Vortex Rings with Swirl: Axisymmetric Solutions of the Euler Equations with Nonzero Helicity

Bruce Turkington

Type: Article

Publication Date: 1989-01-01

Citations: 42

DOI: https://doi.org/10.1137/0520005

View Publication

Locations

SIAM Journal on Mathematical Analysis - View

Similar Works

Action	Title	Year	Authors
+	Desingularization of vortex rings in 3 dimensional Euler flows: with swirl	2019	Daomin Cao Jie Wan Weicheng Zhan
+	Desingularization of vortex rings in 3 dimensional Euler flows: with swirl	2019	Daomin Cao Jie Wan Weicheng Zhan
+	On the steady axisymmetric vortex rings for 3-D incompressible Euler flows	2020	Daomin Cao Weicheng Zhan
+	Existence, uniqueness and stability of steady vortex rings of small cross-section	2022	Daomin Cao Guolin Qin W. Yu Weicheng Zhan Changjun Zou
+	On vortex stretching for anti-parallel axisymmetric flows	2021	Kyudong Choi In‐Jee Jeong
+	Axisymmetric vortex rings	1993	P. G. Saffman
+	Estabilidade não/linear de soluções estacionárias das equações de Euler incompressíveis com simetria helicoidal	2014	Maicon José Benvenutti
+	ON THE STRUCTURE OF HELICAL AXISYMMETRIC SOLUTIONS OF THE NAVIER-STOKES SYSTEM FOR INCOMPRESSIBLE FLUIDS	2024	В. А. Галкин
+	On three-dimensional Navier-Stokes equations with axi-symmetric vortex rings as initial vorticity	2013	Hao Feng
+ PDF Chat	Existence of Vortex Rings in Beltrami Flows	2022	Ken Abe
+	Axisymmetric incompressible flows with bounded vorticity	2007	Raphaël Danchin
+ PDF Chat	On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl	2024	Guolin Qin Jie Wan
+	Desingularization of vortex rings in 3 dimensional Euler flows	2019	Daomin Cao Jie Wan Weicheng Zhan
+ PDF Chat	Helicity of a toroidal vortex with swirl	2016	E. Yu. Bannikova В. М. Конторович S. A. Poslavsky
+	Remarks on orbital stability of steady vortex rings	2023	Daomin Cao Guolin Qin Weicheng Zhan Changjun Zou
+	Existence and stability of viscous vortices	2016	Thierry Gallay Yasunori Maekawa
+ PDF Chat	Steady Ring-Shaped Vortex Sheets	2024	David Meyer Christian Seis
+	Desingularization of vortex rings in 3 dimensional Euler flows	2020	Daomin Cao Jie Wan Weicheng Zhan
+	A Lagrangian approach for vorticity intensification in swirling rings	1998	Carlo Massimo Casciola R. Piva
+ PDF Chat	Instability for axisymmetric blow-up solutions to incompressible Euler equations	2021	Laurent Laflèche Alexis Vasseur Misha Vishik

Works That Cite This (21)

Action	Title	Year	Authors
+ PDF Chat	Magnetohydrodynamic approach to solvability of the three-dimensional stationary Euler equations	2002	Takahiro Nishiyama
+	On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows	2019	Terence Tao
+	Desingularization of Vortices for Two-Dimensional Steady Euler Flows via the Vorticity Method	2020	Daomin Cao Guodong Wang Weicheng Zhan
+	Desingularization of vortex rings in 3 dimensional Euler flows: with swirl	2019	Daomin Cao Jie Wan Weicheng Zhan
+	Desingularization of vortex rings in 3 dimensional Euler flows	2020	Daomin Cao Jie Wan Weicheng Zhan
+	Desingularization of vortices for 2D steady Euler flows via the vorticity method	2019	Daomin Cao Guodong Wang Weicheng Zhan
+	Desingularization of vortex rings in 3 dimensional Euler flows	2019	Daomin Cao Jie Wan Weicheng Zhan
+ PDF Chat	Rigidity of Beltrami fields with a non-constant proportionality factor	2022	Ken Abe
+	On the steady axisymmetric vortex rings for 3-D incompressible Euler flows	2020	Daomin Cao Weicheng Zhan
+ PDF Chat	Axi-symmetric solutions for active vector models generalizing 3D Euler and electron–MHD equations	2023	Dongho Chae Kyudong Choi In-Jee Jeong

Works Cited by This (5)

Action	Title	Year	Authors
+ PDF Chat	Vortex rings: existence and asymptotic estimates	1981	Avner Friedman Bruce Turkington
+	On a free boundary problem arising in plasma physics	1980	Henri Berestycki Haı̈m Brezis
+	On steady vortex flow in two dimensions. I	1983	Bruce Turkington
+	Asymptotic estimates for the plasma problem	1980	Luis Caffarelli Avner Friedman
+	Variational principle for three-dimensional steady-state flows of an ideal fluid	1965	Vladimir I. Arnold