Super-harmonically resonant swirling waves in longitudinally forced circular cylinders

Resonant sloshing in circular cylinders was studied by Faltinsen et al. (2016), whose theory used to describe steady-state resonant waves due time-harmonic container's elliptic orbits. In the limit of longitudinal container motions, a symmetry-breaking planar wave solution occurs, with clockwise and anti-clockwise swirling equally likely. addition this primary harmonic dynamics, previous experiments have unveiled that diverse super-harmonic dynamics are observable far from resonances. Among these, so-called double-crest (DC) first observed Reclari (2014) for rotary sloshing, is particularly relevant, as its manifestation most favored spatial structure external driving. Following Bongarzone (2022a), work we develop weakly nonlinear (WNL) analysis system response forcing. The resulting amplitude equations predicts via stable may also occur under excitation. This finding confirmed our experimental observations, which identify three possible regimes, i.e. (i) DC waves, (ii) irregular motion (iii) corresponding stability boundaries forcing frequency-amplitude plane quantitatively match present theoretical estimates.