Super-harmonically resonant swirling waves in longitudinally forced circular cylinders

Marcotte, Alice; Gallaire, François; Bongarzone, Alessandro

doi:10.1017/jfm.2023.438

Cited by 6 publications

(1 citation statement)

References 64 publications

(187 reference statements)

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“…The number of grid points in the radial and vertical direction is , which largely ensures convergence of the results. This numerical approach has been employed and validated in a series of recent works (Bongarzone, Guido & Gallaire 2022 a ; Marcotte, Gallaire & Bongarzone 2023 a , b ), and a detailed description of its implementation can be found in Appendix A.2 of Viola et al. (2018).…”

Section: Figure 14mentioning

confidence: 99%

A revised gap-averaged Floquet analysis of Faraday waves in Hele-Shaw cells

Bongarzone,

Jouron,

Viola

et al. 2023

J. Fluid Mech.

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Existing theoretical analyses of Faraday waves in Hele-Shaw cells rely on the Darcy approximation and assume a parabolic flow profile in the narrow direction. However, Darcy's model is known to be inaccurate when convective or unsteady inertial effects are important. In this work, we propose a gap-averaged Floquet theory accounting for inertial effects induced by the unsteady terms in the Navier–Stokes equations, a scenario that corresponds to a pulsatile flow where the fluid motion reduces to a two-dimensional oscillating Poiseuille flow, similarly to the Womersley flow in arteries. When gap-averaging the linearised Navier–Stokes equation, this results in a modified damping coefficient, which is a function of the ratio between the Stokes boundary layer thickness and the cell's gap, and whose complex value depends on the frequency of the wave response specific to each unstable parametric region. We first revisit the standard case of horizontally infinite rectangular Hele-Shaw cells by also accounting for a dynamic contact angle model. A comparison with existing experiments shows the predictive improvement brought by the present theory and points out how the standard gap-averaged model often underestimates the Faraday threshold. The analysis is then extended to the less conventional case of thin annuli. A series of dedicated experiments for this configuration highlights how Darcy's thin-gap approximation overlooks a frequency detuning that is essential to correctly predict the locations of the Faraday tongues in the frequency–amplitude parameter plane. These findings are well rationalised and captured by the present model.

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Section: Figure 14mentioning

confidence: 99%

A revised gap-averaged Floquet analysis of Faraday waves in Hele-Shaw cells

Bongarzone,

Jouron,

Viola

et al. 2023

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

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Superharmonic and triadic resonances in a horizontally oscillated stably stratified square cavity

Yalim,

Welfert,

Lopez

2023

J. Fluid Mech.

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The response to harmonic horizontal oscillations of a stably stratified fluid-filled two-dimensional square container is examined as the forcing amplitude is increased. For the studied forcing frequency, the response flow at very small forcing amplitudes is a synchronous periodic flow with piecewise-constant vorticity in regions delineated by the characteristics emanating from the corners of the container, regularized by viscosity. The second temporal harmonic of the forced response flow resonantly excites an intrinsic mode of the stratified container, whose magnitude grows as the square of the forcing amplitude. Above a critical forcing amplitude, a sequence of pairs of other container modes are excited via triadic resonances with the second-harmonic-driven mode. The flows are computed from the Navier–Stokes–Boussinesq equations and the ensuing dynamics is analysed using Fourier techniques, providing a comprehensive picture of the transition to internal wave turbulence.

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The suppression effect of a vertical baffle on three-dimensional swirling and chaotic sloshing in a laterally excited square-based tank

Liu,

Zhao,

Wang

2024

Physics of Fluids

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In order to systematically investigate the suppression effect of a vertical baffle on three-dimensional (3D) swirling and chaotic sloshing in a square-based tank subjected to horizontal harmonic excitation, hundreds of experiments are conducted in a clean tank and baffled tanks with three different configurations. Specifically, the vertical baffle is mounted on the tank bottom parallel to the longitudinal direction, the transverse direction, or the diagonal direction. This experimental work finds that there are four sloshing wave regimes in a clean tank—planar, square-like, swirling, and chaotic—which can be described by the asymptotic multimodal theory. Furthermore, there are only two wave regimes in a longitudinal-baffle tank, the planar and swirling regimes, and the occurrence of swirling requires that the excitation amplitude is sufficiently large. It is confirmed that the longitudinal baffle has a significant suppression effect on the swirling and chaotic motions of the sloshing waves, even though it is parallel to the direction of tank movement. Furthermore, the suppression effect of the diagonal baffle is similar to but somewhat smaller than that of the longitudinal baffle. However, when the transverse baffle is mounted on the bottom of the tank, it is difficult to excite the rotation of the sloshing wave. Therefore, the suppression effect of a bottom-mounted baffle depends largely on the included angle between the vertical baffle and the tank movement direction.

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Super-harmonically resonant swirling waves in longitudinally forced circular cylinders

Cited by 6 publications

References 64 publications

A revised gap-averaged Floquet analysis of Faraday waves in Hele-Shaw cells

A revised gap-averaged Floquet analysis of Faraday waves in Hele-Shaw cells

Superharmonic and triadic resonances in a horizontally oscillated stably stratified square cavity

The suppression effect of a vertical baffle on three-dimensional swirling and chaotic sloshing in a laterally excited square-based tank

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