Conservation of Angular Momentum

Conservation of Angular Momentum
• Angular momentum:
A = m×UTot×R
– UTot is total eastward wind speed as observed in an inertial frame:
UTot = U + Urot, where Urot is the speed due to the rotation of the
earth’s surface.
• In an inertial frame, angular momentum is conserved
(stays constant) in the absence of torques.
• Near the equator, torques are usually quite weak. Hence if
an air parcel moves poleward from the equator, UTot must
increase, while Urot decreases, hence its zonal velocity
(U) must increase.
Numerical Example
• An air parcel which is at rest with respect to the earth’s surface at
the equator moves to 20 degrees latitude while conserving its
angular momentum. What is its zonal velocity (U) relative to the
earth’s surface there?
• In the beginning, f = 0o, U = 0 ms-1. At the end f = 20o, U = ?
• Using the equation derived on the previous page based on the
conservation of angular momentum, we have
– Where f1, U1 are evaluated at the starting latitude, and f2, U2 are
evaluated at the ending latitude.
– Rewriting the above equation, we have
– For this problem f1 = 0, U1 = 0 ms-1, f2 = 20o. Substituting into the
equation, we have
• See also solved example on p.233 of Stull
Subtropical Jet and Polar Front Jet
• Near the equator, there is very little torques in the upper
troposphere and angular momentum is nearly conserved.
• Poleward moving air at the upper branch of Hadley
circulation will acquire a strong component of U (eastward
wind speed) due to conservation of angular momentum.
The jet formed by this process is called the subtropical jet.
• In the subtropics and extratropics, conservation of angular
momentum does not quite work, mainly because of torques
due to momentum transport by the waves (Stull p. 232243) – Note that Stull’s statement that angular momentum
is not conserved mainly due to pressure gradient and
Coriolis forces (p.233) is incorrect.
• In contrast to the subtropical jet, the polar front jet is formed
due to the strong temperature contrast between the
subtropical and polar air masses (see Fig. 10.12. More
about this in Ch. 11)