The Absolute Angular Momentum of Storms: Quasi–Lagrangian Diagnostics 2

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  • 1 Department of Meteorology, University of Wisconsin, Madison 53706
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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.

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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