Final answer:
The concept of potential flows versus vortex flows in aerodynamics can be confusing because potential flows should be irrotational, yet vortices contain rotation. However, vortex flow is a simplified model used to study fluid behavior, and in idealized inviscid flow, the circulation around an airfoil modeled by vortex elements explains lift generation despite the lack of viscosity.
Step-by-step explanation:
The confusion about potential flows and vortex flows in aerodynamics stems from the fact that while potential flows assume no rotation or vorticity, vortex flows do exhibit rotation. The idealization of potential flow is beneficial for many analytical calculations in inviscid (frictionless) fluid dynamics, where the fluid flow is irrotational.
However, in the context of a vortex flow, a point of curl or circulation is indeed present at the center. This seems contradictory, but it's important to realize that vortex flow is a theoretical construct used to simplify and study complex fluid behaviors.
In aerodynamics, particularly within the framework of the Kutta-Joukowski theorem, the circulation around an airfoil in inviscid flow is what generates lift. The vortex element is essentially a conceptual model that helps to explain how circulation can exist around an airfoil without the need for viscosity, which is typically thought to be essential for the generation of lift (according to the boundary layer theory).
Though real fluids are always viscous, potential flow and related concepts are still very useful in understanding the physics of lift in a simplified manner.