Adiabatic decay of internal solitons due to Earth’s rotation within the framework of the Gardner–Ostrovsky equation

Obregon, Maria and Raj, Nawin and Stepanyants, Yury ORCID: https://orcid.org/0000-0003-4546-0310 (2018) Adiabatic decay of internal solitons due to Earth’s rotation within the framework of the Gardner–Ostrovsky equation. Chaos: An interdisciplinary Journal of Nonlinear Science, 28 (3). pp. 1-11. ISSN 1054-1500


Abstract

The adiabatic decay of different types of internal wave solitons caused by the Earth’s rotation is studied within the framework of the Gardner–Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions. It is shown that at the early stage of evolution solitons gradually decay under the influence of weak Earth’s rotation. The characteristic decay time is derived for different types of solitons for positive and negative coefficients of cubic nonlinearity (both signs of that parameter may occur in the oceans). The coefficient of quadratic nonlinearity determines only a polarity of solitary wave or the asymmetry of solitary waves of opposite polarity. It is found that the adiabatic theory describes well the decay of solitons having bell-shaped profiles. In contrast to that, large amplitude table-top solitons, which can exist when the cubic nonlinear term is negative, are structurally unstable. Under the influence of Earth’s rotation, they transfer first to the bell-shaped solitons, which decay then adiabatically. Estimates of the characteristic decay time of internal solitons are presented for the real oceanographic conditions.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published version deposited in accordance with the copyright policy of the publisher.
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019)
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019)
Date Deposited: 29 Mar 2018 02:46
Last Modified: 15 Feb 2021 23:33
Uncontrolled Keywords: internal wave, solitary wave, adiabatic decay, rotating ocean, Gardner–Ostrovsky equation, Gardner soliton
Fields of Research (2008): 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
04 Earth Sciences > 0405 Oceanography > 040503 Physical Oceanography
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Fields of Research (2020): 40 ENGINEERING > 4012 Fluid mechanics and thermal engineering > 401207 Fundamental and theoretical fluid dynamics
37 EARTH SCIENCES > 3708 Oceanography > 370803 Physical oceanography
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 Theoretical and applied mechanics
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970104 Expanding Knowledge in the Earth Sciences
Identification Number or DOI: https://doi.org/10.1063/1.5021864
URI: http://eprints.usq.edu.au/id/eprint/33841

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