Katabatic flow: a closed-form solution with spatially-varying eddy diffusivities

M. G. Giometto, R. Grandi, Jiannong Fang, Peter A Monkewitz, M. B. Parlange

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The Nieuwstadt closed-form solution for the stationary Ekman layer is generalized for katabatic flows within the conceptual framework of the Prandtl model. The proposed solution is valid for spatially-varying eddy viscosity and diffusivity (O’Brien type) and constant Prandtl number (Pr). Variations in the velocity and buoyancy profiles are discussed as a function of the dimensionless model parameters z0≡z^0N^2Prsin(α)|b^s|-1 and λ≡u^refN^Pr|b^s|-1, where z^ 0 is the hydrodynamic roughness length, N^ is the Brunt-Väisälä frequency, α is the surface sloping angle, b^ s is the imposed surface buoyancy, and u^ ref is a reference velocity scale used to define eddy diffusivities. Velocity and buoyancy profiles show significant variations in both phase and amplitude of extrema with respect to the classic constant K model and with respect to a recent approximate analytic solution based on the Wentzel-Kramers-Brillouin theory. Near-wall regions are characterized by relatively stronger surface momentum and buoyancy gradients, whose magnitude is proportional to z0 and to λ. In addition, slope-parallel momentum and buoyancy fluxes are reduced, the low-level jet is further displaced toward the wall, and its peak velocity depends on both z0 and λ.

Original languageEnglish
Pages (from-to)307-317
Number of pages11
JournalBoundary-Layer Meteorology
Issue number2
Publication statusPublished - 1 Feb 2017
Externally publishedYes


  • Prandtl model
  • Slope flows
  • Thermally-driven flows

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