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Related papers: Deformation of vortex patches by boundaries

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Using complementary numerical approaches at high resolution, we study the late-time behaviour of an inviscid, incompressible two-dimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a…

Fluid Dynamics · Physics 2015-12-08 David G. Dritschel , Wanming Qi , J. B. Marston

Studies of particle motion in vortical flows have mainly focused on point-like particles, either inertial or self-propelled. This approximation assumes that the velocity field that surrounds the particle is linear. We consider an…

Fluid Dynamics · Physics 2022-01-17 Sumithra Reddy Yerasi , Rama Govindarajan , Dario Vincenzi

The purpose of this work is to discuss the well-posedness theory of singular vortex patches. Our main results are of two types: well-posedness and ill-posedness. On the well-posedness side, we show that globally $m-$fold symmetric vortex…

Analysis of PDEs · Mathematics 2019-12-24 Tarek M. Elgindi , In-Jee Jeong

We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is used to describe the interaction. The case of integrability…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Alexey V. Borisov , Ivan S. Mamaev

We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show…

Analysis of PDEs · Mathematics 2008-12-12 Franck Sueur

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…

Analysis of PDEs · Mathematics 2021-07-30 Zineb Hassainia , Nader Masmoudi , Miles H. Wheeler

This paper analyzes the space of steady rotating solutions to the two-dimensional incompressible Euler equations nearby vortex patch solutions satisfying a natural nondegeneracy condition. We address the question of desingularization and…

Analysis of PDEs · Mathematics 2026-05-19 Răzvan-Octavian Radu , Noah Stevenson

In this paper, the effectiveness of electromagnetic forces on controlling the motion of a sedimenting elliptical particle is investigated using the immersed interface-lattice Boltzmann method (II-LBM), in which a signed distance function is…

Fluid Dynamics · Physics 2021-03-08 Jianhua Qin , Guodan Dong , Hui Zhang

We simulate the head-on collision between vortex rings with circulation Reynolds numbers of 4000 using an adaptive, multiresolution solver based on the lattice Green's function. The simulation fidelity is established with integral metrics…

Fluid Dynamics · Physics 2024-03-07 Rahul Arun , Tim Colonius

We construct a family of rotating vortex patches with fixed angular velocity for the two-dimensional Euler equations in a disk. As the vorticity strength goes to infinity, the limit of these rotating vortex patches is a rotating point…

Analysis of PDEs · Mathematics 2019-09-04 Daomin Cao , Jie Wan , Guodong Wang , Weicheng Zhan

When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this…

Soft Condensed Matter · Physics 2021-04-14 Thomas Speck , Ashreya Jayaram

A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A…

Fluid Dynamics · Physics 2015-06-22 Lailai Zhu , Luca Brandt

The evolution of a small-amplitude localized vortex disturbance in an unbounded shear flow with the linear velocity profile is investigated. Based on the exact solution of the initial problem for basic flow, a revision is made of the…

Fluid Dynamics · Physics 2007-05-23 I. G. Shukhman , V. B. Levinski

A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…

Classical Physics · Physics 2016-08-16 L. Lacaze , P. Le Gal , S. Le Dizès

One of the main questions regarding planet formation is how to cross the metre-scale barrier. Several theories rely on the formation of dust clumps dense enough to collapse under their own gravity. Vortices are promising candidate sites of…

Earth and Planetary Astrophysics · Physics 2026-04-10 Nathan Magnan , Henrik Nils Latter

We prove the existence of time quasi-periodic vortex patch solutions of the 2$d$-Euler equations in $\mathbb{R}^2$, close to uniformly rotating Kirchhoff elliptical vortices, with aspect ratios belonging to a set of asymptotically full…

Analysis of PDEs · Mathematics 2023-08-16 Massimiliano Berti , Zineb Hassainia , Nader Masmoudi

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…

Analysis of PDEs · Mathematics 2024-12-03 Edison Cuba

We construct a series of patch type solutions for incompressible Euler equation on $\mathbb S^2$, which constitutes the regularization for steady or traveling point vortex systems. We first prove the existence of $k$-fold symmetric patch…

Analysis of PDEs · Mathematics 2024-11-19 Takashi Sakajo , Changjun Zou

The theory of vortex motion in a dilute superfluid of inhomogeneous density demands a boundary layer approach, in which different approximation schemes are employed close to and far from the vortex, and their results matched smoothly…

Soft Condensed Matter · Physics 2009-11-07 J. R. Anglin

We study the dynamics of a gas bubble in a fluid with surface tension, initially near a spherical equilibrium. While there are many studies and applications of radial bubble dynamics, the theory of general deformations from a spherical…

Analysis of PDEs · Mathematics 2024-08-08 Chen-Chih Lai , Michael I. Weinstein