台风强度突变的一个简单模式

A SIMPLE MODEL OF CATASTROPHE OF INTENSITY FOR TROPICAL CYCLONE

本文从描写台风水平运动的基本方程组出发，利用流动稳定性及分岔和突变理论，建立了包含惯性、角动量及气压场等因子的非线性运动模型。研究指出：１台风线性惯性振荡的圆频率为ｆ０／２，非线性对振荡圆频率没有影响；２将径向气压梯度展为ｒ－ｒ０的幂级数，从而建立了描写台风非线性运动的一个简单模型，此模型说明：台风惯性稳定性决定于线性惯性稳定度参数μ（μ＝ａ１－ｆ２０４，ａ１＝－２′ｒ２｜ｒ＝ｒ０）和表征气压场随ｒ作非线性变化的强度参数ｂ。３在ｂ＞０时，参数μ由负变到正，平衡态会发生亚临界分岔（ｓｕｂｃｒｉｔｉｃａｌｂｉｆｕｒｃａｔｉｏｎ），研究表明：即便是线性惯性稳定情况（μ＜０），但由于非线性的作用，在一定位置上会出现非线性惯性不稳定；在ｂ＜０时，参数μ由负变到正，平衡态会发生超临界分岔（ｓｕｐｅｒｃｒｉｔｉｃａｌｂｉｆｕｒｃａｔｉｏｎ），它表明：即便是线性惯性不稳定情况（μ＞０），但由于非线性的作用，在一定位置上会出现非线性惯性稳定。４在非线性气压径向变化的条件下，台风内ｒ＝ｒ０处的径向气压梯度ａ０的变化会引起平衡态的突变（ｃａｔａｓｔｒｏｐｈｅ），我们用它来说明台风强度的突变。理论分析表明：当台风内出?

In this paper,starting with the basic equations describing the horigontal motion of tropical cyclone and using the theories of flow stability,bifurcation and catastrophe,a simple nonlinear model is set up.It is shown that 1 The angular frequency of linear inertial oscillation for the tropical cyclone is f 0/2,the nonlinear factor is not of influence on the angular frequency; 2 The inertial stability of tropical cyclone depends on both the linear stability parameter μ and strength parameter b which indicates the nonlinear change of pressure field; 3 As the parameter μ changes sign from negative to positive,the subcritical and supercritical bifurcation take place in b>0 and b<0 respectively; 4 Under the condition of nonlinear change of pressure field,the catastrophe can be occuried as the change of parameter a 0 which represents the radial pressure gradient.It implies that when the radial pressure gradient decrease gradually even changes sign from positive to negative.