Discussion
Which condition does Kelvin's circulation theorem require?
Answer: A
Kelvin's theorem states that the absolute circulation around a material loop is conserved when the fluid is barotropic, inviscid and subject only to conservative body forces. Barotropy is what makes the solenoidal term vanish. Constant density is a special case of barotropy and is stronger than necessary. Bjerknes generalised the result to the baroclinic case by retaining the solenoidal term explicitly. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.
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