Two-dimensional generalized solitary waves and periodic waves under an ice sheet

Vanden‐Broeck, J.‐M.; Părău, Emilian

doi:10.1098/rsta.2011.0108

Cited by 60 publications

(44 citation statements)

References 18 publications

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“…In deep water, as explained in Ref. 9, there exist many different families of periodic waves with dimples on their free-surface. This is confirmed by the present numerical results.…”

Section: B Periodic Waves In Infinite Depthmentioning

confidence: 99%

Numerical studies of two-dimensional hydroelastic periodic and generalised solitary waves

Gao

Vanden‐Broeck

2014

Physics of Fluids

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Hydroelastic waves propagating at a constant velocity at the surface of a fluid are considered. The flow is assumed to be two-dimensional and potential. Gravity is included in the dynamic boundary condition. The fluid is bounded above by an elastic sheet which is described by the Plotnikov-Toland model. Fully nonlinear solutions are computed by a series truncation method. The findings generalised previous results where the sheet was described by a simplified model known as the Kirchhoff-Love model. Periodic and generalised solitary waves are computed. The results strongly suggest that there are no true solitary waves (i.e., solitary waves characterised by a flat free surface in the far field). Detailed comparisons with results obtained with the Kirchhoff-Love model and for the related problem of gravity capillary waves are also presented.

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“…In deep water, as explained in Ref. 9, there exist many different families of periodic waves with dimples on their free-surface. This is confirmed by the present numerical results.…”

Section: B Periodic Waves In Infinite Depthmentioning

confidence: 99%

Numerical studies of two-dimensional hydroelastic periodic and generalised solitary waves

Gao

Vanden‐Broeck

2014

Physics of Fluids

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“…The excitations of stable elevation solitary waves are achieved by applying multiple loads moving with a speed in the transcritical regime. moving loads, to study periodic hydroelastic waves (Forbes 1986(Forbes , 1988, generalised flexural-gravity solitary waves (Vanden-Broeck & Pȃrȃu 2011) and the unsteady interaction between a fluid-loaded elastic plate and a mean flow (Peake 2001). Although the Kirchhoff-Love model is widely used in the literature, it has some limitations.…”

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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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“…Vanden-Broeck & Pȃrȃu [39] present computations of two-dimensional generalized solitary waves and of periodic waves travelling under an ice sheet. The flow is assumed to be potential.…”

Section: Organization Of the Theme Issuementioning

confidence: 99%

The mathematical challenges and modelling of hydroelasticity

Korobkin

Părău

Vanden‐Broeck

2011

Phil. Trans. R. Soc. A.

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Hydroelasticity brings together hydrodynamics and elastic theories. It is concerned with deformations of elastic bodies responding to hydrodynamic excitations, which themselves depend on elastic deformation. This Theme Issue is intended to identify and to outline mathematical problems of modern hydroelasticity and to review recent developments in this area, including physically and mathematically elaborated models and the techniques used in their analysis.

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Two-dimensional generalized solitary waves and periodic waves under an ice sheet

Abstract: Two-dimensional gravity waves travelling under an ice sheet are studied. The flow is assumed to be potential. Weakly nonlinear solutions are derived and fully nonlinear solutions are calculated numerically. Periodic waves and generalized solitary waves are studied.

Cited by 60 publications

References 18 publications

Numerical studies of two-dimensional hydroelastic periodic and generalised solitary waves

Numerical studies of two-dimensional hydroelastic periodic and generalised solitary waves

New hydroelastic solitary waves in deep water and their dynamics

The mathematical challenges and modelling of hydroelasticity

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