Numerical Simulations of Anelastic and Boussinesq Rotating Convection with Radial Entropy Gradient Boundary Conditions

• Author / Creator

  Ocampo, Benjamin R. S.

• Observations from the gas giants Jupiter or Saturn allow for researchers to construct geophysical fluid dynamical numerical models in an attempt to replicate the observed features. Most models aim at replicating the zonal jets and the eddies observed on these gas giants to understand how they are driven. Two dominant theories have arisen as a result of the controversy of the generation of these features: the weather layer hypothesis and the deep winds hypothesis. The weather layer hypothesis assumes that the zonal jets are driven by cloud physics in the troposphere while the deep winds hypothesis states that these jets are driven by convection in the deep interior. Some success has been seen in the weather layer models as some were able to generate eddies or even great storms. Whereas some success has been seen in the deep winds models as some were able to generate equatorial and high latitude zonal jets. Most deep winds models are based on Boussinesq or anelastic convection in a rotating spherical shell. Convection is implemented by using either constant entropy boundary conditions or constant radial entropy gradient boundary conditions. This allows for the generation of zonal jets for a strong enough thermal forcing since the secondary flow comes from the interaction between the convection cells and the outer boundary. However, based off measurements from the Galileo space probe, they imply that Jupiter has a stably stratified fluid layer near the top of its atmosphere. Typically, these models that replicate the zonal jets do not include the stably stratified fluid layer near the top boundary. Due to developments in general circulation model software, regional models can be used to simulate local fluid dynamics in a rotating spherical shell. However, if models focus on either poles of the planet, conventional spherical coordinate system is not optimal since singularities exist at the poles. Instead, a cubed-sphere curvilinear grid system can be used to successfully resolve these models. This should allow for emphasis of fluid dynamics at the region with a reduced computational cost compared to full spherical shell models. In this thesis, we implement rotating convection models in both full and regional rotating spherical shell models. The full spherical shell model implements the constant conductive radial entropy gradient boundary conditions to allow for anelastic convection in the models and to add the stably stratified fluid layer at the outer boundary. For the regional convection simulation, we model a Boussinesq fluid at the North polar region of a rotating spherical shell using a cubed-sphere curvilinear grid system. The results from the rotating anelastic convective spherical shell models without the stably stratified fluid layer near the outer boundary show zonal flow oscillations for a high enough thermal forcing, where they indicate that the fluid is in a relaxation oscillation regime. Implementing the stratified fluid layer leads to a tendency towards suppression in these oscillations via decrease in their amplitude. However, for a thick enough layer, these oscillations become suppressed such that the model does not evolve into the relaxation oscillation state. The retrograde jets from models with no stratified fluid layer also became smoother when the stably stratified fluid layer is implemented. Long-lived eddies have also been generated for the near-Boussinesq case of the rotating anelastic spherical shell models with the stably stratified fluid layer. These eddies are generated for a large enough thermal forcing and drift around the tangent cylinder. However, increasing the thermal forcing leads to a merging of these long-lived eddies, leading to the generation of anticyclonic great eddies. Other models with a higher density stratification in this thesis did not generate any long-lived eddies. Based on the results from the regional model with horizontal periodic boundary conditions, the fluid motion associated with convective mixing is strong enough to interact with the corners of the geometry. Different open horizontal boundary conditions were implemented in an attempt to eliminate the interaction. However, the results using these conditions lead to either interactions with the corners or numerical problems.

• Subjects / Keywords

  • Fluid dynamics
  • Anelastic
  • Convection
  • Stratified fluid layer
  • Boussinesq
  • Simulations

• Graduation date

  Fall 2017

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R30P0X48K

• 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.