Synthetic equatorial spectrum in the m-ω plane, in terms of u_y (top), u_x (middle), and ζ (bottom). Each vertical slice is normalised separately such that the maximum is unity. The diamonds show the real part of the eigenfrequencies of the linear homogeneous problem, computed as described in Sect. 3.1.1. The colour code refers to the mode categories: the blue diamonds represent the A branch, the green diamonds represent the P branch, and the red diamonds represent the Rossby modes (see Sect. 3.1.1 for a description of these branches). The solid red line shows the theoretical dispersion relation for sectoral Rossby modes in Cartesian coordinates (see Eq. (59)).