Related papers: Finite rotating and translating vortex sheets
We obtain sharp criteria for transverse stability and instability of line solitons in the discrete nonlinear Schr\"{o}dinger equations on one- and two-dimensional lattices near the anti-continuum limit. On a two-dimensional lattice, the…
In this article we consider the evolution of vortex sheets in the plane both as a weak solution of the two dimensional incompressible Euler equations and as a (weak) solution of the Birkhoff-Rott equations. We begin by discussing the…
In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's…
A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength $\lambda$. As the confinement…
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems…
We consider superfluid helium inside a container which rotates at constant angular velocity and investigate numerically the stability of the array of quantized vortices in the presence of an imposed axial counterflow. This problem was…
We rigorously construct continuous curves of rotating vortex patch solutions to the two-dimensional Euler equations. The curves are large in that, as the parameter tends to infinity, the minimum along the interface of the angular fluid…
Stability of off-site vortex solitons in a photorefractive optical lattice is analyzed. It is shown that such solitons are linearly unstable in both the high and low intensity limits. In the high-intensity limit, the vortex looks like a…
We describe the linear and nonlinear stability and instability of certain symmetric configurations of point vortices on the sphere forming relative equilibria. These configurations consist of one or two rings, and a ring with one or two…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
An evolution of a spherical region, subjected to uniform buoyancy force, is investigated. Incompressibility and axial symmetry are assumed, together with a buoyancy discontinuity at the boundary. The boundary turns into a vortex sheet and…
The presented investigation is motivated by the need to uncover connections between underlying rotor fluid-structure interactions and vortex dynamics to fatigue performance and characterization of flexible rotor blades, their hub, and their…
We analyze the instability of a vortex column in a dilute polymer solution at large $\textit{Re}$ and $\textit{De}$ with $\textit{El} = \textit{De}/\textit{Re}$, the elasticity number, being finite. Here, $\textit{Re} = \Omega_0 a^2/\nu_s$…
Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed non-uniform temperature field. We first determine the associated base…
Viscous flow past a finite flat plate moving in direction normal to itself is studied numerically.The plate moves with velocity $at^p$, where $p=0,0.5,1,2$. We present the evolution of vorticity profiles, streaklines and streamlines, and…
Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun by the first two authors is continued. We extend our…
We investigate a steady planar flow of an ideal fluid in a (bounded or unbounded) domain $\Omega\subset \mathbb{R}^2$. Let $\kappa_i\not=0$, $i=1,\ldots, m$, be $m$ arbitrary fixed constants. For any given non-degenerate critical point…
In this paper, we investigate the existence of a finite number of vortex patches for the generalized surface quasi-geostrophic (gSQG) equations with $\alpha \in [1,2)$, focusing on configurations that may rotate uniformly, translate, or…
We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of…
The FitzHugh-Nagumo equations are known to admit traveling front solutions in one spatial dimension that are nonlinearly stable. This paper concerns the stability of traveling front solutions propagating on cylindrical surfaces. It is shown…