Instability analysis of nonlinear surface waves in a circular cylindrical container subjected to a vertical excitation

Jian, Yongjun; Xuequan, E

doi:10.1016/j.euromechflu.2005.03.002

Cited by 6 publications

(7 citation statements)

References 27 publications

(36 reference statements)

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“…Weakly nonlinear analyses (Miles 1984;Meron & Procaccia 1986;Nayfeh 1987;Nagata 1989;Douady 1990;Milner 1991;Zhang & Vinals 1997;Chen & Vinals 1999;Jian & Xuequan 2005;Skeldon & Guidoboni 2007;Rajchenbach & Clamond 2015) have indeed been widely used in the context of Faraday instabilities to study the wave amplitude saturation via super and subcritical bifurcations, as well as to investigate pattern and quasipattern formation (Stuart & Fauve 1993;Edwards & Fauve 1994) or spatiotemporal chaos (Ciliberto & Gollub 1985;Gluckman et al 1993), arising when two modes with nearly the same frequency share the same unstable region in the parameter space and strongly interact. In contradistinction with these previous studies, the presence of a static meniscus calls for a WNL approach not only to estimate the wave amplitude saturation in the WNL regime, but also to predict the Faraday threshold.…”

Section: Introductionmentioning

confidence: 99%

Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis

et al. 2022

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In labscale Faraday experiments, meniscus waves respond harmonically to small-amplitude forcing without threshold, hence potentially cloaking the instability onset of parametric waves. Their suppression can be achieved by imposing a contact line pinned at the container brim with static contact angle $\theta _s=90^{\circ }$ (brimful condition). However, tunable meniscus waves are desired in some applications as those of liquid-based biosensors, where they can be controlled adjusting the shape of the static meniscus by slightly underfilling/overfilling the vessel ( $\theta _s\ne 90^{\circ }$ ) while keeping the contact line fixed at the brim. Here, we refer to this wetting condition as nearly brimful. Although classic inviscid theories based on Floquet analysis have been reformulated for the case of a pinned contact line (Kidambi, J. Fluid Mech., vol. 724, 2013, pp. 671–694), accounting for (i) viscous dissipation and (ii) static contact angle effects, including meniscus waves, makes such analyses practically intractable and a comprehensive theoretical framework is still lacking. Aiming at filling this gap, in this work we formalize a weakly nonlinear analysis via multiple time scale method capable of predicting the impact of (i) and (ii) on the instability onset of viscous subharmonic standing waves in both brimful and nearly brimful circular cylinders. Notwithstanding that the form of the resulting amplitude equation is in fact analogous to that obtained by symmetry arguments (Douady, J. Fluid Mech., vol. 221, 1990, pp. 383–409), the normal form coefficients are here computed numerically from first principles, thus allowing us to rationalize and systematically quantify the modifications on the Faraday tongues and on the associated bifurcation diagrams induced by the interaction of meniscus and subharmonic parametric waves.

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Section: Introductionmentioning

confidence: 99%

Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis

et al. 2022

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“…Thus the forced amplitude must small enough to ensure the validity of small parameter ε in present theory when the forced frequency is given. In order to comparing the results of single layer fluid [7], the contours of the interface displacements and corresponding three dimensional interface figures determined by (13b) for different density ratio γ are plotted in Fig. 2 when the forced frequency is 29.1 Hz and the forced amplitude is 11.4 µm.…”

Section: Resultsmentioning

confidence: 99%

“…One of these is concerned with the instability [5][6][7][8][9][10][11] and chaotic behaviors in the container with a closed basin [12][13][14][15][16][17]. The other relates to solitary standing waves observed in a long narrow channel [18,19].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear interfacial waves in a circular cylindrical container subjected to a vertical excitation

Chang

Jian

et al. 2014

Wave Motion

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“…The method of multiple scales to study the nonlinear Faraday waves in a circular container partially filled with inviscid fluid was employed in Refs. [183,184]. It was shown that different freesurface standing wave patterns can be formed at different values of excitation frequency and amplitude.…”

Section: Breaking Surface Wavesmentioning

confidence: 99%

Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems

Ibrahim

2015

Journal of Fluids Engineering

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Liquid parametric sloshing, known also as Faraday waves, has been a long standing subject of interest. The development of the theory of Faraday waves has witnessed a number of controversies regarding the analytical treatment of sloshing modal equations and modes competition. One of the significant contributions is that the energy is transferred from lower to higher harmonics and the nonlinear coupling generated static components in the temporal Fourier spectrum, leading to a contribution of a nonoscillating permanent sinusoidal deformed surface state. This article presents an overview of different problems of Faraday waves. These include the boundary value problem of liquid parametric sloshing, the influence of damping and surfactants on the stability and response of the free surface, the weakly nonlinear parametric and autoparametric sloshing dynamics, and breaking waves under high parametric excitation level. An overview of the physics of Faraday wave competition together with pattern formation under single-, two-, three-, and multifrequency parametric excitation will be presented. Significant effort was made in order to understand and predict the pattern selection using analytical and numerical tools. Mechanisms for selecting the main frequency responses that are different from the first subharmonic one were identified in the literature. Nontraditional sources of parametric excitation and Faraday waves of ferromagnetic films and ferrofluids will be briefly discussed. Under random parametric excitation and g-jitter, the behavior of Faraday waves is described in terms of stochastic stability modes and spectral density function.

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Instability analysis of nonlinear surface waves in a circular cylindrical container subjected to a vertical excitation

Cited by 6 publications

References 27 publications

Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis

Subharmonic parametric instability in nearly brimful circular cylinders: a weakly nonlinear analysis

Nonlinear interfacial waves in a circular cylindrical container subjected to a vertical excitation

Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems

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