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Theorem

Kelvin's Circulation Theorem

Mathematical Physics

Kelvin's Circulation Theorem states that in an inviscid, barotropic fluid acted on only by conservative forces, the circulation around a closed material loop that moves with the fluid stays constant over time. Named for William Thomson, Lord Kelvin, it is a foundational result of fluid dynamics explaining why vortices in an ideal fluid, once formed, persist rather than spontaneously appearing or dissipating, and it underlies the later Helmholtz theorems on vortex lines.

Facts
Statement
In a barotropic, ideal fluid with conservative body forces, the circulation around a closed curve (which encloses the same fluid elements) moving with the fluid remains constant with time. 1
Proof Year
1869 1
Classification
Statement Form
Identity or Equation 1
Sources
1. Kelvin's circulation theorem (Wikipedia)
  • Statement of the theorem
    In a barotropic, ideal fluid with conservative body forces, the circulation around a closed curve (which encloses the same fluid elements) moving with the fluid remains constant with time.
  • Naming and publication
    The theorem is named after William Thomson, 1st Baron Kelvin who published it in 1869.
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