Latitudinal velocity spectrum. Top: discrete inertial mode eigenspectrum for m = 3, shown in the complex plane. Each point correspond to one mode: all eigenfrequencies have a negative real part (meaning the modes are retrograde) and a negative imaginary part (meaning they are stable). The coloured dots mark the modes whose contribution to the u_y spectrum is most prominent. The vertical dashed lines indicate the central frequencies of each resonant peak in the u_y power spectrum (see bottom panel). Middle: equatorial u_y spectrum, obtained from Eq. (16) for azimuthal order m = 3. The solid black line shows the total spectrum, while each coloured dashed line corresponds to the individual contribution of the normal eigenmodes of the system, as described in the main text. The colours of the dashed lines match the colour scheme of the top panel. The red vertical dashed lines show the local maxima of the total spectrum. Bottom: same as the middle panel, but the vertical scale is linear.