Measuring the Onset of Turbulence in Rayleigh-Benard Convection
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Rayleigh-Benard convection occurs in fluids in enclosed containers under circumstances where heat is applied from below. For cylindrical cells, we define aspect ratio as cell diameter divided by cell height. The cell is characterized by two parameters: Rayleigh (Ra) number is proportional to the temperature difference and Prandtl (Pr) number is the ratio between thermal dissipation and viscosity of the fluid. Using highly resolved numerical simulations of Rayleigh-Benard convection cells with Pr = 0.7, I varied the Rayleigh number in the range 10^5 < Ra < 10^7 to observe the threshold at which turbulence occurs. For a cylindrical cell with an aspect ratio of 1, I observed convection patterns and measured the temperature change over time for 45 distinct points. Using this data, I computed power spectra for each data point using a finite Fourier transformation to determine if any characteristic frequencies exist. Additionally, Nusselt number and temperature data acquired from each simulation can shed light on the threshold at which turbulence begins.