The prominent features of the primary instabilities of a turbulent source flow between finite-span parallel rings with spatially modulated inflow conditions rotating at angular rate Ω are investigated. Two different two-dimensional instabilities that occur at large (αQ≳1.00) and low (αQ≲0.65) flow rates have been traced back to two different physical mechanisms related to jet-wake and mean-core flow, respectively. The effect of the radial aspect ratios Γ on the instability characteristics of the flow between parallel rings is also considered in this paper. Numerical URANS simulations are conducted for three different radial aspect ratios, i.e. Γ=1.25, 1.5, and 2, the corresponding cross-sectional aspect ratios Λ=2(Γ−1)×3.325, and two conceptually different inflow conditions. Their impact on the rotating instabilities in terms of instability mode number and instability frequency is the main focus of this study and is analyzed by fast Fourier transform (FFT) and wavelet analysis. Realistic inflow conditions with a leakage flow are found to overtake the instability for small radius ratios and affect the primary instabilities for large radius ratios.