Localized helically symmetric flows of an ideal fluid

Steady-state solutions of the equations of motion of an ideal incompressible fluid are obtained that describe regular and spatially localized helically symmetric vortex formations. It is shown that, depending on the ratio between the parameters determining the angular momentum and energy flux, the obtained three-dimensional solution may not exist or it may be represented as a linear superposition of a finite number of modes. Description of a wide class of helically symmetric two-dimensional flows is reduced to a quadrature.