Super-harmonically resonant swirling waves in longitudinally forced circular cylinders

Resonant sloshing in circular cylinders was studied by Faltinsen et al. (J. Fluid Mech., vol. 804, 2016, pp. 608–645), whose theory was used to describe steady-state resonant waves due to a time-harmonic container's elliptic orbits. In the limit of longitudinal container motions, a symmetry bre...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 966
Main Authors Marcotte, Alice, Gallaire, François, Bongarzone, Alessandro
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 06.07.2023
Subjects
Amplitude
Amplitudes
Broken symmetry
Circular cylinders
Containers
Cylinders
Dynamics
Electrons
Fluid mechanics
Fluids
Harmonic excitation
JFM Papers
Motion stability
Nonlinear analysis
Swirling
Waves
bifurcation
surface gravity waves
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Summary:Resonant sloshing in circular cylinders was studied by Faltinsen et al. (J. Fluid Mech., vol. 804, 2016, pp. 608–645), whose theory was used to describe steady-state resonant waves due to a 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. (Phys. Fluids, vol. 26, no. 5, 2014, 052104) for circular sloshing, is particularly relevant, as its manifestation is the most favoured by the spatial structure of the external driving. Following Bongarzone et al. (J. Fluid Mech., vol. 943, 2022, A28), in this work we develop a weakly nonlinear 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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2023.438