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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)