Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region

Hooi, M. H.; Tiong, Wei King; Tay, Kim Gaik; Sze, San Nah; Chiew, Kang Leng

doi:10.37934/arfmts.70.1.1327

Cited by 5 publications

(4 citation statements)

References 31 publications

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“…Grimshaw and et al [17] presented numerical simulations of this problem, together with the analogous simulations of a certain cross section of the South China Sea. Moreover, there are several researches that demonstrated the effects of the rotation and background topography on the internal undular in the past few years [18,21,22].…”

Section: Introductionmentioning

confidence: 99%

The Propagation of Nonlinear Internal Waves under the Influence of Variable Topography and Earth’s Rotation in a Two-Layer Fluid

Ismail

Alias

Harun

2020

Fluids

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A nonlinear equation of the Korteweg–de Vries equation usually describes internal solitary waves in the coastal ocean that lead to an exact solitary wave solution. However, in any real application, there exists the Earth’s rotation. Thus, an additional term is required, and consequently, the Ostrovsky equation is developed. This additional term is believed to destroy the solitary wave solution and form a nonlinear envelope wave packet instead. In addition, an internal solitary wave is commonly disseminated over the variable topography in the ocean. Because of these effects, the Ostrovsky equation is retrieved by a variable-coefficient Ostrovsky equation. In this study, the combined effects of both background rotation and variable topography on a solitary wave in a two-layer fluid is studied since internal waves typically happen here. A numerical simulation for the variable-coefficient Ostrovsky equation with a variable topography is presented. Two basic examples of the depth profile are considered in detail and sustained by numerical results. The first one is the constant-slope bottom, and the second one is the specific bottom profile following the previous studies. These indicate that the combination of variable topography and rotation induces a secondary trailing wave packet.

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Section: Introductionmentioning

confidence: 99%

The Propagation of Nonlinear Internal Waves under the Influence of Variable Topography and Earth’s Rotation in a Two-Layer Fluid

Ismail

Alias

Harun

2020

Fluids

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“…Similarly, the evolution of internal undular bores over slowly varying depth regions would also lead to several adiabatic and non-adiabatic effects including the generation of a solitary wavetrain ahead of the transformed internal undular bore, the generation of a step-like wave, etc. [15][16]. Our aim of this work is to simulate the evolution of the internal undular bores over rapidly varying depth regions and study how the variable topography affects the internal undular bores, particularly the leading solitary wave at the leading edge.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Internal Undular Bores in Rapidly Varying Topography

Hooi

Tiong

Tay

2022

ARFMTS

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This paper intends to look at the influence of rapidly varying regions on the propagation of internal undular bores in a two-layer fluid flow. Internal undular bores have been observed in the ocean around the world. The appropriate mathematical model to describe the evolution of internal undular bores in a stratified fluid is the variable-coefficient extended Korteweg-de Vries equation. The governing equation is solved numerically using the method of lines to simulate the propagation of internal undular bores. Our numerical results show that the effects of rapidly varying topography lead to adiabatic and non-adiabatic deformation of the internal undular bores, including the generation of solitary wavetrain, generation of nonlinear wavetrain and generation of rarefaction wave. Besides, multi-phase behaviour is also observed during the evolution.

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“…In a series of articles, Shen [22,23] outlined that there are two supercritical solitary waves and one subcritical downstream cnoidal wave. Solitary waves emerge at the variable topographic effects on the evolution of the internal undular bores of depression [24]. Hoe et al, [25] also investigated the effect of rapidly varying topography by using mathematical model of the variable-coefficient extended KdV.…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave Solutions for Forced Nonlinear Korteweg-de Vries Equation by Using Approximate Analytical Method

Hussin

Mandangan

Azmi

et al. 2022

ARFMTS

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The Multistep Modified Reduced Differential Transform Method (MMRDTM) is proposed in this paper. It is implemented to solve the forced nonlinear Korteweg-de Vries (fnKdV) equations. There are several advantages of the proposed method. Using the suggested approach, a high-speed converging series can be approximated analytically. Furthermore, the number of calculated terms is reduced significantly. The nonlinear term in fnKdV equations is substituted with corresponding Adomian polynomials before applying the multi-step technique. As a result, we provided simpler and more effective ways to solve fnKdV equations. On top of that, the solutions can be approximated more accurately over a longer period of time. To show the MMRDTM's capability and accuracy, we consider several of the fnKdV examples to illustrate the proposed method’s potential in analytical approximation. Then, the features of the solutions are represented in tabular and graphical forms. In conclusion, the proposed method delivers highly accurate and precise solutions for these types of equations.

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Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region

Cited by 5 publications

References 31 publications

The Propagation of Nonlinear Internal Waves under the Influence of Variable Topography and Earth’s Rotation in a Two-Layer Fluid

The Propagation of Nonlinear Internal Waves under the Influence of Variable Topography and Earth’s Rotation in a Two-Layer Fluid

Simulation of Internal Undular Bores in Rapidly Varying Topography

Solitary Wave Solutions for Forced Nonlinear Korteweg-de Vries Equation by Using Approximate Analytical Method

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