On the Roles of the Secondary Circulation in the Formation of Hurricanes
  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. 
Chanh Q. Kieu