Weakly Attenuating Moving Local Vortices in a Cylindrical Circular Tube with Incompressible Fluid

A numerical and analytical study of the possibility of local aerodynamic vortex formation passing through a long cylindrical tube of circular cross-section has been carried out. For this purpose, a grid model was constructed and an algorithm for the direct numerical solution of the Navier–Stokes equation (using the implicit scheme of the alternating directions method) was programmatically implemented for the evolution of the stream function in the axisymmetric case for various variants of local vortices. The results of an analytical study of axisymmetric flows in the form of stationary weakly attenuating solitary waves were used as the initial configuration. A discrete set of configurations has been obtained, solutions according to the Reynolds number in the approximation of purely stationary waves and waves with weak attenuation. The solutions are characterized by a multi-fold more complex structure—vortex multi-rings or multilayer solutions.