par Gligor, D.;Salgado Sánchez, P.;Porter, Jeff;Shevtsova, Valentina 
Référence Physical Review Fluids, 5, 8, 084001
Publication Publié, 2020-08
Référence Physical Review Fluids, 5, 8, 084001
Publication Publié, 2020-08
Article révisé par les pairs
| Résumé : | The influence of the gravity level on the frozen wave instability in finite containers of immiscible liquids is investigated numerically to shed light on the transformation from a supercritical pitchfork bifurcation in normal gravity, which produces stable finite-amplitude waves, to an apparently degenerate bifurcation in weightlessness, leading to large columnar patterns that collide with the container walls. The vibroequilibria effect grows in importance as gravity is reduced and has a symmetry-breaking effect on the bifurcation, selecting frozen waves with the heavier fluid displaced upward along the lateral walls. Three possible growth regimes are identified. With finite gravity, there is an initial gravity-capillary regime with the square-root growth predicted by weakly nonlinear theory, associated with small-amplitude waves. This is followed by a linear growth regime that is dominated by gravity and associated with larger finger-like waves. Lastly, in some cases with reduced gravity, we observe a third regime characterized by the close proximity of the frozen wave crests to the upper wall and an interval of nearly saturated wave amplitude. The defining parameters of the bifurcation diagram are measured and presented as a function of Bond number and, when possible, compared with theoretical predictions. In particular, there is excellent agreement between theory and simulations for the weakly nonlinear cubic (branching) coefficient and reasonable qualitative agreement for the threshold. Differences are attributed to finite-size effects, vibroequilibria, and viscosity. |
