大气涡旋的螺旋结构

The Spiral Structure for Atmospheric Vortex

利用速度场的分解,说明大气中常见的斑图。速度场可分为变形场和旋转场。若大气动力学方程中只有气压梯度力和科里奥利力平衡,此时速度场只有旋转场,地面天气图上气旋反气旋斑图是闭合的。若再加上摩擦力,则斑图为实际的气旋反气旋螺旋。对三维有水平辐散辐合的涡旋,其斑图为三维螺旋型式,常见是漏斗状。台风小口朝上,龙卷风大口朝上。

The 3-D velocity fields of atmosphere can be decomposed into the deformation and rotation fields. The deformation field consists of the velocity divergence, it is symmetry matrix. The rotation field consists of the vorticity, it is anti symmetry matrix. The structure of atmosphere vortex can be determined by the Jacobian matrix of the velocity field, the Jacobian matrix is the sum of the above symmetry matrix and anti-symmetry matrix. The singular point of the velocity field denotes the wind free place. The characteristic values of the Jacobian matrix at the singular point determine the property of vortex. When the pressure gradient force is balanced with the Coriolis force in atmospheric dynamical equations, the 2-D velocity field is only the rotation field, the characteristic value is pure imaginary. The cyclone and anticyclone vortex patterns are a closed form in the surface synoptic map. When the friction is added in the above balance, the 2-D velocity fields have also the deformation field except for the rotation field, the characteristic value is a complex number. The cyclone and anticyclone vortex patterns become spiral form. The 3-D atmospheric vortex pattern is usually the spiral conic form with the deformation and rotation fields. The three characteristic values are one real and two complex. They are a funnel structure. The smaller funnel hole is up for typhoon, the larger funnel hole is up with long and thin for tornado.