Vortex Rings: Existence and Asymptotic Estimates

DOI10.2307/1998335zbMath0497.76031OpenAlexW4242796578MaRDI QIDQ3962664

Avner Friedman, Bruce Turkington

Publication date: 1981

Full work available at URL: https://doi.org/10.2307/1998335

zbMATH Keywords

constraintssteady vortex ringscapacity methodskinetic energy as functional of vorticity

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) General aerodynamics and subsonic flows (76G25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Variational methods for second-order elliptic equations (35J20) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) Variational principles of physics (49S05)

Related Items (42)

Vortex patch problem for steady lake equation ⋮ Filamentation near Hill’s vortex ⋮ A constrained variational problem for an existence theorem of steady vortex rings in Poiseuille flow ⋮ Remarks on orbital stability of steady vortex rings ⋮ Corotating steady vortex flows with N-fold symmetry ⋮ The uniqueness of Hill's spherical vortex ⋮ Stability of Lamb dipoles ⋮ Clustered travelling vortex rings to the axisymmetric three-dimensional incompressible Euler flows ⋮ Smooth approximations and exact solutions of the 3D steady axisymmetric Euler equations ⋮ A computational method of solving free-boundary problems in vortex dynamics ⋮ On strong convergence to 3D steady vortex sheets ⋮ Estimating the non-dimensional energy of vortex rings by modelling their roll-up ⋮ Local uniqueness of vortices for 2D steady Euler flow in a bounded domain ⋮ Rapidly oscillating asymptotic solutions of the Navier-Stokes equations, coherent structures, Fomenko invariants, Kolmogorov spectrum, and flicker noise ⋮ Desingularizations of systems of point vortices ⋮ Vortex motion for the lake equations ⋮ Asymptotic behaviour of global vortex rings ⋮ A steady vortex ring in Poiseuille flow and rearrangements of a function ⋮ Axi-symmetric solutions for active vector models generalizing 3D Euler and electron-MHD equations ⋮ Stability of Hill's spherical vortex ⋮ Global vortex rings and asymptotic behaviour ⋮ The uniqueness of a family of steady vortex rings ⋮ Asymptotic solutions of the Navier-Stokes equations describing periodic systems of localized vortices ⋮ Asymptotic solutions of the Navier-Stokes equations and systems of stretched vortices filling a three-dimensional volume ⋮ Desingularization of vortex rings in 3 dimensional Euler flows ⋮ Asymptotic of Steady Vortex Pair in the Lake Equation ⋮ Planar vortex patch problem in incompressible steady flow ⋮ Steady vortex patches with opposite rotation directions in a planar ideal fluid ⋮ Uniqueness of axisymmetric viscous flows originating from positive linear combinations of circular vortex filaments ⋮ Asymptotic solutions of Navier-Stokes equations and topological invariants of vector fields and Liouville foliations ⋮ Desingularization of vortices for the Euler equation ⋮ Desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem ⋮ Nonlinear stability of planar vortex patches in an ideal fluid ⋮ A remark on the axisymmetric vortex sheet problem in \(\mathbb{R}^ 3\) ⋮ Computation of vortex flows past obstacles with circulation ⋮ Steady vortex rings in a uniform flow and rearrangements of a function ⋮ Regularization of planar vortices for the incompressible flow ⋮ Desingularization of a steady vortex pair in the lake equation ⋮ Existence of solutions for three dimensional stationary incompressible Euler equations with nonvanishing vorticity ⋮ Local uniqueness for vortex patch problem in incompressible planar steady flow ⋮ A variational approach to surface solitary waves ⋮ Existence of vortex rings in Beltrami flows

Cites Work

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• Asymptotic estimates for an axisymmetric rotating fluid
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• On the existence of global vortex rings
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• Existence of axisymmetric equilibrium figures
• A global theory of steady vortex rings in an ideal fluid
• Variational solutions of some nonlinear free boundary problems
• On nonlinear desingularization
• An Introduction to Fluid Dynamics
• On steady vortex rings of small cross-section in an ideal fluid
• Examples of steady vortex rings of small cross-section in an ideal fluid

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