Whitehouse, S. G. (1999) PODGalerkin modelling of the Martian atmosphere. PhD thesis, University of Oxford.

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Abstract
The aim of this thesis is to seek a lowdimensional description of baroclinic instability in general, and of the Martian atmosphere in particular, where both forcing and spatial resonance are relevant to the dynamics of the system being analysed.
The Proper Orthogonal Decomposition (POD) is used to determine a basis for the modal decomposition of climatic simulations of Mars, obtained by using two General Circulation Models (GCMs): (a) a simple GCM, which is an idealised model in which the meteorological primitive equations are solved on a sphere with simplified physical parameters and (b) the Martian GCM, a more realistic model in which a comprehensive range of the relevant Martian physical parameters and topography are represented. Results of these analyses are presented for a range of Martian seasons and climatic conditions. The effects of using different forms of energy norm in performing the analysis is considered, with the objective of providing analyses which represents the physically most significant components of the circulation, with optimal efficiency.
Reduced lowdimensional models that replicated the full simple GCM streamfunction simulations are formulated by projecting the spherical quasigeostrophic equations onto the PODs of the largescale calculations. The resulting models are analysed by using a combination of solution continuation and numerical integration methods. A thorough analysis of the models reveals that a 6D POD model is capable of reproducing the amplitude, frequency and behaviour of the leading oscillatory structures of the simple GCM, to within a 1% error. Such an excellent reproduction of the original system is shown to be due to (1) an accurate vertical formulation scheme, (2) the use of the correct norm, (3) a sufficiently high level of truncation and (4) the fact that the original system is a steady wave flow.
The behaviour of the various regimes observed in the loworder models are comparable with observations from studies of largescale waves and instabilities in planetary atmospheres, including a range of hydrodynamical experiments on baroclinic wave interactions of a stratified fluid in cylindrical containers.
Item Type:  Thesis (PhD) 

Subjects:  D  G > Geophysics O  Z > Partial differential equations D  G > Dynamical systems and ergodic theory A  C > Astronomy and astrophysics D  G > Fluid mechanics H  N > Numerical analysis 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  37 
Deposited By:  Eprints Administrator 
Deposited On:  10 Mar 2004 
Last Modified:  29 May 2015 18:15 
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