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A theory of topographically bound balanced motions and application to atmospheric low-level jets




Silvers, Levi Glenn, author
Schubert, Wayne H., advisor
Randall, David A., committee member
Thompson, David W. J., committee member
Eykholt, Richard E., committee member

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The response of a stratified fluid to forcing from the lower boundary is studied both analytically and numerically. The lower boundary forces a flow field through orographic obstacles and potential vorticity anomalies. It is argued that these mechanisms contribute to the maintenance of low-level jets that are observed regularly in the vicinity of the Rocky Mountains and the Andes. Low-level jets function as one of the primary mechanisms through which topography and surface heating influence regional and global climates. On the ƒ-plane a horizontal transform of the governing equation for potential vorticity leads to a vertical structure equation that is solved using Green's functions. On the sphere a vertical transform of this system leads to a horizontal structure equation that is solved using spheroidal harmonics. These analytic solutions lead to a conceptually simple picture of the fluid response to forcing. However, these derivations only lead to closed analytic solutions for the case of an isentropic lower boundary. When the lower boundary is not isentropic a massless layer must be included in the domain and the solution is then found iteratively. For the cases including a massless layer the system is approximated using finite differences and solved with an over-relaxation procedure. Solutions are presented for the geostrophically balanced, steady response of the fluid to three idealized lower boundaries. An isentropic ridge is studied to determine the role non-heated orography plays on the wind field. Then a flat heated lower boundary and a non-isentropic ridge are studied. The cases with a heated lower surface result in a cyclonic wind field that is anchored over the topography. Observations show a prominent cyclonic wind field centered on both the Rocky Mountains and the Andes. The idealized cases studied in this work allow for the examination of fluid systems analogous to the Great Plains low-level jet and the South American LLJ. Both the mean behavior of these jets and their variability have important climatological and economic impacts on the plains regions of North and South America. One of the purposes of this work is to interpret particular low-level jet systems as part of the orographically bound, balanced motion associated with the potential vorticity anomalies produced by solar heating. This research proposes the jets on opposite sides of the mountains to be a single response to potential vorticity forcing that is the result of radiative heating on the Rockies and the Andes. The orographically bound circulations can also impact monsoon circulations. Although the importance of heated orography to LLJs has tended to be downplayed in the literature, it is shown here to be a significant component in the maintenance of LLJs.


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potential vorticity
low-level jets


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