A number of observational analyses (Willoughby et al.,1982; Willoughby,1990; Black and Willoughby,1992) show that during the development of some intense hurricanes, spiral ranibands form a partial or complete ring of heavy precipitation around the eyewall, and that the ring usually contains a well-defined wind maxima. This pattern of inner and outer convective rings is generally referred to as concentric eyewalls. Hurricanes with concentric eyewalls often undergo characteristic intensity change. As the outer eyewall contracts and intensifies, the intensity of hurricane stops increasing and starts to weaken, associated with a rise of the minimum central pressure, a decrease of the maximum tangential wind, and an increase of the eyewall's radius. Some time later, the outer eyewall replaces the inner one and becomes a new primary eyewall. After the eyewall succession, hurricanes may resume intensification if they do not make landfall shortly. For example, Hurricane Andrew (1992) almost regained its original peak intensity after an eyewall replacement cycle. It was speculated that the destructiveness of Hurricane Andrew was related to the eyewall replacement (Willoughby and Black,1996). Understanding the initial formation and following development of outer eyewalls should help us gain insight on hurricane intensity change associated with concentric eyewall cycles.
In their observational studies of Hurricane Allen (1980) and Hurricane Elena (1985), Molinari and his colleagues (1992, 1995) suggested that upper-tropospheric eddy convergence of angular momentum plays an important role in the intensity change of these two hurricanes. On the other hand, it has been known and accepted in varying degrees that the initial intensification of a tropical cyclone usually occurs after the interaction between the tropical cyclone and an upper-level midlatitude trough or a subtropical low. Inspired by the above facts, we employed a numerical model to study the effect of the environmental forcing on the genesis of concentric eyewalls. As a first step, we used an axisymmetric, nonhydrostatic and cloud-resolving model developed by Rotunno and Emanuel (1987, hereafter RE87). Time varying eddy fluxes of angular momentum in a parameterized way is introduced into the azimuthal momentum equation of RE87. The time variation of the eddy fluxes is bell-like to mimic the observed convergence of the eddy fluxes. The horizontal domain size of the model is 2250km.
We have done three experiments, labeled as EXP1, EXP2, and EXP3. Initial conditions in these three experiments are the same as those in the control run (Exp A) of RE87. In EXP1, eddy forcing is turned off. The behavior of the model hurricane is the same as that of RE87's Exp A. Only one eyewall forms in the whole integration time. In EXP2, eddy forcing is turned on. The forcing attains maximum strength after the model hurricane reaches peak intensity. One eyewall forms at this time. It is about 40km from the storm center. This eyewall is called the first eyewall. Then, later on, a local surface tangential wind maxima appears 280km from the storm center. It moves toward the center with time. Associated with this local wind maxima, there are an in-up-out circulation and a rainband. The rainband finally becomes the secondary eyewall and replaces the first eyewall. The succession process of the concentric eyewalls in the simulation resembles its counterpart in the real world. The secondary eyewall contracts and intensifies, while the first eyewall weakens and dissipates. A significant fluctuation in the model hurricane intensity is found during the eyewall replacement, which is, again, consistent with that of the observed concentric eyewall hurricanes. One possible explanation for the genesis of the secondary eyewall consists of two parts. The first part is that when there is an upper-level trough several hundred kilometers to the west and poleward of a hurricane, the cyclonic vorticity associated with the trough may project a component on to the surface. This can be accomplished downward along angular momentum surfaces, which functions as characteristic surface in moist potential vorticity inversion. This argument was first suggested by Emanuel (1997). The second part is that once there is a local surface wind maxima, it may amplifies through WISHE mechanism (Emanuel 1989). We are currently using NCEP/NCAR reanalysis data set to verify the first part of our explanation. The second part is proved to be true by doing EXP3 in which the eddy forcing is the same as that of EXP2, but the WISHE mechanism is shut off when the local wind maxima is observed, i.e., fixing the surface tangential wind in the calculations of the surface heat fluxes. No secondary eyewall forms in EXP3 even though the eddy forcing is present. We also have done some other sensitive experiments, and have found that our above findings are robust.
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