Domain-filling rolls in two-dimensional fixed-flux Rayleigh-Bénard convection

Abstract

Rayleigh-Bénard convection of large horizontal extent sometimes self-organizes into domain-filling structures. In two dimensions, domain-filling rolls persist - from some but not all initial conditions - when velocity boundary conditions are stress-free. When velocity boundary conditions are no-slip, domain-filling rolls are not found with fixed-temperature thermal boundary conditions, but they have not been sought with fixed-flux thermal boundary conditions. Here we explore the latter missing case, which is hard to predict because no-slip boundaries do not encourage domain-filling rolls, but fixed-flux boundaries give domain-filling structures in three dimensions for either boundary condition on velocity. We simulate convection with fixed-flux, no-slip boundaries in two-dimensional domains with horizontal period 20 times their height and at various combinations of the fixed-flux Rayleigh number R and Prandtl number Pr. Domain-filling rolls, which are easily found when they are weakly nonlinear at small R, are continued to other (R,Pr) by changing these parameters slowly in time. The (R,Pr) regime where we find domain-filling rolls is substantial but has a boundary. When R is too large or Pr too small, relative to each other, a domain-filling roll pair breaks up into two pairs. These findings contrast with other combinations of dimension and boundary conditions, where scale selection has not been seen to depend strongly on parameter values. The present case helps disentangle competing effects of dimension and boundary conditions, and it offers a more stringent test for explanations of scale selection that have been proposed.