Examples of Steady Axisymmetric Flows of an Ideal Incompressible Fluid

Three-dimensional (axisymmetric) flows of an ideal incompressible fluid are considered in multiply connected regions. In a coordinate system fitted to the velocity potential and the stream function the analogs of the powers of a complex variable are constructed for quasiconformal axisymmetric mappings; they are similar with those used for conformal mappings in the two-dimensional case. Quasianalytical polynomials of an arbitrary degree are considered and the functions conjugate to them are chosen. The solutions satisfying the Laplace equation in the cylindrical coordinate system are determined in the form of formal powers in the "operator" form. The solutions of problems of flow past bodies of finite dimensions, in semi-infinite domains, and in axysimmetric channels of complicated shape in the presence of an internal body are presented.