Scalar Description of Three-Dimensional Vortex Flows of an Incompressible Fluid

A third variant of description of flows of an incompressible viscous fluid with the help of a single scalar function was studied. From the continuity equation of an incompressible fluid, divV = 0, it follows directly that the velocity field can be presented through the vector potential V = curl A. A substantial assumption about the solenoidality of the vector potential, divA = 0 was introduced. Without viscosity, it is required that only normal components of velocity are zero on these walls, which is fulfilled due to solution III. More complicated examples of the flows can be constructed from solutions I-III by matching together. Other even more complicated classes of flows can be constructed at the suitable choice of non-linear dependence.