Using the stream function, one can express the velocity in terms of the vector potential 
where , and  is the unit vector pointing in the positive  direction. This can also be written as the vector cross product
where we've used the vector calculus identity
Noting that , and defining , one can express the velocity field as
This form shows that the level surfaces of  and the level surfaces of  (i.e., horizontal planes) form a system of orthogonal stream surfaces.