First case: Omega1= 0.125 rad/s ---> Ta= 5000

Z-Velocity in a radial cross-section

Radial velocity in a radial cross-section

Deficit of velocity between the results obtained and
the theoretical data v(theta)=a*r + b/r

The tore rolls appear clearly in the drawn sections.

Second case: Omega1= 0.073 rad/s ---> Ta= 1712

The Taylor number is not enough high to have instabilities. But the radial is not zero anymore, as it could be the case theoretically.

Third case: Omega1= 0.178 rad/s ---> Ta= 10000

A few remarks about the vizualisations: The maximum velocity in the rolls increases with the Taylor number. And the size of a roll ( his diameter) is forced to be less than the difference of both cylinder radius.

Fourth case: Omega1 = 0.25 rad/s ---> Ta =20000

For such a value of the Taylor number, six rolls appear,
seeming to prove that the number of rolls follows the same law and consists
in the same phenomenon as the Rayleigh-Benard instability.

Fifth case: Omega1= 0.395 rad/s ---> Ta=50000