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a symmetric instability that might contribute to the formation of the
outer eyewall. They, however, could not develop a causal relation between
the location of the outer eyewall and the instability. Montgomery and
Kallenbach
3
implied that the TC concentric eyewalls could result from
radially propagating linear vortex Rossby waves that are dynamically
constrained near a critical radius. Since the development and propagation
of the vortex Rossby waves are attributed to the TC basic state radial
vorticity gradient, the vortex Rossby waves are confined near the radius
of the maximum wind (RMW). Nong and Emanuel
4
studied the formation
of the concentric eyewalls in an axisymmetric model. Their simulations
showed that the secondary eyewall might result from a finite-amplitude
WISHE instability, triggered by external forcing.
Black and Willoughby
1
noted that the outer eyewall formed during
the TC weakening stage (Fig. 1). Shapiro and Willoughby
7
and Willoughby
et al.
9
used a symmetric model (hereafter SW model) to diagnose the
secondary circulation induced by a point heat source in balanced,
axisymmetric vortices. For a heatsourcenearRMW,amaximumofthe
tangential wind tendency lay just inside of RMW, so that the maximum
wind propagated inward in response to the heating, which provided
a plausible physical explanation for the contraction of the outer wind
maximum. However, their simulations did not reproduce a double-peak
structure. The fact that an outer eyewall forms during TC weakening stage
suggests that a rapid decrease of convective heating may play a role in the
formation of double eyewalls. Peng
et al.
5
examined this idea by introducing
a negative heat source in a simple TC model.
Theoretically, concentric eyewalls may be formed as two cyclonic
vortices with different sizes and intensities interact without merging into
a monopole.
2
The criteria for the concentric eyewall formation is that
(1) the core vortex must be at least six times stronger in vorticity than
the neighboring weaker vortex, (2) the neighboring vortex is larger in size
than the core vortex, and (3) a separation distance is within three to four
times of the core vortex radius. Note that in this scenario, a symmetric
positive vortcity belt has been given initially. The interaction between the
two vortices just redistributes the vorticity of the outer vortex. In this study,
we present a different, wave-mean flow interaction scenario. We examine a
new concentric eyewall formation scenario in which a core vortex interacts
with an asymmetric perturbation that has a wave-like structure and zero
symmetric vorticity component in the outer region. We will examine how
the symmetric flow gains energy from the asymmetric perturbation in the
