Vortex Formations in Plane Flows of Viscous and Ideal Fluids

An analytic representation of individual vortex formations with different cross-sections is obtained for plane-parallel flows of viscous and ideal fluids. A flow in which one of the streamlines has cusp is also found. In these flows the vorticity is constant; therefore, the solutions obtained for the equations describing the kinematic variables in ideal fluid flows must simultaneously satisfy the Navier-Stokes equations. © 1997, Plenum Publishing Corporation.