The Fluid Velocity and its Reversal in Simulated Turbulent Rayleigh-B?nard Systems

Abstract

The velocity and reorientations of the large-scale circulation (LSC) in Rayleigh-B?nard convection (RBC) at the Rayleigh numbers R=1 x 10⁶ < Ra < 5 x 10⁷ and Prandtl number P=0.021 (mercury) are studied. The dynamics of Rayleigh-B?nard convection is strongly dependent on these two dimensionless parameters which characterize the strength of the heat input driving the turbulence and the fluid being used in our simulations. Using the spectral element code Nek5000, we numerically simulate Rayleigh-B?nard systems in a cylinder whose diameter is equal to its depth. These fluid-filled cells are surrounded by conducting walls with the top and bottom plates fixed at cold and hot temperatures, respectively. As we increase the heat input into the cell, a turbulent and chaotic motion is produced, and a characteristic of this motion is a noisy yet regular large-scale circulation. In all of our simulations, we witnessed an LSC, described as the global motion of the fluid as it becomes dense at the bottom of the cell and rises from one side as cooler fluid from the top of the cell falls into its place. We extract the vertical velocity of the fluid at eight equally-spaced points around the perimeter of the cylinder located at a fixed radius for three different horizontal levels. Applying a cosine fit using the equation V=a*cos(Θ-b) to a velocity vs angle curve at these three different z-planes allows us to analyze the amplitude and phase of the LSC as a function of time. A careful examination of the cosine fit parameters has enabled us to identify cessations and reorientations of our LSC.