Hydraulic falls under a floating ice plate due to submerged obstructions

Page, Charlotte; Părău, Emilian

doi:10.1017/jfm.2014.92

Cited by 8 publications

(29 citation statements)

References 32 publications

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“…(1985). According to Page & Părău (2014) and references therein, the strain is approximated by the expression . The strain takes on large values at the beginning which is probably due to the impulsively started load (even though we made sure to use initial data corresponding to a static load so as to avoid a non-smooth start-up phase).…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The strain computed here is the linear or axial strain which is used in defining the bending moment of an elastic solid, and which can be measured experimentally using a strainmeter, such as explained in Davys et al (1985). According to Page & Pȃrȃu (2014) and references therein, the strain is approximated by the expression ε = (h/2)η xx . The strain takes on large values at the beginning which is probably due to the impulsively started load (even though we made sure to use initial data corresponding to a static load so as to avoid a non-smooth start-up phase).…”

Section: Numerical Experimentsmentioning

confidence: 99%

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Fully dispersive models for moving loads on ice sheets

2019

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The response of a floating elastic plate to the motion of a moving load is studied using a fully dispersive weakly nonlinear system of equations. The system allows for an accurate description of waves across the whole spectrum of wavelengths and also incorporates nonlinearity, forcing and damping. The flexural–gravity waves described by the system are time-dependent responses to a forcing with a described weight distribution, moving at a time-dependent velocity. The model is versatile enough to allow the study of a wide range of situations including the motion of a combination of point loads and loads of arbitrary shape. Numerical solutions of the system are compared to data from a number of field campaigns on ice-covered lakes, and good agreement between the deflectometer records and the numerical simulations is observed in most cases. Consideration is also given to waves generated by a decelerating load, and it is shown that a decelerating load may trigger a wave response with a far greater amplitude than a load moving at constant celerity.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Fully dispersive models for moving loads on ice sheets

2019

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“…From then on, analytical and numerical investigations of this new model have been gradually carried out. Of note are the works of Toland (2008), who rigorously proved the existence of periodic hydroelastic waves, Guyenne & Pȃrȃu (2012), who discovered that both elevation and depression branches exist below the minimum of the phase speed at finite amplitude in deep water, Wang, Vanden-Broeck & Milewski (2013), who extended the branch of elevation solitary waves to the highly nonlinear regime with the wave profiles featuring multi-packet structure and computed periodic waves with an overhanging structure, Gao & Vanden-Broeck (2014), who investigated generalised solitary waves extensively, and Page & Pȃrȃu (2014), who considered nonlinear hydroelastic hydraulic falls past a submerged bottom obstruction.…”

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confidence: 99%

New hydroelastic solitary waves in deep water and their dynamics

2016

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A numerical study of fully nonlinear waves propagating through a two-dimensional deep fluid covered by a floating flexible plate is presented. The nonlinear model proposed by Toland (Arch. Rat. Mech. Anal., vol. 289, 2008, pp. 325-362) is used to formulate the pressure exerted by the thin elastic sheet. The symmetric solitary waves previously found by Guyenne & Pȃrȃu (J. 750-761) are briefly reviewed. A new class of hydroelastic solitary waves which are non-symmetric in the direction of wave propagation is then computed. These asymmetric solitary waves have a multi-packet structure and appear via spontaneous symmetry-breaking bifurcations. We study in detail the stability properties of both symmetric and asymmetric solitary waves subject to longitudinal perturbations. Some moderateamplitude symmetric solitary waves are found to be stable. A series of numerical experiments are performed to show the non-elastic behaviour of two interacting stable solitary waves. The large response generated by a localised steady pressure distribution moving at a speed slightly below the minimum of the phase speed (called the transcritical regime in the literature) is also examined. The direct numerical simulation of the fully nonlinear equations with a single load reveals that in this range the generated waves are of finite amplitude. This includes a perturbed depression solitary wave, which is qualitatively similar to the large response observed in experiments. The excitations of stable elevation solitary waves are achieved by applying multiple loads moving with a speed in the transcritical regime.

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“…It is worth noting that some large-amplitude solutions calculated here may become unphysical, as the strain of the ice plate may be higher than the yield strain of ice. In this case, the elastic model for the sheet will become unrealistic and different models should be used (see [ 32 ] for a more detailed discussion).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Solitary flexural–gravity waves in three dimensions

Trichtchenko

Părău

Vanden‐Broeck

et al. 2018

Phil. Trans. R. Soc. A.

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The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A 369, 2942–2956 (doi:10.1098/rsta.2011.010410.1098/rsta.2011.0104)). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations.This article is part of the theme issue ‘Modelling of sea-ice phenomena’.

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Hydraulic falls under a floating ice plate due to submerged obstructions

Cited by 8 publications

References 32 publications

Fully dispersive models for moving loads on ice sheets

Fully dispersive models for moving loads on ice sheets

New hydroelastic solitary waves in deep water and their dynamics

Solitary flexural–gravity waves in three dimensions

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