Dynamics of internal envelope solitons in a rotating fluid of a variable depth

Stepanyants, Yury (2019) Dynamics of internal envelope solitons in a rotating fluid of a variable depth. Fluids, 4 (1 (56)). pp. 1-12.

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Abstract

We consider the dynamics of internal envelope solitons in a two-layer rotating fluid with a linearly varying bottom. It is shown that the most probable frequency of a carrier wave which constitutes the solitary wave is the frequency where the growth rate of modulation instability is maximal. An envelope solitary wave of this frequency can be described by the conventional nonlinear Schrodinger equation. A soliton solution to this equation is presented for the time-like version of the nonlinear Schrodinger equation. When such an envelope soliton enters a coastal zone where the bottom gradually linearly increases, then it experiences an adiabatical transformation. This leads to an increase in soliton amplitude, velocity, and period of a carrier wave, whereas its duration decreases. It is shown that the soliton becomes taller and narrower. At some distance it looks like a breather, a narrow non-stationary solitary wave. The dependences of the soliton parameters on the distance when it moves towards the shoaling are found from the conservation laws and analysed graphically. Estimates for the real ocean are presented.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published version made available in accordance with Creative Commons Attribution License 4.0.
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 July 2013 - 5 Sept 2019)
Faculty/School / Institute/Centre: Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 July 2013 - 5 Sept 2019)
Date Deposited: 27 Sep 2019 03:20
Last Modified: 21 Nov 2019 06:05
Uncontrolled Keywords: two-layer fluid; internal waves; nonlinear Schrodinger equation; envelope soliton; modulation instability; Earth’s rotation; variable bottom
Fields of Research : 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
Socio-Economic Objective: 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: 10.3390/fluids4010056
URI: http://eprints.usq.edu.au/id/eprint/36218

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