Related papers: Viscous evolution of point vortex equilibria: The …
We study the 2D Navier-Stokes equations linearized around the Couette flow $(y,0)^t$ in the periodic channel $\mathbb T \times [-1,1]$ with no-slip boundary conditions in the vanishing viscosity $\nu \to 0$ limit. We split the vorticity…
This paper explores experimental and numerical investigation of the spatio-temporal dynamics of a finite-length vortex column in three dimensions using Particle Image Velocimetry (PIV) and Large Eddy Simulation (LES). The research examines…
The evolution and collapse of a gaseous toroidal vortex under the action of self-gravitation are considered using the Hamiltonian mechanics approach. It is shown that evolution occurs in three main stages separated by characteristic time…
Prior modal stability analysis (Kojima et al., Phys. Fluids, vol. 27, 1984) predicted that a rising or sedimenting droplet in a viscous fluid is stable in the presence of surface tension no matter how small, in contrast to experimental and…
We prove a stability result of constant equilibria for the three-dimensional Navier-Stokes-Poisson system uniform in the inviscid limit. We allow the initial density to be close to a constant and the potential part of the initial velocity…
In a novel approach to studying viscous accretion flows, viscosity has been introduced as a perturbative effect, involving a first-order correction in the $\alpha$-viscosity parameter. This method reduces the problem of solving a…
We consider a viscous fluid with kinematic viscosity $\nu $ and initial data consisting of a smooth closed vortex filament with circulation $\Gamma $. We show that, for short enough time, the solution consists of a deformed Lamb-Oseen…
Through Ginzburg-Landau and Navier-Stokes equations, we study turbulence phenomena for viscous incompresible and compressible fluids by a second order phase transition. For this model, the velocity is defined by the sum of classical and…
In this paper, we present strong numerical evidences that the incompressible axisymmetric Euler equations with degenerate viscosity coefficients and smooth initial data of finite energy develop a potential finite-time locally self-similar…
In the high-Reynolds-number regime, this work investigates the long-time dynamics of the three-dimensional incompressible Navier-Stokes equations near the Oseen vortex filament. The flow exhibits a strong interplay between vortex…
We study the stability of the vortex in a 2D model of continuous compressible media in a uniformly rotating reference frame. As it is known, the axisymmetric vortex in a fixed reference frame is stable with respect to asymmetric…
A model is developed describing the approach to a finite-time singularity of the Navier-Stokes equations for two interacting vortices. The model is derived from a combination of the Biot-Savart law and an equation describing the evolution…
A set of equations according to which the conducting medium consists of two fluids - laminar and vortex, has been obtained in the present paper by transforming MHD equations. In a similar way, an electronic fluid is assumed to consist of a…
In this paper, we are concerned with the uniqueness and nonlinear stability of vortex rings for the 3D Euler equation. By utilizing Arnold 's variational principle for steady states of Euler equations and concentrated compactness method…
A viscous instability in shearing laminar axisymmetric hydrodynamic flows around a gravitating center is described. In the linearized hydrodynamic equations written in the Boussinesq approximation with microscopic molecular transport…
The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing…
We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients we derive an evolution equation for the discontinuity front of the…
This paper is concerned with steady vortex rings in an ideal fluid of uniform density, which are special global axi-symmetric solutions of the three-dimensional incompressible Euler equation. We systematically establish the existence,…
We consider the inertial motion of a system constituted by a rigid body with an interior cavity entirely filled with a viscous incompressible fluid. Navier boundary conditions are imposed on the cavity surface. We prove the existence of…
When vortex rings collide head-on at high enough Reynolds numbers, they ultimately annihilate through a violent interaction which breaks down their cores into a turbulent cloud. We experimentally show that this very strong interaction,…