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Standing waves in deep water: Their stability and extreme form (1992)

Mercer, G. N. ; Roberts, A. J.

New York, NY : American Institute of Physics (AIP)

Physics of Fluids 4 (1992), S. 259-269

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ISSN: 1089-7666

Source: AIP Digital Archive

Topics: Physics

Notes: A stable and accurate numerical method to calculate the motion of an interface between two fluids is used to calculate two-dimensional standing water waves. The general method calculates arbitrary time-dependent motion of an interface, possibly including interfacial tension and different density ratios between the fluids. Extremely steep standing waves are determined, significantly steeper than has been previously reported. The peak crest acceleration is used as the determining parameter rather than the wave steepness as the wave steepness is found to have a maximum short of the most extreme wave. Profiles with crest accelerations up to 98% of gravity are calculated (a sequence of raster images of this profile as it evolves in time over one period may be obtained upon application to the authors: e-mail gmercer@xaspam.ua.oz.au or aroberts@xaspam.ua.oz.au), and the shape of these extreme standing wave profiles are discussed. The stability of the standing waves is examined and growth rates of the unstable modes are calculated. It is found that all but very steep standing waves are generally stable to harmonic perturbations. However, standing waves are typically unstable to subharmonic perturbations via a sideband-type instability.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.858354

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Dynamics of human milk extraction: A comparative study of breast feeding and breast pumping (1997)

Zoppou, C. ; Barry, S. I. ; Mercer, G. N.

Springer

Bulletin of mathematical biology 59 (1997), S. 953-973

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ISSN: 1522-9602

Source: Springer Online Journal Archives 1860-2000

Topics: Biology , Mathematics

Notes: Abstract We describe a mathematical model of the flow and deformation in a human teat. Our aim is to compare the theoretical milk yield during infant breast feeding with that obtained through the use of a breast pump. Infants use a peristaltic motion of the tongue, along with some suction, to extract milk, whereas breast pumps use a cyclic pattern of suction only. Our model is based on quasi-linear poroelasticity whereby the teat is modelled as a cylindrical porous elastic material saturated with fluid. We impose a cyclic axial suction pressure difference across the teat and impose a radial compressive force moving along the teat which mimics infant suckling. This is compared to the case of cyclic and steady pumping only which models the action of breast pumps. The results illustrate that there is an optimal time to apply the compressive force during the suction cycle that will increase the flow rate in our theoretical teat. The model and results may be of use in the future design of effective breast pumps.