We study the evolution of a 2D vortex layer at high Reynolds number. Vortex layer flows are
characterized by intense vorticity concentrated around a curve. In addition to their intrinsic …

The nonlinear dynamics of the interface between two deep dielectric fluids in the presence
of a vertical electric field is studied. We consider the limit of a strong external electric field …

In this paper, we consider the Kelvin-Helmholtz instability in the magnetohydrodynamic flow.
The motion of the interface is described by a current-vortex sheet. We examine the linear …

Evolving vortex sheets generally form singularities in finite time. The vortex blob model is an
approach to regularize the vortex sheet motion and evolve past singularity formation. In this …

Kelvin-Helmholtz Instability (KHI)(Helmoltz 1868, Kelvin 1871) is a hydrodynamic instability
in which immiscible, incompressible, and inviscid fluids are in relative and irrotational …

We consider the Euler-α α regularization of the Birkhoff–Rott equation and compare its
solutions with the dynamics of the non regularized vortex-sheet. For a flow induced by an …

In this paper, we study long-time evolutions of the Kelvin–Helmholtz instability with surface
tension and density jump by using the vortex sheet model. Applying a spectrally accurate …

We present two simple and efficient explicit methods for the vortex sheet with surface
tension. The first one is the standard point vortex method, which has been known to be …

We consider a model for a granular flow in the slow erosion limit introduced in [31]. We
propose an up-wind numerical scheme for this problem and show that the approximate …

Vortex rings are turbulent coherent structures that are ubiquitous in various application
domains ranging from gas turbines to aquatic locomotion. The vortex rings are highly …