Barotropic instability and asymmetric mixing in hurricanes with primary and secondary eyewalls

Abstract

Asymmetric vorticity mixing in hurricanes is studied in the context of a nondivergent barotropic framework. The stability of primary and secondary eyewalls is considered through linear analyses and numerical experiments using a pseudospectral model. For the case of unstable primary eyewalls, which are idealized as annular rings of enhanced vorticity embedded in relatively weak vorticity, nonlinear rearrangement occurs in which most of the vorticity initially in the eyewall is transported inward. During this evolution, distinct mesovortices form, orbit the eye, and eventually merge and axisymmetrize near the vortex center. The end state of this type of evolution is an axisymmetric and monotonic vorticity field. Observational evidence of this process occurring in real hurricanes is introduced using aircraft flight-level data. For the case of hurricanes with secondary eyewalls, which are idealized as annular rings of enhanced vorticity with intense vortices at their center, two types of instabilities are discussed. With the first type (type 1), the instability is realized across the secondary eyewall. The nonlinear mixing associated with type 1 instability results in a broader and weaker secondary eyewall. The end state is axisymmetric and stable, but is not monotonic. Secondary wind maxima associated with secondary eyewalls are maintained during this type of mixing. In the second type (type 2), the instability is realized across the moat between the secondary eyewall and the central vortex. The nonlinear mixing associated with type 2 instability perturbs the central vortex and can result in the formation of a nearly steady tripole-like structure. The formation of a tripole offers an explanation for the observed formation and persistence of elliptical eyewalls in hurricanes.