An Analytical Solution for Three-Dimensional Stationary Flows in the Atmospheric Boundary Layer over Terrain

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  • 1 Department of Meteorology, University of Utah, Salt Lake City 84112
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Abstract

An analytical solution to the Navier-Stokes equations for three-dimensional stationary flows of small Reynolds number in the atmospheric boundary layer over terrain is presented.

Analyses of the effects of topography, horizontal pressure gradient and Coriolis forces on the velocity distribution in the atmospheric boundary layer indicate that 1) the horizontal component of the velocity in the boundary layer turns right (left) with increasing height in the Northern (Southern) Hemisphere, 2) upward (downward) motion occurs on the windward (lee) side of the mountain, and 3) upward (downward) motion also occurs on the slope to the right (left) of the geostrophic wind in the Northern Hemisphere, whereas in the Southern Hemisphere downward (upward) motion occurs on the slope to the right (left) of the geostrophic wind.

Abstract

An analytical solution to the Navier-Stokes equations for three-dimensional stationary flows of small Reynolds number in the atmospheric boundary layer over terrain is presented.

Analyses of the effects of topography, horizontal pressure gradient and Coriolis forces on the velocity distribution in the atmospheric boundary layer indicate that 1) the horizontal component of the velocity in the boundary layer turns right (left) with increasing height in the Northern (Southern) Hemisphere, 2) upward (downward) motion occurs on the windward (lee) side of the mountain, and 3) upward (downward) motion also occurs on the slope to the right (left) of the geostrophic wind in the Northern Hemisphere, whereas in the Southern Hemisphere downward (upward) motion occurs on the slope to the right (left) of the geostrophic wind.

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