Search results for "Vortex layer"
showing 2 items of 2 documents
Vortex layers of small thickness
2020
We consider a 2D vorticity configuration where vorticity is highly concentrated around a curve and exponentially decaying away from it: the intensity of the vorticity is $O(1/epsilon)$ on the curve while it decays on an $O(epsilon)$ distance from the curve itself. We prove that, if the initial datum is of vortex-layer type, Euler solutions preserve this structure for a time which does not depend on $epsilon$. Moreover the motion of the center of the layer is well approximated by the Birkhoff-Rott equation.
Singular behavior of a vortex layer in the zero thickness limit
2017
The aim of this paper is to study the Euler dynamics of a 2D periodic layer of non uniform vorticity. We consider the zero thickness limit and we compare the Euler solution with the vortex sheet evolution predicted by the Birkhoff-Rott equation. The well known process of singularity formation in shape of the vortex sheet correlates with the appearance of several complex singularities in the Euler solution with the vortex layer datum. These singularities approach the real axis and are responsible for the roll-up process in the layer motion.