Fourier and POD Analysis of Turbulent Rayleigh-Bénard Convection
Mentor:Janet Scheel, Assistant Professor, Physics, Occidental College
Rayleigh-Bénard convection is a simplified model of fluid dynamics consisting of a fluid-filled container heated from the bottom and cooled from the top. It can be used to demonstrate thermal convection, chaos, and turbulence. Turbulence emerges in multiple physical systems, being especially prolific in nature: in cloud formation, weather patterns, rivers and oceans, and even turbulent blood flow in the heart. Rayleigh-Bénard convection (RBC) is controlled by three parameters: the width-to-height ratio of the container Γ, the Rayleigh number Ra (proportional to the temperature difference between the top and bottom of the cell), and the Prandtl number σ, which characterizes the fluid within the container. Increasing Ra leads to increasing chaos, and then turbulence. One of the most common features of turbulent RBC is large-scale circulation (LSC). An experimentally determined feature of LSC is cessation, where large-scale circulation in the container halts and smaller length scales are prevalent. Using simulations of RBC enabled the investigation of pattern formation during cessations of large-scale circulation, for systems with two different Rayleigh numbers and three different Prandtl numbers. Fourier analysis was used to identify events corresponding to cessations in the LSC. After isolating these events, the application of Fourier analysis to cessations was compared to proper orthogonal decomposition (POD) analysis. We found that while Fourier analysis can help identify cessations, the underlying structure can be better understood with POD analysis. This research was performed at Occidental College under the guidance of Professor Janet Scheel.