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

中文关键词:  热带气旋，螺旋云带，非平衡不稳定，涡旋Rossby-重力惯性混合波

英文关键词:Tropical cyclone, Spiral bands, Unbalanced instability, Mixed vortex Rossby-inertia gravitational wave.

中文摘要:

      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140 km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。

英文摘要:

      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.