Circulation (physics)

Field lines of a vector field v, around the boundary of an open curved surface with infinitesimal line element dl along boundary, and through its interior with dS the infinitesimal surface element and n the unit normal to the surface. Top: Circulation is the line integral of v around a closed loop C. Project v along dl, then sum. Here v is split into components perpendicular (⊥) parallel ( ‖ ) to dl, the parallel components are tangential to the closed loop and contribute to circulation, the perpendicular components do not. Bottom: Circulation is also the flux of vorticity ω = ∇ × v through the surface, 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, reducing the circulation.

In physics, circulation is the line integral of a vector field around a closed curve. In fluid dynamics, the field is the fluid velocity field. In electrodynamics, it can be the electric or the magnetic field.

Circulation was first used independently by Frederick Lanchester, Martin Kutta and Nikolay Zhukovsky.[citation needed] It is usually denoted Γ (Greek uppercase gamma).