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Earth's axis is North-South; then why does air moving towards or away from North or South experience Coriolis force, since $\vec\omega\times \vec v$ will be 0 in this case?

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    $\begingroup$ Because "north/south" is a different direction depending on where you are? If you're looking at a globe, 'north' at the equator points up to the ceiling. But north near the north pole is almost horizontal. $\endgroup$
    – knzhou
    Jul 24, 2016 at 17:25
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    $\begingroup$ To elaborate: $\vec{\omega}$ points towards the North Celestial Pole, not north along the Earth's surface. $\endgroup$
    – Michael Seifert
    Jul 25, 2016 at 18:03

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The Earth is spherical. So at non-zero latitudes, north-south direction is not parallel to the rotational axis. At equator, it's parallel, and you are right that at the equator, there is no Coriolis force acting on north-south moving objects.

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