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Despite the fact that asymmetries in hurricanes, such as spiral rainbands, polygonal eyewalls, and mesovortices, have long been observed in radar and satellite imagery, many aspects of their origin, space--time structure, and dynamics still remain unsolved, particularly their role on the vortex intensification. The underlying inner-core dynamics need to be better understood to improve the science of hurricane intensity forecasting. To fill this gap, a simple 2D barotropic ''dry'' model is used to perform two experiments starting respectively with a monopole and a ring of enhanced vorticity to mimic hurricane-like vortices during incipient and mature stages of development. The empirical normal mode (ENM) technique, together with the Eliassen--Palm (EP) flux calculations, are used to isolate wave modes from the model datasets to investigate their space--time structure, kinematics, and the impact on the changes in the structure and intensity of the simulated hurricane-like vortices. From the ENM diagnostics, it is shown in the first experiment how an incipient storm described by a vortex monopole intensifies by ''inviscid damping'' of a ''discrete-like'' vortex Rossby wave (VRW) or quasi mode. The critical radius, the structure, and the propagating properties of the quasi mode are found to be consistent with predictions of the linear eigenmode analysis of small perturbations. In the second experiment, the fastest growing wavenumber-4 unstable VRW modes of a vortex ring reminiscent of a mature hurricane are extracted, and their relation with the polygonal eyewalls, mesovortices, and the asymmetric eyewall contraction are established in consistency with results previously obtained from other authors. [ABSTRACT FROM AUTHOR]

Presents numerical solutions of the nonlinear long-time asymptotic form of the equations for disturbances to a parabolic jet. Derivation of the governing equations; Numerical scheme for nonlinear integration; Solutions for steadily propagating disturbances.