Kelvin's circulation theorem

Theorem regarding circulation in a barotropic ideal fluid

In fluid mechanics, Kelvin's circulation theorem states: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. The theorem is named after William Thomson, 1st Baron Kelvin who published it in 1869. Stated mathematically: D Γ D t = 0 {\displaystyle {\frac {\mathrm {D} \Gamma }{\mathrm {D} t}}=0} where Γ {\displaystyle \Gamma } is the circulation around a material moving contour C ( t) {\displaystyle C(t)} as a function of time t {\displaystyle t} .

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