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.
After Wentzel, Kramers and Brillouin, who popularized the method in theoretical physics.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Bender CM, Orszag SA (1978) Advanced mathematical methods for scientists and engineers. Mc Graw-Hill, Inc., New York, 593 pp
Defant F (1949) Zur theorie der Hangwinde, nebst Bemerkungen zur Theorie der Bergund Talwinde. Arch Meteor Geophys Biokl Ser A1:421–450
Denby B (1999) Second-order modelling of turbulence in katabatic flows. Boundary-Layer Meteorol 92:67–100
Egger J (1990) Thermally forced flows: theory. In: Blumen W (ed) Atmospheric processes over complex terrain. American Meteorological Society, Boston, MA, pp 43–57
Gordon AL, Comiso JC (1988) Polynyas in the Southern Ocean. Sci Am 258(6):90–97
Grisogono B (1995) A generalized Ekman layer profile within gradually varying eddy diffusivities. Quart J Roy Meteorol Soc 121:445–453
Grisogono B, Oerlemans J (2001a) Katabatic flow: analytic solution for gradually varying eddy diffusivities. J Atmos Sci 58:3349–3354
Grisogono B, Oerlemans J (2001b) A theory for the estimation of surface fluxes in simple katabatic flows. Quart J Roy Meteorol Soc 127:2725–2739
Grisogono B, Oerlemans J (2002) Justifying the WKB approximation in the pure katabatic flows. Tellus 54A:453–463
Grisogono B (2003) Post-onset behaviour of the pure katabatic flow. Boundary-Layer Meteorol 107:157–175
King JC, Conneley WM, Derbyshire SH (2001) Sensitivity of modelled Antarctic climate to surface and boundary-layer flux parameterizations. Quart J Roy Meteorol Soc 127:779–794
Kundu PK, Cohen IM (2002) Fluid mechanics, 2nd ed. Academic Press, San Diego, Calif., London, 730 pp
Mahrt L (1982) Momentum balance of gravity flows. J Atmos Sci 39:2701–2711
Munro DS (1989) Surface roughness and bulk heat transfer on a glacier: comparison with eddy correlation. J Glaciol 35:343–348
Munro DS (2004) Revisiting bulk heat transfer on the Peyto glacier in light of the OG parameterization. J Glaciol 50:590–600
Munro DS, Davies JA (1978) On fitting the log-linear model to wind speed and temperature profiles over a melting glacier. Boundary-Layer Meteorol 15:423–437
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: 129–153
Parish TR, Bromwich DH (1991) Continental-scale simulation of the Antarctic katabatic wind regime. J Climate 4:135–146
Parmhed O, Oerlemans J, Grisogono B (2004) Describing the surface fluxes in the katabatic flow on Breidamerkurjokull, Iceland. Quart J Roy Meteorol Soc 130:1137–1151
Parmhed O, Kos I, Grisogono B (2005) An improved Ekman layer approximation for smooth eddy diffusivity profiles. Boundary-Layer Meteorol 115:399–407
Renfrew IA, Anderson PS (2002) The surface climatology of an ordinary katabatic wind regime in Coats Land, Antarctica. Tellus 54A:463–484
Renfrew IA (2004) The dynamics of idealized katabatic flow over a moderate slope and ice shelf. Quart J Roy Meteorol Soc 130:1023–1045
Renfrew IA, Anderson PS (2006) Profiles of katabatic flow in summer and winter over coats land, Antarctica. Quart J Roy Meteorol Soc 132:779–882
Söderberg S, Parmhed O (2006) Numerical modelling of katabatic flow over a melting outflow glacier. Boundary-Layer Meteorol 120:509–534
Stiperski I, Kavčič I, Grisogono B, Durran DR (2007) Including Coriolis effects in the Prandtl model for katabatic flow. Quart J Roy Meteorol Soc 133:101–106
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 59:3117–3129
Weng W, Taylor PA (2003) On modelling the one-dimensional atmospheric boundary layer. Boundary-Layer Meteorol 107:371–400
Zilitinkevich S, Savijärvi H, Baklanov A, Grisogono B, Myrberg K (2006) Forthcoming meetings on planetary boundary-layer theory, modelling and applications. Boundary-Layer Meteorol 119:591–593
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Kavčič, I., Grisogono, B. (2007). Katabatic flow with Coriolis effect and gradually varying eddy diffusivity. In: Baklanov, A., Grisogono, B. (eds) Atmospheric Boundary Layers. Springer, New York, NY. https://doi.org/10.1007/978-0-387-74321-9_15
Download citation
DOI: https://doi.org/10.1007/978-0-387-74321-9_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-74318-9
Online ISBN: 978-0-387-74321-9
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)