Super-harmonically resonant swirling waves in longitudinally forced circular cylinders

TL;DR

This paper develops a weakly nonlinear analysis to predict super-harmonic swirling waves in longitudinally forced circular cylinders, confirmed by experiments showing stable swirling, irregular, and planar wave regimes with matching stability boundaries.

Contribution

It introduces a novel weakly nonlinear model predicting swirling wave symmetry-breaking under super-harmonic forcing, supported by experimental validation.

Findings

Identification of three super-harmonic regimes: stable planar DC waves, irregular motion, stable swirling DC waves.

Quantitative agreement between theoretical stability boundaries and experimental observations.

Confirmation that super-harmonic excitation can induce symmetry-breaking and swirling in the system.

Abstract

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