title: Transition to chaos of natural convection between two infinite differentially heated vertical plates.
abstract: Natural convection of air between two infinite vertical differentially heated plates is studied analytically in two dimensions (2D) and numerically in two and three dimensions (3D) for Rayleigh numbers Ra up to 3 times the critical value Ra(c)=5708. The first instability is a supercritical circle pitchfork bifurcation leading to steady 2D corotating rolls. A Ginzburg-Landau equation is derived analytically for the flow around this first bifurcation and compared with results from direct numerical simulation (DNS). In two dimensions, DNS shows that the rolls become unstable via a Hopf bifurcation. As Ra is further increased, the flow becomes quasiperiodic, and then temporally chaotic for a limited range of Rayleigh numbers, beyond which the flow returns to a steady state through a spatial modulation instability. In three dimensions, the rolls instead undergo another pitchfork bifurcation to 3D structures, which consist of transverse rolls connected by counter-rotating vorticity braids. The flow then becomes time dependent through a Hopf bifurcation, as exchanges of energy occur between the rolls and the braids. Chaotic behavior subsequently occurs through two competing mechanisms: a sequence of period-doubling bifurcations leading to intermittency or a spatial pattern modulation reminiscent of the Eckhaus instability.
authors.affiliation: CNRS, LIMSI, UPR3251, BP 133, 91403 Orsay Cedex, France and Universite Pierre et Marie Curie-Paris 6, 4, Place Jussieu, 75252 Paris, Cedex 05, France.
authors.forename: Zhenlan
authors.initials: Z
authors.lastname: Gao
authors.forename: Anne
authors.initials: A
authors.lastname: Sergent
authors.forename: Berengere
authors.initials: B
authors.lastname: Podvin
authors.forename: Shihe
authors.initials: S
authors.lastname: Xin
authors.forename: Patrick
authors.initials: P
authors.lastname: Le Quéré
authors.forename: Laurette S
authors.initials: LS
authors.lastname: Tuckerman