Wavelength selection in axisymmetric cellular structures

Abstract

We consider axisymmetric cellular structures, as concentric rolls occurring in Rayleigh-Bénard thermo-convection when forcing a roll at an outer circular boundary. We show that under these circumstances a unique wavenumber is selected. It corresponds to the vanishing of the coefficient of perpendicular diffusion (D⟩ = 0). This condition expresses simply the fact that the rolls can be both bended and steady and do not tend to become more curved (D⟩ < 0) or straight (D⟩ > 0). We make some speculations about the kind of noise occurring when the wavenumber selected by the axisymmetric structure is outside of the band selected by the lateral boundaries