Circulation (physics)

Article summary

normal to the surface. Top: Circulation is the line integral of around a closed loop . Project along , then sum. Here is split into components perpendicular (⊥) parallel ( ‖ ) to , 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 through the surface, and the curl of is heuristically depicted as a helical arrow (not a literal representation). Note the projection of along and curl of may be in the negative sense, reducing the circulation. In physics, circulation is the line integral of a vector field around a closed curve embedded in the field. In fluid dynamics, the field is the fluid velocity field. In electrodynamics, it can be the electric or the magnetic field. The term circulation was introduced by William Thomson (later Lord Kelvin) in 1869 to denote the line integral of velocity around a closed curve as a kinematic measure of rotational motion in a fluid, independent of any particular application. In aerodynamics, circulation appears in a more specialised context in relation to the calculation of lift, where it is evaluated on contours enclosing a body under additional flow assumptions. In this context, circulation was first used independently by Frederick Lanchester, Ludwig Prandtl, Martin Kutta and Nikolay Zhukovsky.…

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