Forced and unforced flexural-gravity solitary waves

Philippe Guyenne; Emilian Parau

doi:10.1016/j.piutam.2014.01.047

Forced and unforced flexural-gravity solitary waves

Philippe Guyenne, Emilian Parau

Fluids & Structures

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Abstract

Flexural-gravity waves beneath an ice sheet are investigated. Forced waves generated by a moving load as well as freely propagating solitary waves are considered for the nonlinear problem as proposed by Plotnikov and Toland [2011]. In the unforced case, a Hamiltonian reformulation of the governing equations is presented in three dimensions. A weakly nonlinear analysis is performed to derive a cubic nonlinear Schrödinger equation near the minimum phase velocity in two dimensions. Both steady and time-dependent fully nonlinear computations are presented in the two-dimensional case, and the influence of finite depth is also discussed.

Original language	English
Pages (from-to)	44-57
Number of pages	14
Journal	Procedia IUTAM
Volume	11
DOIs	https://doi.org/10.1016/j.piutam.2014.01.047
Publication status	Published - 2014

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Cite this

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title = "Forced and unforced flexural-gravity solitary waves",

abstract = "Flexural-gravity waves beneath an ice sheet are investigated. Forced waves generated by a moving load as well as freely propagating solitary waves are considered for the nonlinear problem as proposed by Plotnikov and Toland [2011]. In the unforced case, a Hamiltonian reformulation of the governing equations is presented in three dimensions. A weakly nonlinear analysis is performed to derive a cubic nonlinear Schr{\"o}dinger equation near the minimum phase velocity in two dimensions. Both steady and time-dependent fully nonlinear computations are presented in the two-dimensional case, and the influence of finite depth is also discussed.",

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T1 - Forced and unforced flexural-gravity solitary waves

AU - Guyenne, Philippe

AU - Parau, Emilian

PY - 2014

Y1 - 2014

N2 - Flexural-gravity waves beneath an ice sheet are investigated. Forced waves generated by a moving load as well as freely propagating solitary waves are considered for the nonlinear problem as proposed by Plotnikov and Toland [2011]. In the unforced case, a Hamiltonian reformulation of the governing equations is presented in three dimensions. A weakly nonlinear analysis is performed to derive a cubic nonlinear Schrödinger equation near the minimum phase velocity in two dimensions. Both steady and time-dependent fully nonlinear computations are presented in the two-dimensional case, and the influence of finite depth is also discussed.

AB - Flexural-gravity waves beneath an ice sheet are investigated. Forced waves generated by a moving load as well as freely propagating solitary waves are considered for the nonlinear problem as proposed by Plotnikov and Toland [2011]. In the unforced case, a Hamiltonian reformulation of the governing equations is presented in three dimensions. A weakly nonlinear analysis is performed to derive a cubic nonlinear Schrödinger equation near the minimum phase velocity in two dimensions. Both steady and time-dependent fully nonlinear computations are presented in the two-dimensional case, and the influence of finite depth is also discussed.

U2 - 10.1016/j.piutam.2014.01.047

DO - 10.1016/j.piutam.2014.01.047

M3 - Special issue

VL - 11

SP - 44

EP - 57

JO - Procedia IUTAM

JF - Procedia IUTAM

SN - 2210-9838

ER -