Zonal flow and spectra in two-dimensional Rayleigh–Bénard convection

Thesis

In this thesis, we study two-dimensional Rayleigh-Bénard convection at a wide range of Prandtl numbers.

Following two introductory chapters, the subsequent three chapters focus on a horizontally periodic domain with free-slip top and bottom boundaries. This configuration encourages mean horizontal flows of zero horizontal wavenumber, which can be considered as an idealisation of zonal flows in planetary atmospheres, tokamaks, and annular cylindrical convection experiments. In chapter 3, we study the onset of zonal modes from a steady state that emerges at the onset of convection. In our fourth chapter, we study the dynamics when zonal modes are present. Our study unveils the presence of several bifurcations within the turbulent regime, in particular, a sequence of bifurcations leading to reversals of a very strong zonal flow. Chapter 5 generalises our analysis from a previously studied two-dimensional flow to a quasi-two-dimensional flow. We introduce a third spatial direction, and explore how narrow the domain must be in this direction to render the flow truly two-dimensional.

In chapter 6, we study two-dimensional Rayleigh-B ́enard convection with periodic boundary conditions to emulate the dynamics far from walls. This chapter aims to understand how spectra, fluxes, and global variables vary with both the Rayleigh and Prandtl number.

Finally, the thesis concludes with a summary of the main findings together with an outlook on possible further research directions for each project.

Authors: Winchester, P

• DOI: 10.5287/ora-4r4680b0k
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Fluid Dynamics; Dynamical Systems; Rayleigh-Bénard Convection; Turbulence; Geophysical Fluid Dynamics; Computational Physics
• Subjects: Differentiable dynamical systems; Fluid dynamics; Rayleigh-Bénard convection; Turbulence; Computational physics