meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...

, absolute angular momentum refers to the

angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...

in an 'absolute' coordinate system ( absolute time and space).

Introduction

Angular momentum equates with the cross product of the

position (vector) In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point ''P'' in space in relation to an arbitrary reference origin ''O''. Usually denoted x, r, ...

of a particle (or fluid parcel) and its absolute linear momentum , equal to , the product of mass and velocity. Mathematically, :

\mathbf = \mathbf \times m \mathbf

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 (eastward, northward, and upward). The magnitude of the absolute angular momentum per unit mass :

\left, \frac\ = M = u r \cos (\phi) + \Omega r^2 \cos^2(\phi)

where * represents absolute angular momentum per unit mass of the fluid parcel (in ), * represents distance from the center of the earth to the fluid parcel (in ), * represents earth-relative eastward component of velocity of the fluid parcel (in ), * represents

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

(in ), and * represents angular rate of Earth's rotation (in , usually ). 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 (essentially constant at least on non-geological timescales).

Applications

In the shallow

troposphere The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. From ...

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 Earth radius (denoted as ''R''🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, deno ...

: :

M \approx u a \cos (\varphi) + \Omega a^2 \cos^2(\varphi)

where * represents

(in , usually ) * represents absolute angular momentum per unit mass of the fluid parcel (in ), * represents earth-relative eastward component of velocity of the fluid parcel (in ), * represents

(in ), and * represents angular rate of Earth's rotation (in , usually ). At the North Pole and South Pole (latitude ), no absolute angular momentum can exist ( because ). If a fluid parcel with no eastward wind speed () originating at the equator ( so ) 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 In atmospheric science, the pressure gradient (typically of air but more generally of any fluid) is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The p ...

and

eddy Eddie or Eddy may refer to: Science and technology *Eddy (fluid dynamics), the swirling of a fluid and the reverse current created when the fluid flows past an obstacle * Eddie (text editor), a text editor originally for BeOS and now ported to Lin ...

stresses cause

torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...

that changes the absolute angular momentum of fluid parcels.

References

{{Citation , last=Holton , first=James R. , last2=Hakim , first2=Gregory J. , year=2012 , title=An introduction to dynamic meteorology , version=5 , publisher=

Academic Press Academic Press (AP) is an academic book publisher founded in 1941. It was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes referen ...

, publication-place=Waltham, Massachusetts , isbn=978-0-12-384866-6 , pages=342–343 Angular momentum Meteorological concepts Rotation