In mathematics, a differential operator that can be applied to a vector-valued function (or vector field) in order to measure its tendency to spin.
It consists of a combination of the function's first partial derivatives. One of the more common forms for expressing it is:
in which v is the vector field ( v 1 , v 2 , v 3 ), and v 1 , v 2 , v 3 are functions of the variables x , y , and z , and i , j , and k are unit vectors in the positive x , y , and z directions, respectively. In fluid mechanics, the curl of the fluid velocity of the vector field (i.e., of the fluid itself) is called the vorticity or the rotation because it measures the field's tendency to rotate around a given point.