The dynamics of vortex sheets is of fundamental importance in understanding
the large-scale behavior of shear layers and turbulent mixing. It is well known that
the curvature singularity appears on the vortex sheet of free shear. In this talk,
we discuss self-similar solutions of vortex sheet spirals in an incompressible fluid.
We mainly focus on the double spiral produced by the curvature singularity and
investigate the existence of the self-similar solution. We also present a vortex
shedding model describing wakes behind a solid body by vortex sheets.
Recent advances and applications of the model to various problems including
aerodynamics and biofluid dynamics will be addressed.