3117–3129CrossRefGoogle Scholar
  27. Weng W, Taylor PA (2003) On modelling the one-dimensional atmospheric boundary layer. Boundary-Layer Meteorol 107:371–400CrossRefGoogle Scholar
  28. Zilitinkevich S, Savijärvi H, Baklanov A, Grisogono B, Myrberg K (2006) Forthcoming meetings on planetary boundary-layer theory, modelling and applications. Boundary-Layer Meteorol 119:591–593CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Geophysics, Faculty of ScienceUniversity of ZagrebZagrebCroatia
  2. 2.Department of Geophysics, Faculty of ScienceUniversity of ZagrebZagrebCroatia

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