Some Exact Solutions of Unsteady Viscous Incompressible Fluid Flows with Topology Conservation of Vorticity Vector Field by Ansatz Method

Navier-Stokes equations for an unstable incompressible fluid flow with conservative body forces are discussed in this article. Under topology conservation of vector fields, the governing equations are derived. It is assumed that the fluid flow velocity acts as a generating vector field. Viscous fluid flows were also generated using topology conserving vorticity vector fields. Graphs show the vectors of velocity for different fluids.