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Internal tides and resonance

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Wotherspoon, Simon (1995) Internal tides and resonance. PhD thesis, University of Tasmania.

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Abstract

This thesis is a study of resonant internal tide motion.
One common linear inviscid model represents the motion in terms of a two
dimensional stream function satisfying a standard second order hyperbolic equation.
This model is examined in detail and it is shown that existing solution
techniques can be extended and unified with the classical theory of a single complex
variable. This results in a number of new theoretical devices for the solution
of the model, including c-conformal mapping - a mapping procedure that shares
many of the traits of classical conformal mapping, and c-analytic continuation
- a procedure for extending the domain of a solution analogous to standard
analytic continuation.
These techniques are applied to a study of the model on closed basins. A
crucial distinction relating to the geometry of the corners of the basin is noted,
and the importance of energy sources and sinks is recognized. The analysis is
found both to support the conjectures of other researchers that the existence of
resonant motion may be predicted through an analysis of the characteristic coordinates
of the inviscid model, and to demonstrate that the inviscid model is an
inadequate vehicle for the study of internal tides on basin topographies.
A viscous form of the linear model is then discussed and a number of numerical
solution techniques suitable for basin topographies are devised. The first of these
is a straightforward application of standard collocation methods, but is found
to be computationally expensive. A simpler, more efficient family of techniques
based on the theory of c-analytic continuation is then derived. These methods are
seen to be a natural extension of a Fourier series technique successfully employed
by other authors.
The predictions of the linear models are then compared with the results of
laboratory experiments. Resonance effects are seen to play a major role in determining
the motion of the fluid. However, the strongly resonant motions predicted
by the linear models are not observed, and, in general, the agreement between
model and data is poor. This is attributed to both the sensitivity of the problem
and the difficulty associated with modelling the external forcing.
The large amplitude strongly resonant motions predicted by the linear models
prompt a study of nonlinear internal tide dynamics. A nonlinear model based on
the Navier Stokes equations is considered, and numerical solutions are obtained
via finite differences. These solutions show that for strongly resonant motion the
"Rigid Lid" approximation commonly imposed at the free surface is inadequate
and must be replaced with a more accurate nonlinear boundary condition.

Item Type: Thesis (PhD)
Keywords: Tides, Resonance
Copyright Holders: The Author
Copyright Information:

Copyright 1995 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).

Additional Information:

Includes bibliographical references. Thesis (Ph.D.)--University of Tasmania, 1996

Date Deposited: 04 Feb 2015 23:23
Last Modified: 22 Aug 2016 01:33
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