Absolute angular momentum


In meteorology, absolute angular momentum refers to the angular momentum in an 'absolute' coordinate system.

Introduction

Angular momentum equates with the cross product of the position of a particle and its absolute linear momentum, equal to, the product of mass and velocity. Mathematically,

Definition

Absolute angular momentum sums the angular momentum of a particle or fluid parcel in a relative coordinate system and the angular momentum of that relative coordinate system.
Meteorologists typically express the three vector components of velocity . The magnitude of the absolute angular momentum per unit mass
where
The first term represents the angular momentum of the parcel with respect to the surface of the earth, which depends strongly on weather. The second term represents the angular momentum of the earth itself at a particular latitude.

Applications

In the shallow troposphere of the earth, one can approximate, the distance between the fluid parcel and the center of the earth approximately equal to the mean Earth radius:
where
At the North Pole and South Pole, no absolute angular momentum can exist. If a fluid parcel with no eastward wind speed originating at the equator conserves its angular momentum as it moves poleward, then its eastward wind speed increases dramatically: . After those substitutions,, or after further simplification,. Solution for gives. If , then.
The zonal pressure gradient and eddy stresses cause torque that changes the absolute angular momentum of fluid parcels.