Symmetry-breaking bifurcations in resonant surface waves

Feng, Zhaosheng; Sethna, P. R.

doi:10.1017/s0022112089000455

Cited by 114 publications

(93 citation statements)

References 23 publications

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“…This normal form has been investigated before in the literature in the context of three-dimensional rectangular vessels with almost square cross section (e.g. (18), (30)). A new analysis of this normal form was recently presented in Turner & Bridges (19), obtained by projecting these equations onto a sphere, where all orbits become apparent.…”

Section: Discussionmentioning

confidence: 99%

Dynamic coupling in Cooker's sloshing experiment with baffles

2013

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This paper investigates the dynamic coupling between fluid sloshing and the motion of the vessel containing the fluid, for the case when the vessel is partitioned using non-porous baffles. The vessel is modelled using Cooker's sloshing configuration [M. J. Cooker, Wave Motion 20, 385-395 (1994)]. Cooker's configuration is extended to include n − 1 non-porous baffles which divide the vessel into n separate fluid compartments each with a characteristic length scale. The problem is analysed for arbitrary fill depth in each compartment, and it is found that a multitude of resonance situations can occur in the system, from 1 : 1 resonances to (n + 1)−fold 1 : 1 : · · · : 1 resonances, as well as : m : · · · : n for natural numbers , m, n, depending upon the system parameter values. The conventional wisdom is that the principle role of baffles is to damp the fluid motion. Our results show that in fact without special consideration, the baffles can lead to enhancement of the fluid motion through resonance.

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Section: Discussionmentioning

confidence: 99%

Dynamic coupling in Cooker's sloshing experiment with baffles

2013

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“…Despite the fact that the CASF equations include 3-D continuity and Navier-Stokeslike equations for the mean flow some qualitative properties of the solutions can be established. As an example, we consider in §4 two-mode Faraday waves in almost-square, rectangular containers, as in the well-known experiments by Simonelli and Gollub [9] and Feng and Sethna [10].…”

Section: Introductionmentioning

confidence: 99%

Interaction of Nearly-Inviscid, Multi-mode Faraday Waves and Mean Flows

Higuera

Vega

Knobloch

2001

Coherent Structures in Complex Systems

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“…In that case both the pure modes have the exact same stability properties. Secondly the problem of energy transfer is not considered in the analysis in Feng & Sethna (1989), Faltinsen et al (2003) or Ikeda et al (2012). The analysis of energy transfer is made apparent in the present paper by showing that the orbits of the normal form (1.2) can be projected onto a spheroid in three dimensions.…”

Section: Introductionmentioning

confidence: 90%

“…The most well-known context is sloshing in three dimensions when the horizontal cross-section of the vessel is square or almost square. This configuration has been studied by Feng & Sethna (1989);Faltinsen et al (2003); Ikeda et al (2012); see also §9.2.3 of Faltinsen & Timokha (2009). There are two significant differences from the analysis here.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear energy transfer between fluid sloshing and vessel motion

Turner

Bridges

2013

J. Fluid Mech.

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This paper examines the dynamic coupling between a sloshing fluid and the motion of the vessel containing the fluid. A mechanism is identified which leads to an energy exchange between the vessel dynamics and fluid motion. It is based on a 1:1 resonance in the linearized equations, but nonlinearity is essential for the energy transfer. For definiteness, the theory is developed for Cooker's pendulous sloshing experiment. The vessel has a rectangular cross section, is partially filled with a fluid, and is suspended by two cables. A nonlinear normal form is derived close to an internal 1:1 resonance, with the energy transfer manifested by a heteroclinic connection which connects the purely symmetric sloshing modes to the purely anti-symmetric sloshing modes. Parameter values where this pure energy transfer occurs are identified. In practice, this energy transfer can lead to sloshing-induced destabilization of fluid-carrying vessels.

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Symmetry-breaking bifurcations in resonant surface waves

Cited by 114 publications

References 23 publications

Dynamic coupling in Cooker's sloshing experiment with baffles

Dynamic coupling in Cooker's sloshing experiment with baffles

Interaction of Nearly-Inviscid, Multi-mode Faraday Waves and Mean Flows

Nonlinear energy transfer between fluid sloshing and vessel motion

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