Classification of vector lines and fields by geometric and numerical methods

Abstract Geometric and numerical methods of classification of vector lines and vector fields are proposed. The division of vector lines of arbitrary vector fields into potential and spiral lines is carried out. The division of vortex vector fields into layered and spiral vector fields is carried out. It is shown that any vector field can be represented as a superposition of layered vector fields. Conditions of existence of so-called forceless spiral vector fields are established. The mathematical conditions to be satisfied by the magnetic fields of magnetic clouds of the solar wind are formulated.