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Why obvious formula is incorrect?
Many people think that the formula for the x and y components of the wind shear should be:
where cD is the drag coefficient, is the air density and ux and uy are the wind components.
This formula must be wrong as the vector doesn't even point in the same direction as the wind! Try it with ux=1 and uy=2.
Furthermore, this formula is not rotationally invariant. The magnitude of this vector depends on the coordinate system you choose (assuming wind is indeed a vector)!!