An efficient and general numerical method to compute steady uniform vortices

DOI10.1016/j.jcp.2011.04.035zbMath1408.76123OpenAlexW2040306773MaRDI QIDQ654974

Paolo Luzzatto-Fegiz, Charles H. K. Williamson

Publication date: 28 December 2011

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2011.04.035

zbMATH Keywords

contour dynamicsvortex stabilitysteady vortex flows

Mathematics Subject Classification ID

Related Items (16)

Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations ⋮ On the stability of discrete tripole, quadrupole, Thomson' vortex triangle and square in a two-layer/homogeneous rotating fluid ⋮ The interaction of two asymmetric quasi-geostrophic vortex patches ⋮ Stability and evolution of two opposite-signed quasi-geostrophic shallow-water vortex patches ⋮ Uniformly rotating analytic global patch solutions for active scalars ⋮ The Sadovskii vortex in strain ⋮ Global solutions for the generalized SQG patch equation ⋮ Imperfect bifurcation for the quasi-geostrophic shallow-water equations ⋮ On the existence of stationary patches ⋮ A framework for linear stability analysis of finite-area vortices ⋮ Stability of elliptical vortices from ``Imperfect-velocity-impulse diagrams ⋮ Symmetry in stationary and uniformly rotating solutions of active scalar equations ⋮ Computer-assisted proofs in PDE: a survey ⋮ Determining the stability of steady two-dimensional flows through imperfect velocity-impulse diagrams ⋮ Quasi-geostrophic shallow-water vortex–patch equilibria and their stability ⋮ On Singular Vortex Patches, I: Well-posedness Issues

Uses Software

• NewtonLib

Cites Work

• Unnamed Item
• Steady-state solutions of the Euler equations in two dimensions: Rotating and translating V-states with limiting cases. I: Numerical algorithms and results
• Hamiltonian-Dirac simulated annealing: application to the calculation of vortex states
• Stability of elliptical vortices from ``Imperfect-velocity-impulse diagrams
• A new calculus for two-dimensional vortex dynamics
• Contour surgery: A topological reconnection scheme for extended integrations using contour dynamics
• Two variations on the theme of Lamb--Chaplygin: supersmooth dipole and rotating multipoles
• On continuation of inviscid vortex patches
• Hamiltonian description of the ideal fluid
• Resonant instability in two-dimensional vortex arrays
• Newton Methods for Nonlinear Problems
• Stability of vortices in equilibrium with a cylinder
• A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids
• Stability of a vortex street of finite vortices
• The stability and energetics of corotating uniform vortices
• Steady-State Solutions of the Euler Equations in Two Dimensions II. Local Analysis of Limiting V-States
• Numerical Evidence for the Existence of New Types of Gravity Waves of Permanent Form on Deep Water
• The structure of organized vortices in a free shear layer
• A family of steady, translating vortex pairs with distributed vorticity
• Properties of a Vortex Street of Finite Vortices
• Structure of a Linear Array of Uniform Vortices
• The touching pair of equal and opposite uniform vortices
• Theory of the almost-highest wave. Part 2. Matching and analytic extension
• The stability of elliptical vortices in an external straining flow
• A new family of uniform vortices related to vortex configurations before merging
• Some steady vortex flows past a circular cylinder
• Statistical equilibrium predictions of jets and spots on Jupiter
• The nonlinear evolution of rotating configurations of uniform vorticity
• Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 1. Fundamentals
• Extremal energy properties and construction of stable solutions of the Euler equations
• Exact solutions for rotating vortex arrays with finite-area cores
• A general theory for two-dimensional vortex interactions
• Vortex Dynamics
• Contour dynamics for the Euler equations in two dimensions

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