Yesterday after my post, I got to thinking of a visual way to think of it (Curl). Like Sanctus, I
was thinking of the first two vectors forming a plane (The Gradient Vector and the F vector).
So the Curl is then the "cross" or Vector product (also known as the "outer product"), is then
the Vector "Normal" to the other two (this means it points out of the plane of the first two
vectors).
In Electricity & Magnetism, the Field flux

or field strength is a vector
pointing in circle in the plane (like putting the fingers in your right hand and curling then in
a circle). When you stick your thunb out it points in the direction of the Curl of the two
vectors. This often called the Right Hand Rule.
You see this often in E&M, Rotational Kinematics (Rotation Mechanics of rigid bodies) and
other places.
maddog