Previous studies, both analytic and numerical in nature, have provided convincing evidence that vortex sheets form curvature singularities in finite time. An interesting perspective has been developed by considering the parametrization variable for the sheet location as a complex variable. The analytic properties of the sheet location, regarded as a complex-valued function of the complex parametrization variable, may be determined by knowledge of all singularities, if any, in the complex plane. In particular, singularities may form and move about the plane, and even reach the real axis in finite time, at which point the sheet exhibits a physical singularity. In this paper, we discuss the origin of these complex singularities especially when the initial sheet location is analytic everywhere in the complex plane.
|Number of pages||9|
|Publication status||Published - 1 Jan 1995|
|Event||Fluid Dynamics Conference, 1995 - San Diego, United States of America|
Duration: 19 Jun 1995 → 22 Jun 1995
|Conference||Fluid Dynamics Conference, 1995|
|Country||United States of America|
|Period||19/06/95 → 22/06/95|