Mathematics and Statistics Vol. 9(5), pp. 825 - 834
DOI: 10.13189/ms.2021.090523
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Numerical Solution of Ostrovsky Equation over Variable Topography Passes through Critical Point Using Pseudospectral Method

Nik Nur Amiza Nik Ismail , Azwani Alias ^*, Fatimah Noor Harun
Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia

ABSTRACT

Internal solitary waves have been documented in several parts of the world. This paper intends to look at the effects of the variable topography and rotation on the evolution of the internal waves of depression. Here, the wave is considered to be propagating in a two-layer fluid system with the background topography is assumed to be rapidly and slowly varying. Therefore, the appropriate mathematical model to describe this situation is the variable-coefficient Ostrovsky equation. In particular, the study is interested in the transition of the internal solitary wave of depression when there is a polarity change under the influence of background rotation. The numerical results using the Pseudospectral method show that, over time, the internal solitary wave of elevation transforms into the internal solitary wave of depression as it propagates down a decreasing slope and changes its polarity. However, if the background rotation is considered, the internal solitary waves decompose and form a wave packet and its envelope amplitude decreases slowly due to the decreasing bottom surface. The numerical solutions show that the combination effect of variable topography and rotation when passing through the critical point affected the features and speed of the travelling solitary waves.

KEYWORDS
Solitary Wave, Nonlinear Equation, Ostrovsky Equation, Variable Topography, Background Rotation, Polarity Change, Pseudospectral Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Nik Nur Amiza Nik Ismail , Azwani Alias , Fatimah Noor Harun , "Numerical Solution of Ostrovsky Equation over Variable Topography Passes through Critical Point Using Pseudospectral Method," Mathematics and Statistics, Vol. 9, No. 5, pp. 825 - 834, 2021. DOI: 10.13189/ms.2021.090523.

(b). APA Format:
Nik Nur Amiza Nik Ismail , Azwani Alias , Fatimah Noor Harun (2021). Numerical Solution of Ostrovsky Equation over Variable Topography Passes through Critical Point Using Pseudospectral Method. Mathematics and Statistics, 9(5), 825 - 834. DOI: 10.13189/ms.2021.090523.