The Effects of the Earth's Rotation on Internal Wave Near-resonant Triads and Weakly Nonlinear Models
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Date
2007-08-24T14:35:32Z
Authors
Hu, Youna
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Publisher
University of Waterloo
Abstract
This thesis investigates the effects of the earth's rotation on internal waves from two perspectives of nonlinear internal wave theory: near-resonant triads and weakly nonlinear models.
We apply perturbation theory (multiple scale analysis) to the governing equations of internal waves and develop a near-resonant internal wave triad theory. This theory explains a resonant-like phenomenon in the numerical results obtained from simulating internal waves generated by tide topography interaction. Furthermore, we find that the inclusion of the earth's rotation (nonzero $f$) in the numerical runs leads to a very special type of resonance: parametric subharmonic instability.
Through using perturbation expansion to solve separable solutions to the governing equations of internal waves, we derive a new rotation modified KdV equation (RMKdV). Of particular interest, the dispersion relation of the new equation obeys the exact dispersion relation for internal waves for both small and moderate wavenumbers ($k$). Thus this new RMKdV is able to model wea
kly nonlinear internal waves with various wavenumbers ($k$), better than the Ostrovsky equation which fails at describing waves of small $k$.
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Keywords
Near-resonant Internal Wave Triads, Weakly Nonlinear Models of Internal Waves