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Donald R. Johnson and William K. Downey

Abstract

The azimuthally averaged transport and budget equations for a translating storm volume are derived in generalized coordinates. The mean and eddy lateral modes of transport by rotational and irrotational motion are contrasted in symmetric and asymmetric vortices. By contrasting the transport relations in isobaric, cartesian, and isentropic coordinates, the results establish that hydrostatic-rotational regimes of atmospheric motion are typified by eddy modes of transport in isobaric and cartesian coordinates, while both mean and eddy modes may be present in isentropic coordinates. This requirement for a “handover” from an eddy mode of transport in the hydrostatic-rotational environment of a vortex to a mean mode of transport via irrotational motion within a vortex is discussed.

Evidence for the existence of mean meridional circulation in isentropic coordinates for the Midwest extratropical cyclone of 22–24 April 1968 is presented. The inward mass transport in the lower troposphere and outward mass transport in the upper troposphere are coupled to vertical mass transport through isentropic surfaces associated with the release of latent heat in the middle troposphere.

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William K. Downey and Donald R. Johnson

Abstract

The budgets of mass, absolute angular momentum and kinetic energy for two model-generated cyclones and one anticyclone are examined using a sigma-coordinate framework which moves with the center of the MSL pressure extremum. The mass budgets for all three cases show a concentration of lateral mass transport in the surface boundary layer and at a level near 200 mb. The spin up of the low troposphere during cyclogenesis results from the dominance of the mean mode of lateral transport of absolute angular momentum. The spin up of the upper troposphere results from the combined influence of an inward eddy mode of lateral transport and vertical transport of absolute angular momentum. The eddy mode of lateral transport is determined by the configuration of the upper level flow (particularly jet streaks) and is enhanced by frontogenesis in the low and mid-troposphere as these regions spin up. The increase of kinetic energy in the low troposphere during cyclogenesis results from the dominance of local generation by cross-isobar flow toward the center of the developing vortex. In the upper troposphere the kinetic energy budget is not related uniquely to the development or decay of the surface cyclone. While the anticyclone, to a large extent, displays similar behavior to the cyclone, the eddy mode of lateral transport of angular momentum in the upper troposphere is not enhanced by lower level frontogenetic effects, as in the case of the cyclone.

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Donald R. Johnson and William K. Downey

Abstract

The transport and budget formulations developed for a translating system are used to study the mass and absolute angular momentum budgets of a Midwest cyclone. Using isentropic coordinates a mass circulation is isolated which transports angular momentum into the lower half of the tropospheric vortex and out of the upper half during the cyclone’s development and maturation. The occlusion process, characterized by the vertical development of the cyclone vortex into the middle and upper troposphere, occurred through a redistribution of angular momentum by an upward transport of angular momentum associated with the diabatic release of latent heat and an upward redistribution by internal pressure torques.

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Donald R. Johnson and William K. Downey

Abstract

The concept of absolute angular momentum and its time rate of change is developed for a translating vortex. Storm absolute angular momentum is defined to be the moment of the velocity about an origin translating with the center of the vortex. With this development in generalized coordinates, sources by transport and by internal torques are isolated. An integration over a storm volume reveals that for hydrostatic atmospheres, pressure, viscous, gravitational and inertial torques sum to boundary integrals.

After the vector relations are established for storm absolute angular momentum, the component along the storm axis of rotation through the vortex is determined. By a systematic analysis, the physical basis for a geostrophic torque in an asymmetric baroclinic vortex is established. The role of the geostrophic torque is to transfer angular momentum vertically in isentropic coordinates. Angular momentum is extracted from an isentropic layer with an inward geostrophic mode of mass transport and given to a layer with an outward geostrophic mode. The vertical transfer across the isentropic layer occurs through pressure stresses. Two examples for the Midwest cyclone of 23 April 1968 are presented. Finally, the modes of mean and eddy transport of earth and relative angular momentum as well as sources for the azimuthally averaged storm absolute angular momentum are studied in isobaric, cartesian, and isentropic coordinates.

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