Modelling Internal Solitary Waves and the Alternative Ostrovsky Equation
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Date
2014-04-25
Authors
He, Yangxin
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Internal solitary waves (ISWs) are commonly observed in the ocean, and
they play important roles in many ways, such as transport of mass
and various nutrients through propagation. The fluids considered in this
thesis are assumed to be incompressible, inviscid, non-diffusive and
to be weakly affected by the Earth's rotation. Comparisons of the
evolution of an initial solitary wave predicted by a fully nonlinear
model, IGW, and two weakly-nonlinear wave equations, the Ostrovsky
equation and a new alternative Ostrovsky equation, are done.
Resolution tests have been run for each of the models to confirm that the current choices of the spatial
and time steps are appropriate. Then we have run three numerical
simulations with varying initial wave amplitudes. The rigid-lid
approximation has been used for all of the models. Stratification, flat
bottom and water depth stay the same for all three simulations.
In the simulation analysis, we use the results from the IGW as the standard. Both of the two weakly nonlinear models
give fairly good predictions regarding the leading wave amplitudes,
shapes of the wave train and the propagation speeds. However, the
weakly nonlinear models over-predict the propagation speed of the
leading solitary wave and that the alternative Ostrovsky equation
gives the worst prediction. The difference between the two weakly nonlinear models
decreases as the initial wave amplitude decreases.
Description
Keywords
Internal Solitary Wave, Ostrovsky equation, fluid mechanics, alternative Ostrovsky equation