eprintid: 1477284
rev_number: 25
eprint_status: archive
userid: 608
dir: disk0/01/47/72/84
datestamp: 2016-04-01 10:27:14
lastmod: 2021-10-18 22:30:39
status_changed: 2016-04-01 10:27:14
type: article
metadata_visibility: show
creators_name: Wang, Z
creators_name: Vanden-Broeck, J-M
creators_name: Meng, H
title: A Quasi-Planar Model for Gravity-Capillary Interfacial Waves in Deep Water
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
note: This is the peer reviewed version of the following article: Wang, Z; Vanden-Broeck, J-M; Meng, H; (2014) A Quasi-Planar Model for Gravity-Capillary Interfacial Waves in Deep Water. Studies in Applied Mathematics, 133 (2) pp. 232-256, which has been published in final form at: http://dx.doi.org/10.1111/sapm.12043. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving (http://olabout.wiley.com/WileyCDA/Section/id-820227.html#terms).
abstract: A dynamical model equation for interfacial gravity-capillary (GC) waves between two semi-infinite fluid layers, with a lighter fluid lying above a heavier one, is derived. The model proposed is based on the fourth-order truncation of the kinetic energy in the Hamiltonian of the full problem, and on weak transverse variations, in the spirit of the Kadomtsev-Petviashvilli equation. It is well known that for the interfacial GC waves in deep water, there is a critical density ratio where the associated cubic nonlinear Schrödinger equations changes type. Our numerical results reveal that, when the density ratio is below the critical value, the bifurcation diagram of plane solitary waves behaves in a way similar to that of the free-surface GC waves on deep water. However, the bifurcation mechanism in the vicinity of the minimum of the phase speed is essentially similar to that of free-surface gravity-flexural waves on deep water, when the density ratio is in the supercritical regime. Different types of lump solitary waves, which are fully localized in both transverse and longitudinal directions, are also computed using our model equation. Some dynamical experiments are carried out via a marching-in-time algorithm.
date: 2014-08
date_type: published
official_url: http://dx.doi.org/10.1111/sapm.12043
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1007096
doi: 10.1111/sapm.12043
lyricists_name: Vanden-Broeck, Jean-Marc
lyricists_id: JVAND65
actors_name: Vanden-Broeck, Jean-Marc
actors_id: JVAND65
actors_role: owner
full_text_status: public
publication: Studies in Applied Mathematics
volume: 133
number: 2
pagerange: 232-256
issn: 0022-2526
citation:        Wang, Z;    Vanden-Broeck, J-M;    Meng, H;      (2014)    A Quasi-Planar Model for Gravity-Capillary Interfacial Waves in Deep Water.                   Studies in Applied Mathematics , 133  (2)   pp. 232-256.    10.1111/sapm.12043 <https://doi.org/10.1111/sapm.12043>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1477284/7/Vanden-Broeck_WVM2.pdf