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

Internal undular bores have been observed in many parts of the world. This paper intends to look at the variable topographic effects on the evolution of the internal undular bores of depression. Here, the internal undular bores is considered to be propagating in a two-layer fluid system. The topogr...

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Main Authors: Hooi, Mun Hoe, Tiong, Wei King, Tay, Kim Gaik, Sze, San Nah, Chiew, Kang Leng
Format: Article
Language:English
Published: Semarak Ilmu Publishing 2020
Subjects:
QA Mathematics
Online Access:http://ir.unimas.my/id/eprint/46963/1/Simulation_of_Internal_Undular_Bores_of_Depression.pdf
http://ir.unimas.my/id/eprint/46963/
https://semarakilmu.com.my/journals/index.php/fluid_mechanics_thermal_sciences/article/view/6180
https://doi.org/10.37934/arfmts.70.1.1327
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spelling my.unimas.ir-469632024-12-19T07:52:19Z http://ir.unimas.my/id/eprint/46963/ Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region Hooi, Mun Hoe Tiong, Wei King Tay, Kim Gaik Sze, San Nah Chiew, Kang Leng QA Mathematics Internal undular bores have been observed in many parts of the world. This paper intends to look at the variable topographic effects on the evolution of the internal undular bores of depression. Here, the internal undular bores is considered to be propagating in a two-layer fluid system. The topography is assumed to be slowly varying. Therefore, the appropriate mathematical model is the variable-coefficient extended Korteweg-de Vries equation. The governing equation is solved numerically using the method of lines. We are especially interested in looking at the transformation of two types of internal undular bore of depression, which are Korteweg de Vries-type and table-top internal undular bore. Our numerical results show that the internal undular bore of depression transformed into a positive undular bore as it propagates over a slowly increasing slope and when it involves polarity change. In front of the transformed internal bore, a series of isolated solitary waves or a solitary wavetrain is generated as a non-adiabatic response to the interaction between the internal undular bore with the changing bottom surface. The solitary wavetrain is observed to be climbing the negative pedestal. As time increases, the amplitude of the individual solitary wavetrain is decreasing and finally the solitary wavetrain will die out due to the pedestal. However, if there is no polarity change, the internal undular bores deforms adiabatically and its amplitude decreases slowly until it reaches new limiting amplitude value due the increasing bottom surface. On the other hand, when the slope is decreasing slowly, the internal undular bore deforms adiabatically where its amplitude increases slowly. There is a multi-phase behaviour is observed during the evolution as the results of the interaction between the internal bore and the varying slope. In this case, there is no polarity change. The transformation of internal undular bores of depression depends on the nature of the topographic change. Semarak Ilmu Publishing 2020 Article PeerReviewed text en http://ir.unimas.my/id/eprint/46963/1/Simulation_of_Internal_Undular_Bores_of_Depression.pdf Hooi, Mun Hoe and Tiong, Wei King and Tay, Kim Gaik and Sze, San Nah and Chiew, Kang Leng (2020) Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 70 (1). pp. 13-27. ISSN 2289 - 7879 https://semarakilmu.com.my/journals/index.php/fluid_mechanics_thermal_sciences/article/view/6180 https://doi.org/10.37934/arfmts.70.1.1327
institution Universiti Malaysia Sarawak
building Centre for Academic Information Services (CAIS)
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sarawak
content_source UNIMAS Institutional Repository
url_provider http://ir.unimas.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Hooi, Mun Hoe
Tiong, Wei King
Tay, Kim Gaik
Sze, San Nah
Chiew, Kang Leng
Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region
description Internal undular bores have been observed in many parts of the world. This paper intends to look at the variable topographic effects on the evolution of the internal undular bores of depression. Here, the internal undular bores is considered to be propagating in a two-layer fluid system. The topography is assumed to be slowly varying. Therefore, the appropriate mathematical model is the variable-coefficient extended Korteweg-de Vries equation. The governing equation is solved numerically using the method of lines. We are especially interested in looking at the transformation of two types of internal undular bore of depression, which are Korteweg de Vries-type and table-top internal undular bore. Our numerical results show that the internal undular bore of depression transformed into a positive undular bore as it propagates over a slowly increasing slope and when it involves polarity change. In front of the transformed internal bore, a series of isolated solitary waves or a solitary wavetrain is generated as a non-adiabatic response to the interaction between the internal undular bore with the changing bottom surface. The solitary wavetrain is observed to be climbing the negative pedestal. As time increases, the amplitude of the individual solitary wavetrain is decreasing and finally the solitary wavetrain will die out due to the pedestal. However, if there is no polarity change, the internal undular bores deforms adiabatically and its amplitude decreases slowly until it reaches new limiting amplitude value due the increasing bottom surface. On the other hand, when the slope is decreasing slowly, the internal undular bore deforms adiabatically where its amplitude increases slowly. There is a multi-phase behaviour is observed during the evolution as the results of the interaction between the internal bore and the varying slope. In this case, there is no polarity change. The transformation of internal undular bores of depression depends on the nature of the topographic change.
format Article
author Hooi, Mun Hoe
Tiong, Wei King
Tay, Kim Gaik
Sze, San Nah
Chiew, Kang Leng
author_facet Hooi, Mun Hoe
Tiong, Wei King
Tay, Kim Gaik
Sze, San Nah
Chiew, Kang Leng
author_sort Hooi, Mun Hoe
title Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region
title_short Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region
title_full Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region
title_fullStr Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region
title_full_unstemmed Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region
title_sort simulation of internal undular bores of depression propagating over a slowly varying region
publisher Semarak Ilmu Publishing
publishDate 2020
url http://ir.unimas.my/id/eprint/46963/1/Simulation_of_Internal_Undular_Bores_of_Depression.pdf
http://ir.unimas.my/id/eprint/46963/
https://semarakilmu.com.my/journals/index.php/fluid_mechanics_thermal_sciences/article/view/6180
https://doi.org/10.37934/arfmts.70.1.1327
_version_ 1819914973498834944
score 13.223943

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