Dynamics of internal envelope solitons in a rotating fluid of a variable depth
Article
Article Title | Dynamics of internal envelope solitons in a rotating fluid of a variable depth |
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ERA Journal ID | 212518 |
Article Category | Article |
Authors | |
Author | Stepanyants, Yury |
Journal Title | Fluids |
Journal Citation | 4 (1), pp. 1-12 |
Article Number | 56 |
Number of Pages | 12 |
Year | 2019 |
Publisher | MDPI AG |
Place of Publication | Switzerland |
ISSN | 2311-5521 |
Digital Object Identifier (DOI) | https://doi.org/10.3390/fluids4010056 |
Web Address (URL) | https://www.mdpi.com/2311-5521/4/1/56 |
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. |
Keywords | two-layer fluid; internal waves; nonlinear Schrodinger equation; envelope soliton; modulation instability; Earth’s rotation; variable bottom |
ANZSRC Field of Research 2020 | 401207. Fundamental and theoretical fluid dynamics |
370803. Physical oceanography | |
490109. Theoretical and applied mechanics | |
Byline Affiliations | School of Agricultural, Computational and Environmental Sciences |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q5308/dynamics-of-internal-envelope-solitons-in-a-rotating-fluid-of-a-variable-depth
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