Velocity profiles of the normal modes for the constant { E,V } case, obtained by solving Eq. (28). The modes should be truncated at a value ξ = Ξ corresponding to the vertical dotted lines, in order to satisfy the boundary conditions (11). Other zeros are displayed. Only modes of lowest L for fixed Ξ are shown. Note that the core-halo structure described in Sect. 4.1.2 disappears when the velocity has no internal zeros, between L = 0.021 and L = 0.022.