Abstract

Rigorous bounds on heat transfer in rapidly rotating convection have existed for several years in the case of free-slip or stress-free boundary conditions. No-slip boundary conditions result in a phenomenon known as Ekman pumping, which significantly impacts the heat transport. A recent collaborative effort in which the author was involved significantly sharpened the bound on heat transfer in the presence of Ekman pumping. The resulting publication was targeted for an audience consisting primarily of physicists and other non-mathematicians. This work stems from the same effort, but is intended for a mathematical audience. Two additional, new results are presented that provide a more solid mathematical footing. These are firstly, a rigorous justification of the infinite Prandtl limit relied on in the referenced work, and secondly, a maximum principle for the temperature field, which provides the needed justification for the application of the background method.

Degree

MS

College and Department

Physical and Mathematical Sciences

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2020-04-09

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd11176

Keywords

Ekman pumping, Nusselt number, rotating convection, heat transfer

Language

English

Share

COinS