Introduction

Raynovskyy, Ihor; Timokha, Alexander

doi:10.1201/9780429356711-1

Cited by 1 publication

(6 citation statements)

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“…All together, the experimental measurements are in very good quantitative agreement with the theoretical regime bounds for , below which the super-harmonic irregular and swirling regimes appear to be suppressed by dissipative mechanisms, e.g. viscous dissipation occurring in the fluid bulk, sidewall and free-surface boundary layers (Case & Parkinson 1957; Miles 1967; Raynovskyy & Timokha 2020; Bongarzone et al. 2022 b ) as well as in the neighbourhood of the moving contact line (Keulegan 1959; Dussan 1979; Hocking 1987; Cocciaro, Faetti & Festa 1993; Viola & Gallaire 2018).…”

Section: Methodssupporting

confidence: 74%

“…The occurrence of the jump-down transition was to be expected as it is produced by dissipative mechanisms (see also § 6.5), which are overlooked by the present inviscid analysis. The associated damping, which is a function of the wave amplitude and of the forcing acceleration amplitude (see Raynovskyy & Timokha (2018 b ), Raynovskyy & Timokha (2020) and the discussion in Appendix A of Bongarzone et al. 2022 a ), is responsible for the modulation in the phase lag between the external driving and the wave response, which was shown by Bäuerlein & Avila (2021) (for unidirectional sloshing waves in a rectangular container) to be of crucial importance for a correct prediction of the jump-down frequency.…”

Section: Methodsmentioning

confidence: 99%

“…Nevertheless, the reintroduction of surface tension in the multimodal theory can be challenging. In particular, it is not clear yet how to account for static meniscus and contact line dynamics (Raynovskyy & Timokha 2020). Moreover, in these cases, the element of the Fourier basis (Bessel) functions no more coincide with the actual natural sloshing modes.…”

Section: Harmonic Sc Resonancementioning

confidence: 99%

“…Below a critical liquid depth, typically for circular cylinders, such amplification (secondary or internal resonances) can happen in the vicinity of the primary resonance. These cases, which require a reordering of the asymptotic scaling, can still be tackled in the framework of the multimodal theory by employing the so-called adaptive modal approach (see chapters 7–9 of Faltinsen & Timokha 2009; Raynovskyy & Timokha 2020). However, secondary resonances may also occur more broadly even far from the primary resonance zone and for , as in the case of the DC super-harmonic resonance.…”

Section: Harmonic Sc Resonancementioning

confidence: 99%

“…By applying the Narimanov–Moiseev multimodal sloshing theory (Narimanov 1957; Moiseev 1958; Dodge, Kana & Abramson 1965; Faltinsen 1974; Narimanov, Dokuchaev & Lukovsky 1977; Lukovsky 1990; Lukovsky & Timokha 2011, 2015; Takahara & Kimura 2012; Lukovsky 2015), capable of accurately describing the nonlinear wave dynamics near primary harmonic resonances and in the absence of secondary resonances (Faltinsen, Rognebakke & Timokha 2005; Faltinsen et al. 2016; Raynovskyy & Timokha 2018 a , 2020), i.e. for a non-dimensional fluid depth , they derived the response curves for planar elliptic-type tank excitation.…”

Section: Introductionmentioning

confidence: 99%

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Super-harmonically resonant swirling waves in longitudinally forced circular cylinders

2023

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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.

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