Notes on the role of viscosity, vorticity and dissipation in incompressible flows

A critical analysis is carried out of the incompressible flow equations, and it is shown that the assumption of the fluid being non-viscous, or that regions exist in the flow where viscosity may be neglected, is practically never necessary. On the other hand, the role of the generation and dynamics of vorticity is highlighted, as well as its importance for the description of the flow development and for assessing why and when simplified models may be devised. The evolution of some simple flows is also briefly described, and the connection between viscosity and the origin of lift on an airfoil is illustrated. Finally, the possible utility of the energy balance equation, which is usually neglected in incompressible flow analyses, is discussed. In particular, it is pointed out that dissipation exists and may be significant also in irrotational regions, and that its evaluation may often be carried out in a straightforward manner by means of the Bobyleff-Forsyth formula.