What is a good reference, paper or book, where I could study the relationship or form of the turbulent terms with respect to the Coriolis and Centrifugal components in the motion equations? I mean writing of the terms, as it is shown for the Reynolds stresses when the turbulent equations are expressed in terms of the mean values commonly found in any turbulence book.

Let u denotes the velocity in the rotating frame of reference and v in the inertial frame. w is the angular velocity. One has v = u + r*w

You just take the usual NS eqs and put u + r*w instead of v. Then you will automatically get the centrifugal and Coriolis component. Then you average in time all the terms. Only w does not need to be averaged. Also the Reynolds stress tensor is not affected by the rotation w, since it is a rigid rotation.

Some examples can be found in Astrophysics:

Balbus and Hawley, Review of Modern Physics, 70, 1 (1998)

Tassoul, Theory of rotating stars (princeton series in Astrophysics, Princeton Univ. Press 1978).pages 207-215

PG