Faculty Mentor(s)
Dr. Zachary Williams, Physics
Document Type
Poster
Event Date
4-12-2024
Abstract
Convection cells are found in a variety of contexts throughout physics, including plasmas within the stellar interior and in neutral fluids such as planetary atmospheres. Rayleigh Benard Convection (RBC) is the most well studied model for this behavior, describing convection in fluids that are heated from below and cooled from above, resulting in a temperature gradient which can drive instabilities. Under the right conditions, this instability develops and drives convective heat transport, which is still actively researched in fluid and plasma dynamics today. We study the neutral fluid configuration of this system using a novel modeling approach that approximates the solutions of the 2D nonlinear Boussinesq equations via a truncated sum of linear eigenmodes. The contribution of each eigenmode to the nonlinear state is determined by an appropriately defined inner product, which we discuss. The effectiveness of this approximation is assessed by calculating the error between the truncated sum and the full nonlinear solution. Importantly, we find that a number of stable eigenmodes contribute significantly to the nonlinear state. As a physical application of this new modeling approach to describe RBC, we calculate the Nusselt number time averaged over the saturated dynamics.
Recommended Citation
Repository citation: Donley, Gillian and Fraser, A. E., "Investigation of Convection Cells Via Truncated Eigenmode Decomposition" (2024). 23rd Annual A. Paul and Carol C. Schaap Celebration of Undergraduate Research and Creative Activity (2024). Paper 24.
https://digitalcommons.hope.edu/curca_23/24
April 12, 2024. Copyright © 2024 Hope College, Holland, Michigan.
Comments
The research reported in this presentation was supported through funding from the Clare Booth Luce Research Scholars.
One author appears on poster that is not listed in the abstract booklet: A. E. Fraser (University of Colorado, Boulder).