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I read that the rotation of Earth on it's axis caused the deflection of wind along the equator but the air and the Earth are moving together so where do the energy comes from to produce coriolis effect?

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The Coriolis force does not require energy. The Coriolis force causes an apparent deflection of the path of a moving object when viewed with respect to a rotating frame of reference. However, in an inertial reference frame the object is moving in a straight line at constant speed (assuming no other forces act on it) so no energy is required - the apparent deflection simply results from viewing the path of the object from a non-inertial reference frame.

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    $\begingroup$ Note also that, even in the rotating frame, the Coriolis force does no work: $P=\vec{v}\cdot\vec{F}_{\mathrm{Corr}}=\vec{v}\cdot\left(-2m\vec{\omega}\times\vec{v}\right)=0$. $\endgroup$
    – Buzz
    Commented Feb 5 at 14:20
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The big picture of wind movements on Earth is convection cells driven by the difference in temperature between equator and poles, which in turn is owing to the heat from the Sun, the spherical shape of Earth, and the effect of the tilted axis of rotation.

This convection leads to counter-moving high and low air masses going in the equator-to-poles directions, and the Coriolis effect pushes them aside. After that you have all the complications of land masses, varying sea temperature, and turbulence.

see also

https://rwu.pressbooks.pub/webboceanography/chapter/8-2-winds-and-the-coriolis-effect/#:~:text=The%20surface%20winds%20created%20by,left%20in%20the%20Southern%20Hemisphere.

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