Symmetry and Stability in Taylor-Couette Flow

DOI10.1137/0517023zbMath0603.76053OpenAlexW1987468503WikidataQ98107900 ScholiaQ98107900MaRDI QIDQ3740433

Martin Golubitsky, I. N. Stewart

Publication date: 1986

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/dba0c5bf81d5898f745f9ac0c7abcc32ead44c19

zbMATH Keywords

linear stabilitysymmetry groupCouette flowlinearized Navier-Stokes equationimaginary eigenvaluesconcentric rotating cylindersreduced bifurcation equationcounterrotating cylindersstabilities of solutions

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Hydrodynamic stability (76E99)

Related Items (34)

Hopf-steady-state mode interactions with 0(2) symmetry ⋮ Chaos in counter-rotating Couette flow ⋮ Bifurcations of Poiseuille flow between parallel plates: Three- dimensional solutions with large spanwise wavelength ⋮ Bifurcations of stationary, standing and travelling waves in triply diffusive convection ⋮ The effects of centrifugal force on the stability of axisymmetric viscous flow in a rotating annulus ⋮ The 2:1 steady/Hopf mode interaction in the two-layer Bénard problem ⋮ A classification of degenerate Hopf bifurcations with O(2) symmetry ⋮ Modulated waves in Taylor-Couette flow Part 1. Analysis ⋮ Modulated waves in Taylor-Couette flow Part 2. Numerical simulation ⋮ Classification and unifolding of degenerate Hopf bifurcations with 0(2) symmetry: No distinguished parameter ⋮ Pattern formation and bistability in flow between counterrotating cylinders ⋮ Multiple bifurcations in triple convection with non-ideal boundary conditions ⋮ Path-following methods in bifurcation problems ⋮ 3-mode Interactions with O(2) Symmetry and a Model for Taylor-Couette flow ⋮ On the origin of wave patterns in fluidized beds ⋮ Synchrony and asynchrony for neuronal dynamics defined on complex networks ⋮ Hidden symmetries and pattern formation in Lapwood convection ⋮ Hopf-Hopf mode interactions with O(2) symmetry ⋮ Degenerate \(O(2)\)-equivariant bifurcation equations and their applications to the Taylor problem ⋮ Hopf bifurcation in a three-dimensional system ⋮ Influence of fluid thermal sensitivity on the thermo-mechanical stability of the Taylor–Couette flow ⋮ The effect of outer cylinder rotation on Taylor–Couette flow at small aspect ratio ⋮ Hopf bifurcation in the presence of symmetry ⋮ Secondary bifurcations of Taylor vortices into wavy inflow or outflow boundaries ⋮ Perturbations of normally hyperbolic manifolds with applications to the Navier-Stokes equations ⋮ Bifurcation and symmetry breaking ⋮ Hopf bifurcations in Langmuir circulations ⋮ DEGENERATE BIFURCATIONS WITH Z₂⊕Z₂-SYMMETRY ⋮ The subharmonic bifurcation solution of nonlinear Mathieu's equation and Euler dynamic buckling problems ⋮ Symmetry and instability in rotating hydrodynamic and magnetohydrodynamic flows ⋮ Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry ⋮ Modulated rotating waves in O(2) mode interactions ⋮ Toric geometry and equivariant bifurcations. ⋮ Finite aspect ratio Taylor-Couette flow: Shil'nikov dynamics of 2-tori

This page was built for publication: Symmetry and Stability in Taylor-Couette Flow