The Spiral Structure for Atmospheric Vortex
大气涡旋的螺旋结构

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.