Comparison between the explicit semi-analytical evaluation of the velocities and relative chemical potential perturbations (corresponding to ζ = 0) and the numerical calculation of the same quantities using the FF approach with different values of ζ. For v_n and v_ad, lines represent the direction of their poloidal component and color its magnitude. This comparison is made for magnetic field model II, using the HHJ EoS. The computation is done over an equally spaced grid (u = 1 in equation (55)) of resolution N_r = 60, N_θ = 91, using an analytical expression for f_B to minimize numerical errors.