Does the Coriolis Effect Determine the Direction of Curl in Hemispheres?

[Keru]

Two quick questions. Does the Coriolis effect mean that in the northern hemisphere the curl will always have a negative value and in the southern hemisphere a positive one? Is the curl in the eye of the cyclones equal to zero?
Thanks.

 

[Matterwave]

The Coriolis effect is proportional to $-2(\vec{\omega}\times\vec{v})$ where $\vec{\omega}$ is pointing up out of the North pole, along the axis of Earth's rotation. Whether this curl is positive or negative depends on the vector $\vec{v}$ and can not be generalized to "northern vs southern hemisphere" effects. However, if something (say a bullet) is moving initially along a straight line in the Northern hemisphere, its trajectory will be deflected (by the Coriolis force) in a clockwise direction, while in the Southern hemisphere the trajectory would be deflected in a counter-clock-wise direction.

 

[Meir Achuz]

By "curl" do you mean \nabla\times or something else?

 

[Matterwave]

Haha! I had a brain fart and associated a cross product $\vec{\omega}\times\vec{v}$ as a curl. Now I'm not sure what the OP is asking.

 

[Keru]

By "curl" do you mean ∇×\nabla\times or something else?

Yes i meant ∇×. Sorry I am not english native speaker, searched for the translation and that's the best i had.