Related papers: Stability of Hill's spherical vortex
Vortex blob methods are typically characterized by a regularization length scale, below which the dynamics are trivial for isolated blobs. In this article we observe that the dynamics need not be trivial if one is willing to consider…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations are considered. It is shown that if the inflow is rapidly increasing (pushy) in time, the corresponding laminar profile of the incompressible Euler flow is…
The incompressible Navier-Stokes equations in R^3 are shown to admit a unique axisymmetric solution without swirl if the initial vorticity is a circular vortex filament with arbitrarily large circulation Reynolds number. The emphasis is on…
We revisit the problem of stationary distribution of vorticity in three-dimensional turbulence. Using Clebsch variables we construct an explicit invariant measure on stationary solutions of Euler equations with the extra condition of fixed…
Motivated by applications to vortex rings, we study the Cauchy problem for the three-dimensional axisymmetric Navier-Stokes equations without swirl, using scale invariant function spaces. If the axisymmetric vorticity is integrable with…
In this article we consider the physical justification of the Vortex-Wave equation introduced by Marchioro and Pulvirenti in the case of a single point vortex moving in an ambient vorticity. We consider a sequence of solutions for the Euler…
The study of the Euler equations in flows with constant vorticity has piqued the curiosity of a considerable number of researchers over the years. Much research has been conducted on this subject under the assumption of steady flow. In this…
We give a sufficient condition for the nonlinear stability of steady flows of a two-dimensional ideal fluid in a bounded multiply-connected domain, which generalizes a stability criterion proved by Arnold in the 1960s. The most important…
We consider the hydrodynamics of an incompressible fluid on a 2D periodic domain. There exists a family of stationary solutions with vorticity given by $\Omega^*=\alpha\cos (\mathbf{p} \cdot \mathbf{x} )+\beta \sin (\mathbf{p} \cdot…
We prove the existence of critical points of the $N$-vortex Hamiltonian $H_\Omega (x_1,\ldots, x_N) =\sum\limits^N_{i=1}\Gamma^2_i h(x_i) + \sum\limits_{i,j=1\atop j\not= k}^N…
We present explicit expressions of the helicity conservation in nematic liquid crystal flows, for both the Ericksen-Leslie and Landau-de Gennes theories. This is done by using a minimal coupling argument that leads to an Euler-like equation…
In gauge theories with an extended Higgs sector the classical equations of motion can have solutions that describe stable, closed finite energy vortices. Such vortices separate two disjoint Higgs vacua, with one of the vacua embedded in the…
The quintessential vortex solution in (3+1)-dimensional nonrelativistic, incompressible fluid mechanics is the Burgers vortex. We show that, in a finite domain, conformal fluids also admit hot vortex solutions with everywhere…
A rotating stationary solution of the vacuum Einstein equations with a cosmological constant is exhibited which reduces to de Sitter's interior cosmological solution when the angular momentum goes to zero. This solution is locally…
In this paper, we obtain uniformly rotating vorticity with sufficiently large angular velocity in the unit disk. The solution consists of either a small nearly-ellipse vortex patch which is highly concentrated near the origin or a $2+1$…
We consider the classical Cauchy problem for the 3d Navier-Stokes equation with the initial vorticity $\omega_0$ concentrated on a circle, or more generally, a linear combination of such data for circles with common axis of symmetry. We…
Coherent vortices are often observed to persist for long times in turbulent 2D flows even at very high Reynolds numbers and are observed in experiments and computer simulations to potentially be asymptotically stable in a weak sense for the…
A {\em vortex pair} solution of the incompressible $2d$ Euler equation in vorticity form $$ \omega_t + \nabla^\perp \Psi\cdot \nabla \omega = 0 , \quad \Psi = (-\Delta)^{-1} \omega, \quad \hbox{in } \mathbb{R}^2 \times (0,\infty)$$ is a…
Helmholtz's equations provide the motion of a system of N vortices which describes a planar incompressible fluid with zero viscosity. A relative equilibrium is a particular solution of these equations for which the distances between the…
We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter-rotating as well as with co-rotating cylinders. The full, time…