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Strongly Nonlinear Flow over and around a Three-Dimensional Mountain as a Function of the Horizontal Aspect Ratio

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  • 1 Department of Meteorology and Geophysics, University of Innsbruck, Austria
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Abstract

The influence of the obstacle shape, expressed through the ratio of spanwise to streamwise extension β, on flow over and around a mesoscale mountain is examined numerically. The initial wind U as well as the buoyancy frequency N are constant; the earth’s rotation and surface friction are neglected. In these conditions the flow response depends primarily on the nondimensional mountain height Hm = hmN/U (where hm is the maximum mountain height) and the horizontal aspect ratio β. A regime diagram for the onset of wave breaking, lee vortex formation, and windward stagnation is compiled. When β is increased, smaller Hm are required for the occurrence of all three features. It is demonstrated that lee vortices can form with neither wave breaking above the lee slope nor upstream stagnation. For β ⩽ 0.5 a vortex pair can appear although the isentropes above the lee slope do not overturn for any Hm. For β > 1, on the other hand, lee vortex formation is triggered by wave breaking. On the windward side two distinct processes can lead to a complete blocking of the flow: the piling up of heavier air ahead of the barrier and the upstream propagation of columnar modes, which are generated by the wave breaking process for β > 1. “High-drag” states and “downslope windstorms” exist above the threshold of wave breaking as long as no lee vortices appear (or, at least, as long as they are very small). Hence, the interval of Hm where a high-drag state occurs becomes progressively larger for larger β. With the growth of lee vortices the maximum wind speed along the leeward slope is dampened. The normalized drag drops rapidly below its linear counterpart and asymptotically approaches zero.

Corresponding author address: Dr. Manfred H. Bauer, Zentralanstalt für Meteorologie und Geodynamik, Regionalstelle für Tirol und Vorarlberg, Fürstenweg 180, 6020 Innsbruck, Austria.

Email: manfred.bauer@zamg.ac.at

Abstract

The influence of the obstacle shape, expressed through the ratio of spanwise to streamwise extension β, on flow over and around a mesoscale mountain is examined numerically. The initial wind U as well as the buoyancy frequency N are constant; the earth’s rotation and surface friction are neglected. In these conditions the flow response depends primarily on the nondimensional mountain height Hm = hmN/U (where hm is the maximum mountain height) and the horizontal aspect ratio β. A regime diagram for the onset of wave breaking, lee vortex formation, and windward stagnation is compiled. When β is increased, smaller Hm are required for the occurrence of all three features. It is demonstrated that lee vortices can form with neither wave breaking above the lee slope nor upstream stagnation. For β ⩽ 0.5 a vortex pair can appear although the isentropes above the lee slope do not overturn for any Hm. For β > 1, on the other hand, lee vortex formation is triggered by wave breaking. On the windward side two distinct processes can lead to a complete blocking of the flow: the piling up of heavier air ahead of the barrier and the upstream propagation of columnar modes, which are generated by the wave breaking process for β > 1. “High-drag” states and “downslope windstorms” exist above the threshold of wave breaking as long as no lee vortices appear (or, at least, as long as they are very small). Hence, the interval of Hm where a high-drag state occurs becomes progressively larger for larger β. With the growth of lee vortices the maximum wind speed along the leeward slope is dampened. The normalized drag drops rapidly below its linear counterpart and asymptotically approaches zero.

Corresponding author address: Dr. Manfred H. Bauer, Zentralanstalt für Meteorologie und Geodynamik, Regionalstelle für Tirol und Vorarlberg, Fürstenweg 180, 6020 Innsbruck, Austria.

Email: manfred.bauer@zamg.ac.at

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