$$Ro= {{g \cdot d \cdot \alpha \Delta T} \over {\Omega^2 \cdot (b-a)^2}}$$
Reynolds number
$$Re = {{r_i^2 \Omega} \over {\nu}}$$
Taylor number in co-rotating system
$$Ta = {{4d^4 \Omega^2} \over {\nu^2}}$$
Taylor number in differential rotating system
$$Ta = {{4d_o^4 \Omega^2} \over {\nu^2}}$$
Rossby number
$$Ro = {{\Omega_i - \Omega_o} \over {\Omega_o}}$$
Ekman number in differential rotating system
$$E = {{\nu} \over {d \Omega_o}}$$
Libration
$$\Omega_1 (t) = \Omega_0 + \epsilon \cdot cos(\omega t)$$
shear Reynolds number
$$Re_S = {{2 R_1 R_2} \over {R_2 + R_1}} \cdot {{(R_2-R_1) ( \Omega_2 - \Omega_1)} \over {\nu}}$$