Katabatic Flow: A Closed-Form Solution with Spatially-Varying Eddy Diffusivities

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• 作者：M. G. Giometto ; R. Grandi ; J. Fang ; P. A. Monkewitz…
• 关键词：Prandtl model ; Slope flows ; Thermally ; driven flows
• 刊名：Boundary-Layer Meteorology
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：162
• 期：2
• 页码：307-317
• 全文大小：
• 刊物类别：Earth and Environmental Science
• 刊物主题：Atmospheric Sciences; Meteorology; Atmospheric Protection/Air Quality Control/Air Pollution;
• 出版者：Springer Netherlands
• ISSN：1573-1472
• 卷排序：162

文摘

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 \(z_0 \equiv \hat{z}_0 \hat{N}^2 Pr \sin {(\alpha )} |\hat{b}_\mathrm{s} |^{-1}\) and \(\lambda \equiv \hat{u}_{\mathrm{ref}}\hat{N} \sqrt{Pr} |\hat{b}_\mathrm{s} |^{-1}\), where \(\hat{z}_0\) is the hydrodynamic roughness length, \(\hat{N}\) is the Brunt-Väisälä frequency, \(\alpha \) is the surface sloping angle, \(\hat{b}_\mathrm{s}\) is the imposed surface buoyancy, and \(\hat{u}_{\mathrm{ref}}\) 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 \(\textit{K}\) 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 \(\lambda \). 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 \(\lambda \).