Revisiting Valley Flows

Alan Shapiro School of Meteorology, University of Oklahoma, Norman, Oklahoma

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Matheus Gomes School of Meteorology, University of Oklahoma, Norman, Oklahoma

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Abstract

We introduce a quasi-analytical model of thermally induced flows in valleys with sloping floors, a feature absent from most theoretical valley wind studies. One of the main theories for valley winds—the valley volume effect—emerged from field studies in the European Alps in the 1930s and 1940s. According to that theory, along-valley variations in the heating rate arising from variations in valley geometry generated the pressure gradient that drove the valley wind. However, while those early studies were conducted in valleys with relatively flat (horizontal) floors, valleys with sloping floors are ubiquitous and presumably affected directly by slope buoyancy (Prandtl mechanism). Our model is developed for the Prandtl setting of steady flow of a stably stratified fluid over a heated planar slope, but with the slope replaced by a periodic system of sloping valleys. As the valley characteristics do not change along the valley, there is no valley volume effect. The 2D linearized Boussinesq governing equations are solved using Fourier methods. Examples are explored for symmetric (with respect to valley axis) valleys subject to symmetric and antisymmetric heating. The flows are 2D, but the trajectories are intrinsically 3D. For symmetric heating, trajectories are of two types: i) helical trajectories of parcels trapped within one of two counterrotating vortices straddling the valley axis and ii) trajectories of environmental parcels that approach the valley horizontally, move under and then over the helical trajectories, and then return to the environment. For antisymmetric heating, three types of trajectories are identified.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Alan Shapiro, ashapiro@ou.edu

Abstract

We introduce a quasi-analytical model of thermally induced flows in valleys with sloping floors, a feature absent from most theoretical valley wind studies. One of the main theories for valley winds—the valley volume effect—emerged from field studies in the European Alps in the 1930s and 1940s. According to that theory, along-valley variations in the heating rate arising from variations in valley geometry generated the pressure gradient that drove the valley wind. However, while those early studies were conducted in valleys with relatively flat (horizontal) floors, valleys with sloping floors are ubiquitous and presumably affected directly by slope buoyancy (Prandtl mechanism). Our model is developed for the Prandtl setting of steady flow of a stably stratified fluid over a heated planar slope, but with the slope replaced by a periodic system of sloping valleys. As the valley characteristics do not change along the valley, there is no valley volume effect. The 2D linearized Boussinesq governing equations are solved using Fourier methods. Examples are explored for symmetric (with respect to valley axis) valleys subject to symmetric and antisymmetric heating. The flows are 2D, but the trajectories are intrinsically 3D. For symmetric heating, trajectories are of two types: i) helical trajectories of parcels trapped within one of two counterrotating vortices straddling the valley axis and ii) trajectories of environmental parcels that approach the valley horizontally, move under and then over the helical trajectories, and then return to the environment. For antisymmetric heating, three types of trajectories are identified.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Alan Shapiro, ashapiro@ou.edu
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