Dynamic Behavior And Numerical Simulation Of A Low-Dimensional Model For Rayleigh-Benard And Other Problems Of Diffusion

Convection phenomena widely exist in nature: the sun transfers heat to the earth through the radiation effect,and through convection,heat is transferred from the sun to the air;Implicit temperature salinity convection in oceans,rivers,and reservoirs;"The radioactive decay of elements in the Earth’s vein plate generates thermal energy,which drives the plate,causing the crust to move under the influence of convection,thus creating different landforms.".These can be approximated by the Rayleigh-Benard convection problem(hereinafter referred to as the RB convection problem): there is a rectangular body that is closed up and down,heated from below,and the temperature above is considered to be approximately constant,forming a temperature difference from above to below,which indirectly drives the internal fluid movement.The RB convection problem is reduced to a mathematical problem,corresponding to a class of infinite dimensional nonlinear dynamic systems.The dynamic behavior of nonlinear systems is extremely complex,and it is often quite difficult to directly study infinite dimensional nonlinear systems.Low mode analysis is commonly used to discuss nonlinear systems.This article mainly discusses RB convection composed of heat conduction equation and Navistox equation(abbreviated as NS equation),introduces three-dimensional Lorenz system and four-dimensional Lorenz-Stenflo system,analyzes the properties of equilibrium points of the system,and discusses the linear stability,local stability,and the existence of global attractors of the equilibrium points.On this basis,further explore the diffusion RB convection problem,intercept a low-dimensional Lorenz type model,analyze the dynamic behavior of the system,and combine numerical simulation to intuitively display the dynamic behavior of the system.The first chapter of this article describes the concept of chaotic systems and the current research situation at home and abroad,and introduces the innovation points and research methods of this article.The second chapter explains the basic knowledge,including the research history of RB convection problem and the derivation of the traditional the third mock examination Lorenz equation.Chapter 3 explores the mathematical model of the four mode Lorenz Stenflo system,quantitatively analyzes the equilibrium point and stability of the system,and conducts numerical simulation using Matlab tools to qualitatively analyze the dynamic behavior of the system.Analyze the effect of airflow rotation on atmospheric flow.Chapter 4 introduces the diffusion RB convection problem,deduces a five mode mathematical model from physical equations,analyzes its chaotic properties and numerical simulation.Explain the effect of diffusion factors on diffusion RB convection.The fifth chapter studies the mechanical mechanism of the third mock examination laser chaotic system from the mechanical point of view,explores the internal factors that produce chaos,and analyzes the influence of different torques on chaos.Namely,the influence of different external force factors on the laser reflection.