TY - JOUR
T1 - Re-entrant hexagons in non-Boussinesq convection
AU - Madruga, Santiago
AU - Riecke, Hermann
AU - Pesch, Werner
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2006/2/10
Y1 - 2006/2/10
N2 - 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.
AB - 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.
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U2 - 10.1017/S0022112005007640
DO - 10.1017/S0022112005007640
M3 - Article
AN - SCOPUS:32044444826
VL - 548
SP - 341
EP - 360
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -