## Abstract

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 z_{0} 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 z_{0} and λ.

Original language | English |
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Pages (from-to) | 307-317 |

Number of pages | 11 |

Journal | Boundary-Layer Meteorology |

Volume | 162 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Feb 2017 |

Externally published | Yes |

## Keywords

- Prandtl model
- Slope flows
- Thermally-driven flows