Permeability sets the linear path instability of buoyancy-driven disks

The prediction of trajectories buoyancy-driven objects immersed in a viscous fluid is key problem dynamics. Simple-shaped objects, such as disks, present great variety trajectories, ranging from zig-zag to tumbling and chaotic motions. Yet, similar studies are lacking when the object permeable. We perform linear stability analysis steady vertical path thin permeable disk, whose flow through microstructure modelled via stress-jump model based on homogenization theory. relative velocity associated with presents recirculation region detached body, which shrinks eventually disappears disk becomes more In analogy solid one non-oscillatory several oscillatory modes identified found destabilize fluid–solid coupled system away its straight trajectory. Permeability progressively filters out wake dynamics instability path. Modes dominated by oscillations first stabilized, followed those characterized weaker, or absent, oscillations, typically tilting induced inclined For sufficiently large permeabilities, undergoes divergence instability, expected lead oblique constant inclination, nonlinear regime. A further permeability increase reduces unstable range all until quenching instabilities.