Convective Fluid Flow Dynamics and Chaos

Author

Siyu Guo, Southern Illinois University CarbondaleFollow

Date of Award

8-1-2024

Degree Name

Doctor of Philosophy

Department

Engineering Science

First Advisor

Luo, Albert

Abstract

The convective fluid dynamics and chaos between two parallel plates with temperature discrepancy has been investigated via classic and extended Lorenz system. Both the classic 3-dimensional and extended 5-dimensional Lorenz system are developed by truncating a double Fourier series, which is the solution of the streamline function. Boundary conditions are also considered. The implicit discrete mapping method has been employed to solve the classic and extended Lorenz system, and the motion stability is determined by the eigenvalue analysis. Bifurcation diagram varying with Rayleigh parameter and Prandtl parameter are obtained by solving the stable and unstable period-m motions (m=1,2,4). Symmetric period-1 to asymmetric period-4 motions have been illustrated in the phase space. Therefore, the route from period-1 to period-4 motions to chaos through the period-doubling bifurcation has been demonstrated in the classic and extended Lorenz system. For the extended 5-dimensional Lorenz system, the harmonic frequency-amplitude characteristics are also presented, which provides energy distribution in the parameter space. On bifurcation tree, the non-spiral and spiral homoclinic orbits have been seen and been illustrated in 2-D view and 3-D view. Such homoclinic orbits represent the asymptotic convection steady state that generates the chaos in the convective fluid dynamics. The rich dynamical behaviors of the convective fluid are discovered, and this investigation may help one understand the chaotic dynamics for other thermal convection problems.