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High-order unidirectional model with adjusted coefficients for large-amplitude long internal waves

journal contribution
posted on 03.06.2020 by Wooyoung Choi, Changhong Zhi, Ricardo Lopes-Barros
To describe large amplitude internal solitary waves in a two-layer system, we consider the high-order unidirectional (HOU) model that extends the Korteweg–de Vries equation with high-order nonlinearity and leading-order nonlinear dispersion. While the original HOU model is valid only for weakly nonlinear waves, its coefficients depending on the depth and density ratios are adjusted such that the adjusted model can represent the main characteristics of large amplitude internal solitary waves, including effective wavelength, wave speed, and maximum wave amplitude. It is shown that the solitary wave solution of the adjusted HOU (aHOU) model agrees well with that of the strongly nonlinear Miyata–Choi–Camassa (MCC) model up to the maximum wave amplitude, which cannot be achieved by the original HOU model. To further validate the aHOU model, numerical solutions of the aHOU model are presented for the propagation and interaction of solitary waves and are shown to compare well with those of the MCC model. The aHOU model is further extended to the case of variable bottom and is solved numerically. In comparison with the MCC model for variable bottom, it is found that the aHOU model is a simple, but reliable theoretical model for large amplitude internal solitary waves, which would be useful for practical applications.

Funding

US National Science Foundation through Grant No. OCE-1634939.

China Scholarship Council

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Ocean Modelling

Volume

151

Issue

July 2020

Publisher

Elsevier

Version

AM (Accepted Manuscript)

Rights holder

© Elsevier Ltd

Publisher statement

This paper was accepted for publication in the journal Ocean Modelling and the definitive published version is available at https://doi.org/10.1016/j.ocemod.2020.101643.

Acceptance date

26/05/2020

Publication date

2020-06-05

Copyright date

2020

ISSN

1463-5003

Language

en

Depositor

Dr Ricardo Lopes Barros. Deposit date: 3 June 2020

Article number

101643

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