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

We present a numerical and theoretical investigation on the natural convect ion of a low Prandtl number fluid (Pr = 0.025) in 2D and 3D side-heated enc losures tilted alpha = 80 degrees with respect to the vertical position. Th e choice of this inclination angle comes from a previous linear stability a nalysis of the basic (plane-parallel) flow that predicts the same critical Ra for longitudinal oscillatory and stationary transversal modes. In both t he 2D and 3D enclosures the first transition gradually leads to a transvers al 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 enclos ure, the onset of oscillations is due to a fully three-dimensional standing wave composed of three counter-rotating longitudinal rolls. The further ev olution of the 3D flow qualitatively agrees with previous experiments (J. C rystal Growth, 102 (1990) pp. 54-69): a quasiperiodic flow followed by a fr equency 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 p revious experiments. (C) 2001 Editions scientifiques et medicales Elsevier SAS.