(a) Assume that there is no wind velocity in the east-west direction around the point X. What is the expression for the east-west wind velocity uY at the points Y? Convention: positive velocities point from west to east.
(The angular velocity of the Earth about its spin axis is Ω, the radius of the Earth is a, and the thickness of the atmosphere is much smaller than a.)
Given constants:
The schematic below shows the Hadley circulation in the Earth's tropical atmosphere around the spring equinox. Air rises from the equator and moves poleward in both hemispheres before descending in the subtropics at latitudes ±φd (where positive and negative latitudes refer to the northern and southern hemisphere respectively). The angular momentum about the Earth's spin axis is conserved for the upper branches of the circulation (enclosed by the dashed oval). Note that the schematic is not drawn to scale.
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