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Title: Nonlinear dynamics of wave packets within the framework of the Ostrovsky equation and its generalisations
Author: Whitfield, A. J.
ISNI:       0000 0004 7230 7255
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2016
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The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wavepacket. There is currently no entirely satisfactory description of the wavepacket dynamics or why they form. This thesis examines the initial value problem within the context of the Ostrovsky, or rotation-modified KdV, equation. The linear Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. This point divides the spectrum into regions of modulational stability and instability, differing from the KdV equation for which the whole spectrum is stable. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong it is shown a soliton solution of the nonlinear Schrodinger equation accurately predicts the shape, and phase and group velocities of the wavepackets. In the strong rotation limit it is suggested that these wavepacket solitons form from an instability in the inertia-gravity wavetrain radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to be modulated, nonlinear cnoidal waves. A set of perturbed Whitham modulation equations are derived. When rotational effects are relatively weak it is shown the wavepackets are described by cnoidal wavepacket solutions of the perturbed modulation equations.
Supervisor: Johnson, E. R. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available