Generalised Hough functions (normalised) as a function of the horizontal coordinate x at different pseudo-radii from ζ = 0.153 (blue) to ζ = 1 (yellow) at Ω/Ω_K = 0.2 for gravity-like solutions {k = 0, m = 1} with ωⁱⁿ = 10⁻⁴ rad s⁻¹ corresponding to (the solid lines) and Rossby-like solutions {k = −2, m = −1} with ωⁱⁿ = −5.5 × 10⁻⁵ rad s⁻¹ corresponding to (the dotted lines) in the case of a star: (a) uniformly rotating, (b) differentially rotating according to the pseudo-radius, (c) differentially rotating according to the colatitude and (d) differentially rotating according to the pseudo-radius and the colatitude.