Modulational instability of wave trains in a rotating ocean

Nikitenkova, S. P. and Singh, N. N. and Stepanyants, Y. A. ORCID: https://orcid.org/0000-0003-4546-0310 (2016) Modulational instability of wave trains in a rotating ocean. In: 20th Australasian Fluid Mechanics Conference (AFMC 2016), 5-8 Dec 2016, Perth, Australia.


Abstract

The problem of modulational stability of quasi-monochromatic
wave-trains propagating in a rotating fluid which provides both the small-scale Boussinesq dispersion and large-scale Coriolis dispersion is studied. We derive two-dimensional non-linear Schrödinger (NLS) equation from the basic set of Boussinesq equations for shallow water waves taking into account the Coriolis force caused by Earth’ rotation. For unidirectional waves propagating in one direction only the considered set of equations reduces to the Gardner–Ostrovsky equation which is applicable only within a finite range of wavenumbers. It is shown that the narrow-band wave-trains are modulationally stable for relatively small wavenumbers k < kc and unstable for k > kc, where kc is some critical wavenumber. The derived NLS equation is applicable even for waves with very small wavenumbers up to zero. The detailed analysis of coefficients of the NLS equation is presented both for one-dimensional and two-dimensional cases. The conditions of self-modulation and self-focussing are determined and presented graphically on the plane of parameters. Application of results obtained to the real oceanic conditions is discussed.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2016 Australasian Fluids Mechanics Society (AFMS). Paper #531.
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: 18 May 2017 03:46
Last Modified: 15 Feb 2021 23:33
Uncontrolled Keywords: modulation instability, rotating ocean, wave train, NLS equation, Lighthill criterion
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 > 970104 Expanding Knowledge in the Earth Sciences
URI: http://eprints.usq.edu.au/id/eprint/30491

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