摘要
建立了圆柱坐标下湿层结参数在垂直方向不为常数时的非轴对称雨团数学模型,着重讨论了其中的位势不稳定问题。抽象出了暴雨发生前期、盛期和发生后的三种典型湿层结参数的垂直分布。得到了此时位势不稳定的判据,分别给出了不稳定扰动增长率与稳定扰动振荡圆频率的上、下界。并在该参数取分2段常数的情况下,进行了解析求解。得到以下结论:该模型雨团在水平方向可有螺旋结构,这与用雷达资料得到的实际情况一致。在暴雨发生前期,有位势不稳定发生;且螺旋臂条数越多,雨团半径越小,不稳定增长率的上界越大。在暴雨盛期,整层为弱位势稳定层结,无位势不稳定发生;扰动螺旋臂条数越少,半径越大,其振荡圆频率下界越大。在暴雨结束后,整层为强位势稳定层结,也无位势不稳定发生;扰动螺旋臂条数越多,半径越小,其振荡圆频率的上界越大。在该参数取为2段常数情况下,且下层与上层其分别为负、正值时,有位势不稳定发生,且雨团的螺旋臂越多、半径越小及不稳定层次越厚,其增长率越大。该不稳定雨团的垂直结构在下层大体为半个正弦波,波长随不稳定层次的增厚而增大;在上层则为指数分布,且随高度增加迅速趋于0。
This paper presents a study on potential instability and vertical structure of unstable disturbance in rain clusters.Firstly,we develop a non-axisymmetrical linearized mathematic model for rain clusters in circular cylindrical coordinates with consideration of nonconstant humid stratification coefficient.Secondly,we Abstract three typical vertical distributions of humid stratification coefficient for heavy rain,and obtain the corresponding unstable criterion and variation range of unstable growth rate or stable disturbed frequency.Finally,we get the analytic solution when humid stratification coefficient represents two different constants.Main conclusions are as follows： there are spiral structures in rain clusters of this model.Before heavy rain occurs,the aerosphere is unstable.The more the volume of spiral band and the smaller the radius of rain clusters are,the greater the upper bound of unstable growth rate is.When heavy rain develops strongly,the aerosphere is weakly stable.The less the volume of spiral band and the bigger the radius of rain clusters are,the greater the lower bound of stable disturbed frequency is.After heavy rain occurs,the aerosphere is strongly stable.The more the volume of spiral band and the smaller the radius of the rain clusters are,the greater the upper bound of stable disturbed frequency is.When humid stratification coefficient represents two different constants and its value in lower atmosphere is minus,the aerosphere is potentially unstable.The vertical structure of unstable disturbance represents approximate sine wave form in unstable layer and its wave length increases with the increase of unstable layer thickness.In stable layer,the vertical structure of disturbance represents exponential function form and its disturbed amplitude is very small.The amplitude rapidly changes to zero with the increase of unstable layer thickness.The simpler the vertical structure of disturbance is,the greater the unstable growth rate is.
出处
《气象科学》
CSCD
北大核心
2012年第5期550-558,共9页
Journal of the Meteorological Sciences
基金
国家自然科学基金资助项目(40975031
41005074)
关键词
雨团
数学模型
湿层结参数
位势不稳定
不稳定判据
Rain clusters
Mathematic model
Humid stratification coefficient
Potential instability
Unstable criterion
