where W0 = r0 sin $ is the distance to the rotation axis. Qint is the angular velocity of the displaced fluid element, while Qext is the ambient angular velocity in the medium both being considered at point W (in W0 one has Qint = Qext). Let us call j the specific angular momentum j = W2 Q with the appropriate index. One writes
One now assumes conservation of the specific angular momentum of the displaced fluid element. Thus jint at the distance W from the rotation axis is the same as at the distance W0 corresponding to the equilibrium position. This allows us to write, developing to the first order,
Developing the density as in (5.3), one has for (6.45)
g fdiint dQexA , 1 d Q2 B4) . - I —:---:— 1 + — ,_—1 sinÛ
the derivatives are taken in r0. As in Sect. 5.1, we search a solution of the form r -r0 = A exp(iWt) and get with (5.25) the oscillation frequency in a rotating medium
6.4 Effects of Rotation on Convection 127
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