Advection of a Passive Scalar over a Finite-Amplitude Ridge in a Stratified Rotating Atmosphere

William Blumen Department of Astrophysical, Planetary and Atmospheric Sciences, University of Colorado, Boulder, CO 80309

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Brian D. Gross Department of Astrophysical, Planetary and Atmospheric Sciences, University of Colorado, Boulder, CO 80309

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Abstract

A basic uniform current flows over a two-dimensional finite-amplitude ridge of characteristic male L and amplitude ε. The disturbance field is constrained by the geostrophic momentum approximation, by uniform potential vorticity (uniform Brunt-Väisälä frequency N) and by the constant Coriolis parameter f. Solutions are represented as the sum of a steady disturbance, recently found by Blumen and Gross, and a relatively weak translating disturbance. The translating disturbance is a passive scalar that is advected by the steady mountain circulation. The propagation speed over a ridge in an unbounded atmosphere is shown to increase with the parameter ε/D, where D=fL/N is the deformation depth. The steady mountain circulation produces frontolysis in the disturbance field on the windward slope and frontogenesis on the leeward slope. These frontogenetical features are primarily controlled by the steady horizontal velocity, which is divergent on the windward side and convergent in the Ice. The steady mountain circulation also disrupts the initial state of thermal wind balance imposed on the disturbance potential temperature and cross-stream velocity fields. An approximate evaluation of the ageostrophic circulation required to restore thermal wind balance is provided. This circulation, which may be direct or indirect, is related to the spatial structure of the initial disturbance and to its relative position on the ridge. Comparison with a related study by Bannon, and an evaluation of the principal limitations of both models complete the study.

Abstract

A basic uniform current flows over a two-dimensional finite-amplitude ridge of characteristic male L and amplitude ε. The disturbance field is constrained by the geostrophic momentum approximation, by uniform potential vorticity (uniform Brunt-Väisälä frequency N) and by the constant Coriolis parameter f. Solutions are represented as the sum of a steady disturbance, recently found by Blumen and Gross, and a relatively weak translating disturbance. The translating disturbance is a passive scalar that is advected by the steady mountain circulation. The propagation speed over a ridge in an unbounded atmosphere is shown to increase with the parameter ε/D, where D=fL/N is the deformation depth. The steady mountain circulation produces frontolysis in the disturbance field on the windward slope and frontogenesis on the leeward slope. These frontogenetical features are primarily controlled by the steady horizontal velocity, which is divergent on the windward side and convergent in the Ice. The steady mountain circulation also disrupts the initial state of thermal wind balance imposed on the disturbance potential temperature and cross-stream velocity fields. An approximate evaluation of the ageostrophic circulation required to restore thermal wind balance is provided. This circulation, which may be direct or indirect, is related to the spatial structure of the initial disturbance and to its relative position on the ridge. Comparison with a related study by Bannon, and an evaluation of the principal limitations of both models complete the study.

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