See the MRF development

Reynolds-Averaged Navier-Stokes formulation in the rotating frame.

Acceleration term expressed for a rotating frame around the z axis ($\vec \Omega$).

Notation: I: inertial, R: rotating

General vector:

$\left [ \frac{d \vec A}{dt} \right ]_I = \left [ \frac{d \vec A}{dt} \right ]_R + \vec \Omega \times \vec A$