The aortic sinus vortex

This paper describes an analytic and a numerical method for the aortic sinus problem. Both methods are based on the dynamics of point vortices, and both exploit a particular conformal mapping from a model aortic sinus to the upper half plane. The analytic description is based on an isolated point vortex in equilibrium with a free stream. This inviscid model is used to study the stability of the aortic sinus vortex and to elucidate the mechanism of aortic valve closure, but it cannot be used to study the formation of the sinus vortex and it gives a somewhat incorrect picture of the flow pattern. These difficulties are overcome by the introduction of a numerical method for the aortic sinus problem with fluid viscosity. We use Chorin's vortex method combined with conformal mapping. The conformal mapping approach gives an explicit formula for the vortex velocities and it resolves the singularities associated with the corners of the domain. This method is then used to study the formation of the sinus vortex and to confirm the predictions of the point vortex model with respect to the role of the vortex in valve closure.