热带气旋螺旋云带动力不稳定的性质

Unstable dynamical properties of spiral bands in tropical cyclones.

热带气旋螺旋云带的不对称特征,在热带气旋的路径和强度变化中起着重要作用,对其动力性质的研究是整个热带气旋研究中的重要组成部分。文中分别对一个正压无辐散涡旋模型和正压原始方程涡旋模型进行线性化,采用标准模方法计算扰动的谱点和谱函数,研究扰动在基本流场中的不稳定问题,从而讨论了热带气旋中螺旋云带动力不稳定的性质。将一指定的基流廓线代入这两个模型,均会出现不稳定扰动。前者的流动为涡旋运动,仅在不稳定扰动的两个峰值之间可以看出螺旋状的结构特征,在距涡旋中心140km的外围,不稳定扰动沿径向没有波动分布,没有螺旋云带状结构。此处相应于涡旋Rossby波的停滞半径(stagnation radius),在此半径之内出现的螺旋结构称为内螺旋云带,而在此半径之外出现的螺旋云带称为外螺旋云带。也就是说前者仅出现了眼壁(最大风速半径之内的最大扰动中心)、内螺旋云带,而后者则出现了眼壁、内螺旋云带和外螺旋云带。这说明滤去重力惯性波的正压无辐散涡旋模型(前者)只适合于解释热带气旋不稳定内螺旋云带的形成和结构,当综合考虑不稳定内、外螺旋云带的形成时,水平辐合、辐散的作用不能忽略,此时必须要用正压涡旋模型(后者)。在该模型中因最不稳定扰动随涡旋半径的不同,其分别体现了涡旋Rossby波和重力惯性波的特点,故其是不稳定的涡旋Rossby-重力惯性混合波,其不稳定的性质是非平衡的。由此可知,要同时解释内、外螺旋云带的生成和结构,则非平衡的涡旋Rossby-重力惯性混合波不稳定理论应是更合适的选择。

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