ROBUST HETEROCLINIC CYCLES IN TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION WITHOUT BOUSSINESQ SYMMETRY

DOI10.1142/S0218127402006047zbMath1051.76023MaRDI QIDQ4736310

Joana D'Arc Prat, Isabel Mercader, Edgar Knoblauch

Publication date: 9 August 2004

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

mode interactionsConvectionheteroclinic cycles

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Convection in hydrodynamic stability (76E06) Forced convection (76R05)

Related Items (13)

Instabilities induced by a weak breaking of a strong spatial resonance ⋮ Dynamic patterns in the reduced Craik–Leibovich equations ⋮ The \(1:\sqrt 2\) mode interaction and heteroclinic networks in Boussinesq convection ⋮ Nonlinear Marangoni convection in circular and elliptical cylinders ⋮ Mode selection in concentric jets: the steady–steady 1 : 2 resonant mode interaction with O(2) symmetry ⋮ Invariant states in inclined layer convection. Part 1. Temporal transitions along dynamical connections between invariant states ⋮ Experimental observation of near-heteroclinic cycles in the von Kármán swirling flow ⋮ Robust heteroclinic cycles in the one-dimensional complex Ginzburg-Landau equation ⋮ Dynamics in the 1:2 spatial resonance with broken reflection symmetry ⋮ The 1 : 2 spatial resonance on a hexagonal lattice in two-layered Rayleigh–Bénard problems ⋮ Heteroclinic cycles and periodic orbits for the O(2)-equivariant 0:1:2 mode interaction ⋮ A heteroclinic network in mode interaction with symmetry ⋮ Weakly nonlinear mode interactions in spherical Rayleigh–Bénard convection

Cites Work

• O(2)-symmetric bifurcation theory for convection rolls
• Pattern selection in long-wavelength convection
• Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry
• High-order splitting methods for the incompressible Navier-Stokes equations
• Complex dynamics in the 1:3 spatial resonance
• Mode interactions in Rayleigh-Bénard convection
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• Back in the Saddle Again: A Computer Assisted Study of the Kuramoto–Sivashinsky Equation
• The dynamics of coherent structures in the wall region of a turbulent boundary layer
• The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance
• Planform selection by finite-amplitude thermal convection between poorly conducting slabs
• Bifurcation from O(2) symmetric heteroclinic cycles with three interacting modes
• Coherence and chaos in a model of turbulent boundary layer
• Mode interaction models for near-wall turbulence
• Kuramoto–Sivashinsky Dynamics on the Center–Unstable Manifold
• NUMERICAL STUDY OF PATTERNS AND THEIR EVOLUTION IN FINITE GEOMETRIES
• THE 1:2 MODE INTERACTION IN RAYLEIGH–BÉNARD CONVECTION WITH AND WITHOUT BOUSSINESQ SYMMETRY
• On flow between counter-rotating cylinders
• Strong resonance in two-dimensional non-Boussinesq convection
• Large-scale flows and resonances in 2-D thermal convection
• New type of complex dynamics in the \(1:2\) spatial resonance

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