On the mechanics of helical flows in an ideal incompressible nonviscous continuous medium

Abstract

We find a general solution to the problem on the motion in an incompressible continuous medium occupying at any time a whole domain D ⊂ R3 under the conditions that D is an axially symmetric cylinder and the motion is described by the Euler equation together with the continuity equation for an incompressible medium and belongs to the class of helical flows (according to I.S. Gromeka’s terminology), in which sreamlines coincide with vortex lines. This class is constructed by the method of transformation of the geometric structure of a vector field. The solution is characterized in Theorem 2 in the end of the paper.