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.
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StatementIn 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 Classification
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Source Kelvin's circulation theorem (Wikipedia)
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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.
In Group: Electromagnetism, Optics and Continuum Mechanics, Lead section
In fluid mechanics, Kelvin's circulation theorem states:In a barotropic
In Branch: Mathematical Physics, Lead section
In fluid mechanics, Kelvin's circulation theorem states:In a barotropic
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