The Effects of Aspect Ratio on Onset Pattern Formation in Simulated Rayleigh-Benard Convection

Abstract

This talk will discuss onset patterns in Rayleigh-Benard Convection. Rayleigh-Benard Convection refers to a fluid-filled cell which is heated from the bottom and cooled at the top. At a large enough temperature difference between the bottom and top plate, the hot fluid rises while simultaneously the cool fluid sinks, driving a convective motion. Just above this critical temperature difference, a distinct and stable pattern appears. The aspect ratio, which is defined as the diameter to depth ratio of the cylindrical cell, affects the pattern that is formed. This presentation will focus on the transition from purely modal patterns found in smaller aspect ratios to patterns of straight parallel rolls found in moderate to large aspect ratios. We used the spectral element code Nek5000 to create numerical simulations of such systems for a range of aspect ratios with either insulating or conducting sidewall boundary conditions. The vertical temperature difference at which convection begins is characterized by the dimensionless parameter known as the critical Rayleigh number, which is proportional to the change in temperature. This talk will describe how the critical Rayleigh number is related to the aspect ratio. The critical Rayleigh numbers for aspect ratio 1 through 9 are estimated and compared with the results of previous work. This talk will also discuss the effects of the kinematic viscosity and thermal diffusivity of the fluid, which is described by the dimensionless Prandtl number, on onset pattern formation and critical Rayleigh number.