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Norman A. Phillips

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Norman A. Phillips

Abstract

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Norman A. Phillips

Abstract

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Norman A. Phillips

Abstract

A study is made of the hydrostatic and quasi-geostrophic motion of two superimposed layers of homogeneous and incompressible fluids of different densities, these fluids being contained between two rigid, horizontal plates. It is found that the local time derivatives of the pressure heights in the two layers and the height of their interface can be determined from partial differential equations similar to those developed by Charney for the equivalent-barotropic model.

The possibility of using this two-layer model to represent motions of a continuously stratified, baroclinic troposphere is explored by comparing the behavior of small perturbations superimposed on a zonal current in the two-layer model with the results of the continuous baroclinic perturbation theories of Eady and Fjørtoft. The remarkable similarity of behavior of the two-layer and the continuous perturbation models, which appears from this comparison, suggests that if the initial flow patterns of the two-layer model are determined from the initial flow patterns of the troposphere in a specified manner the later flow patterns in the troposphere can be inferred from the forecast flow patterns of the two-layer model.

This hypothesis is subjected to a preliminary test by computing the instantaneous sea-level pressure tendencies and vertical motions (in the middle troposphere) at the beginning of the severe storm of 24–25 November 1950 over eastern North America. The order of magnitude of the predicted quantities and their general distribution agree in many respects with the observed pressure changes and hydrometeors, but some disagreement exists. It is suggested that a part of this disagreement may be due to the effect of large normal accelerations on the validity of the quasi-geostrophic assumption.

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Norman A. Phillips

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The flux of energy due to the pressure force acting across the boundary of a subsiding mass of cold air is investigated. It is shown that for mean values of the subsiding motion of the order of −1 cm sec−1 or larger, energy is transferred from the cold air to the surrounding atmosphere. A method is developed whereby this flux across a portion of a frontal surface can be calculated from a three-dimensional frontal analysis, and this technique is then applied to a specific example. The importance of the addition of this energy to the current flowing around the cold air is discussed, and it is suggested that at least a portion of the energy for the indirect circulations which are often observed downstream is supplied by the direct circulation involving the subsiding cold air mass.

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Yoshimitsu Ogura and Norman A. Phillips

Abstract

The approximate equations of motion derived by Batchelor in 1953 are derived by a formal scale analysis, with the assumption that the percentage range in potential temperature is small and that the time scale is set by the Brunt-Väisälä frequency. Acoustic waves are then absent. If the vertical scale is small compared to the depth of an adiabatic atmosphere, the system reduces to the (non-viscous) Boussinesq equations. The computation of the saturation vapor pressure for deep convection is complicated by the important effect of the dynamic pressure on the temperature. For shallow convection this effect is not important, and a simple set of reversible equations is derived.

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