Provided the closed curve encloses the airfoil, the choice of curve is arbitrary. The circulation on every closed curve around the airfoil has the same value, and is related to the lift generated by each unit length of span. In airfoil action, the magnitude of the circulation is determined by the Kutta condition. This equation applies around airfoils, where the circulation is generated by airfoil action and around spinning objects experiencing the Magnus effect where the circulation is induced mechanically. This is known as the Kutta–Joukowski theorem. If V is a vector field and d l is a vector representing the differential length of a small element of a defined curve, the contribution of that differential length to circulation is dΓ: It is usually denoted Γ ( Greek uppercase gamma). In electrodynamics, it can be the electric or the magnetic field.Ĭirculation was first used independently by Frederick Lanchester, Martin Kutta and Nikolay Zhukovsky. In fluid dynamics, the field is the fluid velocity field. In physics, circulation is the line integral of a vector field around a closed curve. Note the projection of v along d l and curl of v may be in the negative sense, reducing the circulation. 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). Here v is split into components perpendicular (⊥) parallel ( ‖ ) to d l, the parallel components are tangential to the closed loop and contribute to circulation, the perpendicular components do not. Top: Circulation is the line integral of v around a closed loop C. Line integral of the fluid velocity around a closed curve Field lines of a vector field v, around the boundary of an open curved surface with infinitesimal line element d l along boundary, and through its interior with dS the infinitesimal surface element and n the unit normal to the surface.
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