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Abstract
Secondary circulations (SC) associated with hurricanes are traditionally regarded
as small perturbations superimposed on the primary circulations (PC). The reason behind
this treatment roots in an observation that the magnitude of the SC is about 10 orders
of magnitude smaller than that of the PC. This approximation underlines all of the
hurricane theories up until now. Recently, Kieu (2004) proposes a revitalizing theory
for the development of hurricanes for which a class of exact solutions of the primitive
equations is obtained explicitly without appealing to scaling approximation. The solutions
share some of the most important dynamical aspects with observations. According to
this theory, the SC turns out to be particular important in determining the three-dimensional
structure and temporal evolution of axisymmetric hurricanes. Like all theories for
the hurricane development, Kieu's theory however contains an infinite growth of the
SC with time. In this study, it will be shown that the infinite growth does not occur.
In fact, the solution becomes stationary after a period of time and the SC is able
to maintain itself without blowing exponentially if the nonlinear terms in the vertical
momentum equation are included. In addition, the SC tends to force the peripheral
convection to converge toward the center and builds up a more concentric vortex with
a typical hurricane-eye structure. Some potential roles of the SC in the formation
of hurricane eyes are discussed.