A Euler–Poincaré framework for the multilayer Green–Nagdhi equations

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Title: A Euler–Poincaré framework for the multilayer Green–Nagdhi equations
Author(s): Percival, JR
Cotter, CJ
Holm, DD
Item Type: Conference Paper
Abstract: The Green–Nagdhi equations are frequently used as a model of the wave-like behaviour of the free surface of a fluid, or the interface between two homogeneous fluids of differing densities. Here we show that their multilayer extension arises naturally from a framework based on the Euler–Poincaré theory under an ansatz of columnar motion. The framework also extends to the travelling wave solutions of the equations. We present numerical solutions of the travelling wave problem in a number of flow regimes. We find that the free surface and multilayer waves can exhibit intriguing differences compared to the results of single layer or rigid lid models.
Publication Date: 11-Aug-2008
Date of Acceptance: 19-Mar-2008
URI: http://hdl.handle.net/10044/1/54801
DOI: https://dx.doi.org/10.1088/1751-8113/41/34/344018
ISSN: 1751-8113
Publisher: IOP Publishing
Start Page: 344018
End Page: 344031
Journal / Book Title: Journal of Physics A: Mathematical and Theoretical
Volume: 41
Issue: 34
Copyright Statement: © 2008 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in [insert name of journal]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at http://iopscience.iop.org/article/10.1088/1751-8113/41/34/344018/meta
Conference Name: Meeting held in Honor of Darryl D Holms on Geometry and Analysis in Physical Systems
Keywords: Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics, Mathematical
01 Mathematical Sciences
02 Physical Sciences
Mathematical Physics
Publication Status: Published
Start Date: 2007-07-22
Finish Date: 2007-07-28
Conference Place: Lausanne, Switzerland
Appears in Collections:Faculty of Engineering
Earth Science and Engineering
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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