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A generalized two dimensional quasigeostrophic model of thermal convection Open Access


Other title
rotating fluids
Type of item
Degree grantor
University of Alberta
Author or creator
Laycock, Thomas Daniel
Supervisor and department
Dumberry, Mathieu (Physics)
Examining committee member and department
Heimpel, Moritz (Physics)
Sutherland, Bruce (Physics and Earth & Atmospheric Sciences)
Dumberry, Mathieu (Physics)
Aurnou, Jonathan (Earth, Planetary, and Space Sciences at UCLA)
Reuter, Gerhard (Earth & Atmospheric Sciences)
Department of Physics
Date accepted
Graduation date
Doctor of Philosophy
Degree level
The processes responsible for generating the mean azimuthal atmospheric winds observed on Jupiter and Saturn, which feature large prograde equatorial jets and jets of alternating direction at higher latitudes, have yet to be conclusively resolved. Results from three dimensional numerical models of thermal convection in a thin spherical shell have supported the theory that they are a surface manifestation of organized flow deep within the planets. While these models have been able to reproduce the general features of the observed zonal flow, computational limits restrict them to parameter regimes many orders of magnitude more modest than those thought to exist in the planets. A more efficient numerical model is required to study this phenomenon at more realistic parameter values, and would permit an investigation of the dependence of the solution on the parameters of the system and initial conditions, as well as the long time scale dynamics of zonal winds. The current thesis takes advantage of the rigid columnar flow structures that are produced by the rapid planetary rotation, as observed in the results of 3D simulations, to develop a two dimensional quasigeostrophic model of the system for a Boussinesq fluid. By averaging the equations of motion over Taylor columns in the axial direction, and simulating the mean variables in a 2D virtual equatorial plane, the essential dynamics can be modeled while collapsing the problem into one fewer dimension. To develop such a model, the standard quasigeostrophic framework, and existing numerical models based upon it, have been generalized to the geometry inside the tangent cylinder which circumscribes the inner spherical boundary of the convecting shell. Here, buoyancy in the axial direciition, which is not considered in the traditional QG framework, is responsible for forcing axial convection and the turbulence which leads to jet generation. Thus, in addition to the traditional QG equations, we must also solve the averaged axial flow equation to model this effect. Numerical simulations of our 2D QG model demonstrate that this approach can capture much of the dynamics of 3D convection. The system variables all have amplitudes which are the same order of magnitude as solutions from full three dimensional models. Additionally, alternating zonal jets similar to those observed on Jupiter can be produced.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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