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David D. Houghton
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David Houghton and Warren Washington

Abstract

The problem of obtaining a realistic balanced relationship between the pressure field and the nondivergent velocity is examined for a global primitive equation model. Both a theoretical discussion of the atmospheric adjustment process and actual numerical examples of initialization are used to show that pressure at low latitudes must be the derived quantity and not the input data. For the two-layer version of the NCAR general circulation model, the latitudes of 27½N and S are shown to be acceptable for separating the equatorial belt, where velocity is used as input data, from regions of higher latitudes, where pressure is used as input data.

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David D. Houghton
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David D. Houghton
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David D. Houghton

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David D. Houghton
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David D. Houghton

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Calculations are made with the NCAR six-layer general circulation model to determine the time evolution of errors initially confined to a region 4000 km in diameter superimposed upon real global data. Three experiments are made to distinguish between the effects of an error located initially on the northern or southern sides of the jet stream or in the tropical area. Results show that the largest error centers generally evolve in the jet stream; however, the propagation rate is much less than advection effects would suggest. Coverage of the Northern Hemisphere is accomplished as much by propagation across the north pole and via the tropical belt as it is via the jet stream. It is not complete even after seven days. As a whole the tropics are more sensitive than the middle latitudes to initial errors. Cross-equatorial effects are most pronounced at and just east of the initial longitude of the error.

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David D. Houghton

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An incompressible, stratified, hydrostatic, inviscid fluid model is used to demonstrate non-linear effects in the interaction of finite amplitude gravity waves. A statically stable density stratification is approximated by the superposition of ten homogeneous fluid layers with a very deep layer on top. Computations are made using a two-step Lax-Wendroff finite difference system. The solutions reveal intrawave distortions comparable to those predicted by analytical studies of one- and two-layer fluid models. During the interaction of two waves, the solutions show overall changes in wave speed which are of the same magnitude as the variations in wave speed that cause the intrawave distortions. These changes are related differently to the horizontal fluid velocities in the waves.

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David D. Houghton

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A quasi-Lagrangian formulation for an inviscid barotropic fluid is presented and shown to afford a convenient basis for analysis of certain ageostrophic jet flows. Material fines serve as the references to delineate the north-south variations in the fluid, and Eulerian representation is used in the east west direction. Several desirable features are shown for the use of material lines in this manner. First, by orienting the lines approximately parallel to the jet axis, flows with finite horizontal curvature may be represented simply. This is illustrated by a development with east-west variations represented by only two harmonies and a mean. The solution of this semi-spectra model agrees closely with a non-spectral numerical solution for over three days. Second, the Lagrangian movement of the material lines gives an indication of non-linear adjustment motions and demonstrates a mixing in the fluid.

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Kenneth B. Mielke and David D. Houghton

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