A generalized two dimensional quasigeostrophic model of thermal convection

• Author / Creator

  Laycock, Thomas Daniel

• 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.

• Subjects / Keywords

  • Rotating fluids
  • Turbulence
  • Quasigeostrophy
  • Jupiter

• Graduation date

  Spring 2015

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3G96K

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.