The concentric eyewall structure often displays in the strong tropical cyclones, such as hurricane 'Gilbert' occurred in the Atlantic basin in 1988. The analyses of hurricane 'Gilbert' (Black and Willoughby, 1992) showed that the primary eyewall appeared first, and then the outer eyewall formed. Later on, the outer eyewall strengthened and contracted while the inner eyewall showed sign of weakening. Finally, the outer eyewall completely replaced the inner eye-wall.

Currently, two main theories have been proposed to explain the formation physics of the concentric eyewalls. The first speculates that symmetric instability plays an important role in the formation of the outer eyewall (Willoughby et al. ,1982, 1984, 1988). The second theory provides simple formulae for phase and group velocities that may be used in distinguishing vortex Rossby-wave from gravity-inertia waves in observational data (Montgomery and Kallenbach, 1997). The theory also speculates a remarkable wave-mean-flow interaction during the formation of a secondary eyewall. However, the above mentioned formation mechanism could not illustrate the location of the outer eyewall. Furthermore, the formation of the symmetrically unstable in the upper tropospheric outflow layer for the former mechanism (Willoughby et al., 1984) and the wave-mean-flow interaction mechanism for the latter one (Montgomery and Kallenbach, 1997) are not revealed clearly. So it is worth to get insight into the physical process of the formation of the double eyewalls. On the contrary, it is evident that the outer eyewall formation of hurricane 'Gilbert' is associated with the external forcing. Consequently, this paper will focus on the tropical cyclone's response to external source forcing with the aid of gradient adjustment theory in order to provide another possible formation mechanism of the concentric eyewalls.

The strong vortex will mutually adjust the thermodynamic field and dynamic field to a state of gradient balance whilst forced by an external source, namely, the gradient adjustment process, which is dealt with a linearized two-layer model in this paper. The analyses show that on account of heterogeneous radial distribution of the external source forcing, the adjustment of the thermodynamic and dynamic field results in the two-peak tangential wind nature, which is analogous to the concentric double eyewalls character in the strong typhoon. Consequently, the gradient adjustment may be another possible mechanism of the formation of the concentric eyewalls typhoon.