English: Field lines of a vector field v, around the boundary of an open curved surface and through its interior. Top: circulation of v is calculated by projecting v along the line element dl, then summing (line integral around closed loop). Bottom: Circulation is also flux of vorticity through surface, n is the unit normal to the surface, dS the surface element, and the curl of v is heuristically depicted as a helical arrow (not a literal representation). Note the projection of v along dl and curl of v may be in the negative sense, corresponding to negative contributions to the circulation.