Unstable dynamical properties of spiral bands in tropical cyclones

KeyWord:Tropical cyclone, Spiral bands, Unbalanced instability, Mixed vortex Rossby-inertia gravitational wave.

Abstract:

      Spiral bands are the asymmetric feature of tropical cyclones, and play an important role in the changes in the path and intensity of tropical cyclones. So the study on their dynamical property constitutes an important part in the whole research on tropical cyclones. A nondivergent barotropic vortex model and a barotropic primitive equation vortex model are linearized respectively in this paper, and then the spectrum points and spectrum functions of their perturbations are computed using the normal mode method to study the unstable problem of perturbations in the basic flow, thereby, the unstable dynamic property of spiral bands in tropical cyclones are discussed. It is shown that unstable spiral bands appear in the both models after substituting the prescribed profile of basic flow into them. The flow of the former model exhibits a vortex motion, wherein the spiral-band structure is only discernible between the two peak values of unstable perturbations. When the radius is larger than 140km, there is no wave structure along the radial direction, so no spiral-band structure appears. This radius, i.e. km, corresponds to the stagnation radius of vortex Rossby wave. The spiral bands appearing within this radius can be called as the inner spiral band, while those outside of this radius can be called as the outer spiral band. That’s to say, only the eye wall (the most unstable perturbation center within the maximum wind radius) and inner spiral band-like structures appear in the former model, but the eye wall, inner and outer spiral bands-like structures can be seen in the second model. This suggests that the nondivergent barotropic model filtering inertial-gravitational waves is suitable to discuss the formation and structure of unstable inner spiral bands, but when the formation of unstable inner and outer spiral bands is to be studied, then the function of horizontal convergence and divergence can not be ignored, and the barotropic vortex model shall be used. In this model, the properties of the most unstable perturbations are different with radius, showing characteristics of vortex Rossby waves within and characteristics of inertial-gravitational waves outside the stagnation radius, respectively. So such perturbations shall be viewed as the unbalanced unstable mixed wave of these two kinds of waves. If the unstable inner and outer spiral bands are to be discussed together, the instability theory of unbalanced mixed waves of vortex Rossby waves and inertial-gravitational waves shall be a better choice.