BOUSSINESQ TYPE MODEL TO SIMULATE THE UNDULAR BORE PHENOMENON
An undular bore is a surface wave phenomenon, occurred at the transition from supercritical flow to subcritical flow. It is characterized by a smooth wave and followed by a waves train without any wave breaking. The present research studied the appearance of undular bore phenomenon by mathematica...
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| Format: | Dissertations |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/46198 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | An undular bore is a surface wave phenomenon, occurred at the transition from
supercritical flow to subcritical flow. It is characterized by a smooth wave and
followed by a waves train without any wave breaking. The present research
studied the appearance of undular bore phenomenon by mathematical modelling
and numerical simulation. To simulate the phenomenon correctly, it is required a
mathematical model that can describe the non-linear and dispersive effects at once,
that is a non-hydrostatic model. In this study, we used a Boussinesq-type model as
the governing equations. The equations were derived using perturbation method of
potential functions with high orders. The equation is an extension of the standard
Boussinesq equations.
The Boussinesq-type equations were solved numerically using an explicit finite
difference method, with predictor-corrector procedure, and considering water depth
and flux as the independent variables. The model was validated by the solitary wave
propagation simulation. This numerical scheme showed there is a balance of nonlinear
and dispersive effects.
The numerical model was implemented to simulate the development of undular
bores. It was shown that the numerical results of this study have a good agreement
with the experimental result or other researcher’s results. We also investigated the
effect of the Froude number and channel slope to the undular bore development. The
greater Froude number or dishcarge influx, the amplitude of undulations increased
with faster phase velocity. Furthermore, we also investigated the energy balance of
undular bore quantitatively. It is shown that there is no energy loss in the development
of undular bore using this Boussinesq-type equation. |
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