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Semi-geostrophic Flow over Orography in a Stratified Rotating Atmosphere. Part I: Some Aspects of Nonuniform Flow over an Isolated Obstacle

Brian D. GrossDepartment of Astrophysical, Planetary, and Atmospheric Sciences, University of Colorado, Boulder, Colorado

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William BlumenDepartment of Astrophysical, Planetary, and Atmospheric Sciences, University of Colorado, Boulder, Colorado

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Abstract

Steady, three-dimensional, inviscid flow over orography is examined by means of a semi-geostrophic model. A nonuniform basic current, represented by a deformation flow, is employed. A constant Coriolis parameters ƒ and uniform potential vorticity (constant Brunt-Väisälä frequency N) characteristic this model. A nondimensional mountain height ε/D ≲ 0.5, based on the deformation depth D ∼ 3 × 103 m, and a Rossby number Ro ≲ 0.3, based on the mountain breadth L ≳ 3.5 × 105 m, provide constraints on the flow field. Analytic solutions are represented in geostrophic coordinate space as the sum of the deformation flow and an anticyclonic mountain vortex. Although the two solutions are independent in geostrophic coordinate space, these flows are coupled nonlinearly in the transformation to physical coordinate space.

A solution is presented for flow over an isolated mountain. The decomposition of the physical space solution into fields of translation, rotation, divergence, and deformation forms the basis of the present analysis. The principal features associated with the solution are a region of relatively strong cyclonic vorticity in the lee of the mountain, accompanied by a region of convergence, and a region of weaker cyclonic vorticity on the windward slope, accompanied by a region of divergence. It is the ageostrophic component of the vorticity that provides these cyclonic centers, which are associated with enhanced deformation upstream and downstream of the peak. Further, the lee-side cyclonic vorticity enhancement is associated with the advection of geostrophic deformation, a feature of semi-geostrophic models that is absent in quasi-geostrophic models. By displacing the basic current's axis of dilatation into the lee of the obstacle, a deformation advection pattern is established that enhances the lee-side cyclonic vorticity center. The uniform flow solution is characterized by a single band of cyclonic vorticity north of the peak. This pattern is also established by the advection of geostrophic deformation. The possible relevance of the present model results to physical mechanisms that promote the initiation of lee cyclogenesis is discussed.

Abstract

Steady, three-dimensional, inviscid flow over orography is examined by means of a semi-geostrophic model. A nonuniform basic current, represented by a deformation flow, is employed. A constant Coriolis parameters ƒ and uniform potential vorticity (constant Brunt-Väisälä frequency N) characteristic this model. A nondimensional mountain height ε/D ≲ 0.5, based on the deformation depth D ∼ 3 × 103 m, and a Rossby number Ro ≲ 0.3, based on the mountain breadth L ≳ 3.5 × 105 m, provide constraints on the flow field. Analytic solutions are represented in geostrophic coordinate space as the sum of the deformation flow and an anticyclonic mountain vortex. Although the two solutions are independent in geostrophic coordinate space, these flows are coupled nonlinearly in the transformation to physical coordinate space.

A solution is presented for flow over an isolated mountain. The decomposition of the physical space solution into fields of translation, rotation, divergence, and deformation forms the basis of the present analysis. The principal features associated with the solution are a region of relatively strong cyclonic vorticity in the lee of the mountain, accompanied by a region of convergence, and a region of weaker cyclonic vorticity on the windward slope, accompanied by a region of divergence. It is the ageostrophic component of the vorticity that provides these cyclonic centers, which are associated with enhanced deformation upstream and downstream of the peak. Further, the lee-side cyclonic vorticity enhancement is associated with the advection of geostrophic deformation, a feature of semi-geostrophic models that is absent in quasi-geostrophic models. By displacing the basic current's axis of dilatation into the lee of the obstacle, a deformation advection pattern is established that enhances the lee-side cyclonic vorticity center. The uniform flow solution is characterized by a single band of cyclonic vorticity north of the peak. This pattern is also established by the advection of geostrophic deformation. The possible relevance of the present model results to physical mechanisms that promote the initiation of lee cyclogenesis is discussed.

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