On conservation of vorticity

In many fluid systems, the vorticity (curl of velocity) provides an important field description of the flow, giving insight into structure and dynamics. One challenge with this viewpoint is that the obvious boundary conditions are on velocity, not spatial derivatives of velocity. Historical efforts to formulate mathematical descriptions of boundary conditions on vorticity have focused on individual special cases. Recent studies have succeeded in generalizing conditions for multiple boundary types by considering the conservation of vorticity in a volume of fluid, but even these efforts are based on the assumption of the fluid being incompressible and Newtonian. Using a continuum mechanics based approach, we present a vorticity conservation formulation that decouples fundamental kinematics and dynamics from material properties. This approach simplifies some of the previous analysis, clarifies the physical mechanisms of vorticity generation at boundaries, and facilitates generalization of a vorticity boundary condition to a broad class of fluid mechanics problems.