FORMAION OF PATTERN,TRANSITION,CHAOS AND TURBULENCE IN RAYLEIGH-BENARD CONVECTION

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The mechanism of the pattern formation, transition, chaos and properties of turbulence in Rayleigh-Benard convection was investigated by numerical calculation of the nonlinear equilibrium solution and by the stability analysis. The present project consists of the following four researches.1. The mechanism of the pattern formation in the thermal convection between two hoizontal planes with infinite extent is investigated. An amplitude equation is derived by the weakly nonlinear stability theory and its coefficients are evaluated numerically. The conditions for the onset of hexagonal or roll-like patterns are determined.2. The onset and stability of the convection in a vessel of finite volume is investigated. It is shown that the number of vortices varies depending on the lateral extent of the vessel.3. The stability and the transition of the thermal convection is investigated by numerical simulation. It is found that a large scale circular motion appears as a result of the thermal instability first, but thermal convection with two circular vorties take the place of the large scale circular motion when the temperature of the bottom is raised.4. When the vessel is placed at an angle from the horizontal plan, the thermal convection always appears even if the difference of the temperatures at the top and bottom is very small. The occurrence of the convection is found due to the imperfect pitchfork bifurcation. The equilibrium solution for the thermal convection was obtained numerically and its stability was clarified.