Flow transitions of a low-Prandtl-number fluid in an inclined 3D cavity

Abstract

We present a numerical and theoretical investigation on the natural convection of a low Prandtl number fluid ( Pr=0.025) in 2D and 3D side-heated enclosures tilted α=80° with respect to the vertical position. The choice of this inclination angle comes from a previous linear stability analysis of the basic (plane-parallel) flow that predicts the same critical Ra for longitudinal oscillatory and stationary transversal modes. In both the 2D and 3D enclosures the first transition gradually leads to a transversal stationary centered shear roll. In the 2D geometry the flow becomes time-dependent and multicellular (3 rolls) at the onset of a Hopf bifurcation, followed by subsequent period-doubling. On the other hand, in the 3D enclosure, the onset of oscillations is due to a fully three-dimensional standing wave composed of three counter-rotating longitudinal rolls. The further evolution of the 3D flow qualitatively agrees with previous experiments (J. Crystal Growth, 102 (1990) pp. 54–68): a quasiperiodic flow followed by a frequency locked state. The main contribution of this work is the analysis of the flow structure underlying the secondary frequency: a transversal wave composed of two shear rolls that coexist with the three longitudinal cells. This is the first numerical work that explicitly illustrates this scenario which was suggested at the onset of the biperiodic regime in many of the previous experiments.