Stability of periodic arrays of vortices

DOI10.1063/1.868802zbMath1023.76527arXivpatt-sol/9510003OpenAlexW1982434635MaRDI QIDQ4425513

Laurette S. Tuckerman, Thierry Dauxois, Stephan Fauve

Publication date: 18 November 2003

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

Full work available at URL: https://arxiv.org/abs/patt-sol/9510003

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) Wakes and jets (76D25) Flow control and optimization for incompressible viscous fluids (76D55)

Related Items (13)

Speaker-wire vortices in stratified anabatic Prandtl slope flows and their secondary instabilities ⋮ Periodic solutions for a second-order partial difference equation ⋮ On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteria ⋮ Another exact solution for two-dimensional, inviscid sinh Poisson vortex arrays ⋮ Vortex arrays for sinh-Poisson equation of two-dimensional fluids: Equilibria and stability ⋮ Double-periodic arrays of vortices ⋮ Three-dimensional stability of periodic arrays of counter-rotating vortices ⋮ The pitfalls of investigating rotational flows with the Euler equations ⋮ Linear stability of a doubly periodic array of vortices to three-dimensional perturbations ⋮ Spatio-temporal dynamics of forced periodic flows in a confined domain ⋮ Inviscid two dimensional vortex dynamics and a soliton expansion of the sinh-Poisson equation ⋮ Nontrivial solutions for a nonlinear discrete elliptic equation with periodic boundary conditions ⋮ Morse Index of Multiple Blow-up Solutions to the Two-Dimensional Sinh-Poisson Equation

Cites Work

• Real periodic solutions of the Liouville equation
• Exact solutions of a nonlinear boundary value problem: The vortices of the two-dimensional sinh-Poisson equation
• Nonlinear stability of fluid and plasma equilibria
• The structure of organized vortices in a free shear layer
• Final equilibrium state of a two-dimensional shear layer
• Instabilities in two-dimensional spatially periodic flows. Part I: Kolmogorov flow
• A row of counter-rotating vortices
• On Chaplygin's investigations of two-dimensional vortex structures in an inviscid fluid
• On long-lived vortices in 2-D viscous flows, most probable states of inviscid 2-D flows and a soliton equation
• Nonlinear stability of counter-rotating vortices
• Asymmetry and Hopf bifurcation in spherical Couette flow
• On finite amplitude oscillations in laminar mixing layers

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