Logo image
Lorenz方程式之流體動態模型的新物理觀點
Thesis

Lorenz方程式之流體動態模型的新物理觀點

丁於楷
Masters, 國立清華大學, 動力機械工程學系
2014

Abstract

Lorenz方程式 混沌現象 流體力學 Lorenz equations Chaos theory Fluid mechanics
New physical insight into the variables and parameters of nonlinear Lorenz equations are discussed in this work. In 1963, the equations are derived from the model of natural convection by Lorenz and are noted for chaotic motion. The chaos means system has an irregular motion, and is sensitive to initial conditions. The Lorenz equations have been studied in many papers, which are focus on the stability and the chaotic dynamics. However, the physical implication comparing the Lorenz equations with natural convection attracts little attention in past literatures. Therefore, first step is to derive the Lorenz equations which are ordinary differential equations from the original partial differential equations of natural convection, including assumptions, the derivation, and the simulation results. Then, derive the Lorenz equations again with different forced conditions, which are viscosity, buoyancy, and diffusion. With respect to the simulations of the modified Lorenz equations, observe the relation between the variables and the forced conditions. At last, due to the nonlinear passivity theory and known physical implication, propose the physical insight into the variables and parameters of the Lorenz equations. The study propose that the variables of Lorenz equations, x, y, z, are kinetic energy, thermodynamic potential energy, and total energy respectively. Use kinds of method or theory to prove it. Moreover, it’s better to verify the insight by experiment in the future. Expect that the analysis method applies to the known chaotic systems.

Metrics

1 Record Views

Details

Logo image