The goal of this study is to investigate steady vortexflows of homogeneous ideal fluid, whose helicity,locally defined as h = u · ∇ × u [1], is bounded. In thiscase, a set of constitutive hydrodynamic equations con-tains both Euler equations and continuity equations: (1) Here, u is the flow velocity and pressure p is normal-ized to the density.For steady flows of ideal fluid, trajectories ofmarked particles coincide with streamlines [2] andform integral lines. The proposed geometric descrip-tion is based on the assumption that the integral flowlines are geodesics at the second-order surfaces beingparametrized and fill in the space occupied by the fluid.At the same time, the velocity field is formed by geode-sic flows determined by these surfaces. In this case, anindividual integral second-order surface is character-ized by the vector function f and is given in a paramet-ric form. The parameters t and τ are responsible formotion along a specific geodesic transition from onegeodesic to another on the same surface. The vectors and are tangents and vector [ × ] is the normalto the integral surface. Primes denote differentiation,and indices signify the differentiation variables. Fordescribing a transition from one integral surface toanother, the variable n is used defining the vector (2) where the functions α , β , and γ depend on t , τ , and n .The direction vectors , , and specify a curvi-linear coordinate system used furthermore for describ-ing vortex flows.A tangential geodesic flux J satisfying the condition D