ESS227
Prof. Jin-Yi Yu
Bjerknes
Circulation Theorem
•The circulation theorem is obtained by taking the line
integral of Newton’s second law
for a closed chain of fluid particles.
∫
(
) dl
neglect
č
becomes zero after integration
Term 1
Term 2
Term 3
Term
1: rate of change of relative circulation
Term
2: solenoidal term (for a barotropic fluid, the density is a function only of
pressure,
and the solenoidal term is zero.)
Term 3: rate of
change of the enclosed area projected on the equatorial plane