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Linear and nonlinear progressive Rossby waves on a rotating sphere

Callaghan, TG 2005 , 'Linear and nonlinear progressive Rossby waves on a rotating sphere', PhD thesis, University of Tasmania.

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We present an analysis of incompressible and compressible flow of a thin layer of
fluid with a free-surface on a rotating sphere. Our general aim is to investigate
the nature of progressive Rossby wave structures that are possible in this rotating
system, with the goal of expanding previous research by conducting an in-depth
analysis of wavespeed/amplitude relationships.
A linearized theory for the incompressible dynamics, closely related to the theory
developed by B. Haurwitz, is constructed, with good agreement observed between
the two separate models. This result is then extended to the numerical solution of
the full model, to obtain highly nonlinear large-amplitude progressive-wave solutions
in the form of Fourier series. A detailed picture is developed of how the progressive
wavespeed depends on the wave amplitude. This approach reveals the presence
of nonlinear resonance behaviour, with different disjoint solution branches existing
at different values of the amplitude. Additionally, we show that the formation of
localised low pressure systems is an inherent feature of the nonlinear dynamics, once
the forcing amplitude reaches a certain critical level.
We then derive a new free-surface model for compressible fluid dynamics and repeat
the above analysis by first constructing a linearized solution and then using this
to guide the computation of nonlinear solutions via a bootstrapping process. It is
shown that if the value of the pressure on the free-surface is assumed to be zero,
which is consistent with the concept of the atmosphere terminating, then the model
almost reduces to the incompressible dynamics with the only difference being a
slightly modified conservation of mass equation. By forcing wave amplitude in the
model we show that the resonant behaviour observed in the incompressible dynamics
is again encountered in the compressible model. The effect of the compressibility
is observed to become apparent through damped resonance behaviour in general,
so that in some instances two neighbouring disjoint solution branches from the
incompressible dynamics are seen to merge into one continuous solution branch when
compressible dynamics are incorporated. In closing, some conjectures are made as to how these results might help explain certain observed atmospheric phenomena.
In particular it is conjectured that the process of atmospheric blocking is a direct
result of critically forced stationary Rossby waves.

Item Type: Thesis - PhD
Authors/Creators:Callaghan, TG
Keywords: Fluid dynamics, Rossby waves
Copyright Holders: The Author
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Copyright 2005 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
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Thesis (PhD)--University of Tasmania, 2005.

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