On the oscillatory hydrodynamic instability of gravitational thermal flows of liquid metals in variable cross-section containers

Natural convective flows of liquid metals in open or closed ducts and containers play a relevant role in a variety of applications in mechanical, materials, and nuclear engineering. This analysis follows and integrates the line of inquiry started in past authors’ work about the typical properties of these flows and associated hierarchy of bifurcations in rectangular geometries. The Navier–Stokes and energy equations are solved in their time-dependent and non-linear formulation to investigate the onset and evolution of oscillatory disturbances and other effects breaking the initially unicellular structure of the flow. It is shown that a kaleidoscope of oscillatory patterns is made possible by the new degree of freedom represented by the opposite inclination of the walls with respect to the horizontal direction. Even minute variations in the geometry and/or initial conditions can cause significant changes. Multiple states exist which can replace each other in given sub-regions of the space of parameters. Observed regimes include stationary convection, weakly oscillating rolls, coalescing rolls, traveling waves, and modulated (pulso-traveling) disturbances. Most interestingly, traveling waves can propagate either in the downstream or in the upstream direction according to whether the walls are converging or diverging.