Re-entrant hexagons in non-Boussinesq convection

Santiago Madruga*, Hermann Riecke, Werner Pesch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


While non-Boussinesq hexagonal convection patterns are known to be stable close to threshold (i.e. for Rayleigh numbers R≈ Rc, it has often been assumed that they are always unstable to rolls for slightly higher Rayleigh numbers. Using the incompressible Navier-Stokes equations for parameters corresponding to water as the working fluid, we perform full numerical stability analyses of hexagons in the strongly nonlinear regime (∈ ≡ (R - Rc)/Rc= O (1). We find 're-entrant' behaviour of the hexagons, i.e. as ∈ is increased they can lose and regain stability. This can occur for values of ∈ as low as ∈ = 0.2.. We identify two factors contributing to the re-entrance: (i) far above threshold there exists a hexagon attractor even in Boussinesq convection as has been shown recently and (ii) the non-Boussinesq effects increase with ∈. Using direct simulations for circular containers we show that the re-entrant hexagons can prevail even for sidewall conditions that favour convection in the form of competing stable rolls. For sufficiently strong non-Boussinesq effects hexagons even become stable over the whole ∈ - range considered, O ≤ ∈ ≤ 1.5.

Original languageEnglish (US)
Pages (from-to)341-360
Number of pages20
JournalJournal of fluid Mechanics
StatePublished - Feb 10 2006

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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