The dynamics of concentric secondary wind maxima in intense tropical-cyclone-like vortices is investigated using a non-linear non-divergent semispectral barotropic numerical model, formulated in a cylindrical coordinate system moving with the vortex. The numerical model is initialised with a variety of symmetric tangential wind profiles with secondary wind maxima of different radial scales, magnitudes and locations relative to the vortex centre. The numerical calculations are carried out on an f- and beta-plane. The model is integrated for 96 hours and analyses are carried out every eight hours. Linear stability analysis shows that all initial vortices have unstable, fast-growing barotropic normal modes at azimuthal wave-numbers two, three and four. In full agreement with the predictions of the linear stability analyses at all analysis times, the concentric secondary wind maxima disappear in favour of the linear normal modes in all cases investigated within time periods ranging from a few hours to two days. During the decay of the secondary wind maxima, the vortices remain at their initial position on the f-plane, whereas on the beta-plane, the vortices move to the Northwest. The secondary wind maxima decay faster on the beta-plane than on the f-plane. Symmetric tangential wind speeds increase at radii inside and outside of the secondary wind maxima and lead to broader symmetric tangential wind profiles than before. The ultimate disappearance of the secondary wind maxima is followed by the decay or modification of the associated eigenmodes, caused by temporal changes in the stability characteristics of the symmetric vortex. Furthermore, the temporal excitation and decay of linear barotropic normal modes of azimuthal wave-number one leads to looping and erratic motion of all vortices examined. The loops and track deflections vary in horizontal scale between 50 and 200 km.
The numerical experiments described above show in agreement with the linear stability analyses that symmetric concentric secondary wind maxima in barotropic vortices are short-lived phenomena. This finding raises the question whether observed symmetric concentric secondary wind maxima in real tropical cyclones are indeed axi-symmetric patterns or narrow vortex asymmetries that project on to symmetric patterns as a result of measurement inconsistencies. Furthermore, the existence of symmetric concentric secondary wind maxima is associated with erratic or looping vortex-track deflections of considerable horizontal scale. Further observational evidence is needed to confirm this association of secondary wind maxima with sudden or quasi-regulartrack changes in real tropical cyclones.