Chapter 5 - Vorticity Dynamics

Abstract

The vorticity field is the curl of the velocity field, and is twice the rotation rate of fluid particles. The vorticity field is a vector field, and vortex lines may be determined from a tangency condition similar to that relating streamlines to the fluid velocity field. However, vortex lines have several special properties and their presence or absence within a region of interest may allow certain simplifications of the field equations for fluid motion. In particular, vortex lines are carried by the flow and cannot end within the fluid, and this constrains their possible topology. Vorticity is typically present at solid boundaries and it may diffuse into the flow via the action of viscosity. Vorticity may be generated within a flow wherever there is an unbalanced torque on fluid elements, such as when pressure and density gradients are misaligned. The characteristics and geometry of a vortex line allow the velocity it induces at a distant location to be determined. Thus, multiple vortex lines that are free to move within a fluid may interact with each other. In a rotating coordinate frame, the observed vorticity depends or the frame's rotation rate.