Nonlinear Models of Finite Amplitude Interfacial Waves in Shallow Two-Layer Fluid

Kurkina, Oxana and Kurkin, Andrey and Pelinovsky, Efim and Stepanyants, Yury ORCID: https://orcid.org/0000-0003-4546-0310 and Talipova, Tatiana (2019) Nonlinear Models of Finite Amplitude Interfacial Waves in Shallow Two-Layer Fluid. In: Applied Wave Mathematics II: Selected Topics in Solids, Fluids, and Mathematical Methods and Complexity. Mathematics of Planet Earth. Springer Nature, Cham, Switzerland, pp. 61-87. ISBN 9783030299507


Abstract

We present an example of systematic use of asymptotic methods for the description of long waves at the interface between two fluids of different densities. The governing equations for weakly nonlinear long interfacial waves are consistently derived for a general case of nonpotential flow and taking into account surface tension between two layers. Particular attention is given to the situations when some terms in the resulting fifth-order KdV-type evolution equation become small, vanish, or change their sign.


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Item Type: Book Chapter (Commonwealth Reporting Category B)
Refereed: Yes
Item Status: Live Archive
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -)
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -)
Date Deposited: 12 Aug 2020 04:08
Last Modified: 15 Feb 2021 23:34
Uncontrolled Keywords: Asymptotic method; long wave; stratified fluid; internal wave; KdV equation
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/10.1007/978-3-030-29951-4_4
URI: http://eprints.usq.edu.au/id/eprint/37505

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