A solution class of the Euler equation in a torus with solenoidal velocity field. III

We continue the study of the problem on the existence conditions for solenoidal solutions of the Euler equation in a torus $D$ with respect to a pair $(\mathbf{V},p)$ of vector and scalar fields such that the lines of the vector field $\mathbf{V}$ have a simple structure, coinciding with parallels and meridians of toroidal surfaces that are concentrically embedded in $D$. Here, in contrast to the previous two papers, the right-hand side of the Euler equation, i.e., the vector field $\mathbf{f}$ in $D$, is not given in a special form but is considered to be arbitrary.