Dynamics and stability of gravity-capillary solitary waves

Over the past several years, it has been recognized that a new class of solitary waves can propagate in nonlinear dispersive wave systems if the phase speed of linear waves attains a local extremum at some finite wavenumber. Near such a point, solitary waves in the form of small-amplitude wavepackets can be obtained for which the phase speed of the carrier oscillations matches the group speed of their envelope. Such an extremum is found in the analysis of water waves when the restoring forces of both gravity and surface tension are taken into account, and certain kinds of these gravity-capillary solitary waves have been observed in experiments. While past theoretical studies have focussed mainly on determining steady solitary wave profiles, very little work has been done on examining their stability properties which is the thrust of this thesis. Beginning in the weakly nonlinear regime, an asymptotic analysis of linear stability is presented and comparison is made with numerical computations. Contrary to predictions of the nonlinear Schrbdinger (NLS) equation, some free solitary wave types are found to be unstable owing to exponentially effects terms that lie beyond standard two-scale perturba- tion theory. Moreover, numerical simulations show that unstable gravity-capillary solitary waves may decompose into stable solitary waves that have soliton properties. Stability results are then extended to the fully nonlinear regime to treat both free and forced situa- tions using numerical techniques to solve the full hydrodynamic equations in steady form. A dramatic difference is found between the linear stability of free and forced waves in both weakly and fully nonlinear cases, and results obtained here are compared with laboratory experiments.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mechanical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2001

Author dc:creator

• Calvo, David C. (David Christopher)

Advisor dc:contributor.advisor

• Triantaphyllos R. Akylas.

• Mechanical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/88871

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/88871