Simulation of Internal Undular Bores in a Two-Layer Fluid Flow with Variable Topography

Mun Hoe, Hooi (2021) Simulation of Internal Undular Bores in a Two-Layer Fluid Flow with Variable Topography. Masters thesis, Universiti Malaysia Sarawak.

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Abstract

In ocean layers, the internal nonlinear wavetrain is often found in the structure of internal undular bores, connecting two different basic flow states and having the structure of slowly odulated nonlinear periodic wave with a solitary wave at its leading edge. Previous studies showed that the depth variation of the fluid influences the evolution of internal solitary waves. On a constant depth region, the leading solitary wave of the undular bore behaves like an isolated single solitary wave, propagates in constant velocity. However, this may not be true when the depth is changing. Hence, it is important to study the effects of depth variation to the evolution of internal undular bores propagating over the varying depth region. In this thesis, we would like to study the propagation of internal undular bores of both positive and negative polarities in a two-layer fluid system over variable topography in the framework of the variable-coefficient extended Korteweg-de Vries equation, which will be solved numerically using the methods of lines. In our work, we consider four different ypes of variable depth regions such as a slowly decreasing depth, a slowly increasing depth, a rapidly decreasing depth and a rapidly increasing depth. We examine the behaviour of the leading solitary wave of internal undular bores and compare it with that of isolated single internal solitary wave subject to the same varying depth effects. Our numerical results show that the evolution of the internal undular bores has an adiabatic and non-adiabatic deformation depending on the specific slowly varying depth profile. The wave structure at the leading edge of transformed bore shows (i) generation of solitary wavetrain; (ii) generation of nonlinear wavetrain; (iii) generation of step-like wave; (iv) generation of new undular bore; (v) generation of rarefaction wave. The varying depth effects could cause the evolving wave structure involving multi-phase behaviour and variation of characteristic scale of oscillation. We show that all the effects mentioned above can also be observed in the cases of rapidly varying depth. One should highlight is that the evolution of the internal undular bore does not involve adiabatic deformation due to the effects of rapid varying depth. In addition, the leading solitary wave undergoes soliton fission when the internal undular bore of positive polarity propagates over a rapidly decreasing depth region and the internal undular bore of negative polarity propagates over a rapidly increasing depth region. The study of the evolution of internal undular bore provides a useful insight to comprehend the behaviour of internal undular bore propagating over the variable topography.

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